diff --git a/src/class24/Code01_SlidingWindowMaxArray.java b/src/class24/Code01_SlidingWindowMaxArray.java
index 071eba7..d115951 100644
--- a/src/class24/Code01_SlidingWindowMaxArray.java
+++ b/src/class24/Code01_SlidingWindowMaxArray.java
@@ -9,11 +9,12 @@ public class Code01_SlidingWindowMaxArray {
 		if (arr == null || w < 1 || arr.length < w) {
 			return null;
 		}
-		int[] res = new int[arr.length - w + 1];
+		int N = arr.length;
+		int[] res = new int[N - w + 1];
 		int index = 0;
 		int L = 0;
 		int R = w - 1;
-		while (R < arr.length) {
+		while (R < N) {
 			int max = arr[L];
 			for (int i = L + 1; i <= R; i++) {
 				max = Math.max(max, arr[i]);
@@ -30,6 +31,8 @@ public class Code01_SlidingWindowMaxArray {
 		if (arr == null || w < 1 || arr.length < w) {
 			return null;
 		}
+		// qmax 窗口最大值的更新结构
+		// 放下标
 		LinkedList<Integer> qmax = new LinkedList<Integer>();
 		int[] res = new int[arr.length - w + 1];
 		int index = 0;
diff --git a/src/class24/Code04_MinCoinsOnePaper.java b/src/class24/Code04_MinCoinsOnePaper.java
index a0a73b8..cfda95a 100644
--- a/src/class24/Code04_MinCoinsOnePaper.java
+++ b/src/class24/Code04_MinCoinsOnePaper.java
@@ -110,10 +110,8 @@ public class Code04_MinCoinsOnePaper {
 		return dp[0][aim];
 	}
 
-	// 这种解法课上不讲
-	// 因为需要理解窗口内最小值的更新结构
-	// 后面的课会讲
 	// dp3时间复杂度为：O(arr长度) + O(货币种数 * aim)
+	// 优化需要用到窗口内最小值的更新结构
 	public static int dp3(int[] arr, int aim) {
 		if (aim == 0) {
 			return 0;
@@ -132,6 +130,8 @@ public class Code04_MinCoinsOnePaper {
 		// 因为用了窗口内最小值的更新结构
 		for (int i = N - 1; i >= 0; i--) {
 			for (int mod = 0; mod < Math.min(aim + 1, c[i]); mod++) {
+				// 当前面值 X
+				// mod  mod + x   mod + 2*x   mod + 3 * x
 				LinkedList<Integer> w = new LinkedList<>();
 				w.add(mod);
 				dp[i][mod] = dp[i + 1][mod];
@@ -244,7 +244,7 @@ public class Code04_MinCoinsOnePaper {
 
 		System.out.println("当货币很少出现重复，dp2比dp3有常数时间优势");
 		System.out.println("当货币大量出现重复，dp3时间复杂度明显优于dp2");
-		System.out.println("dp3的讲解放在窗口内最大值或最小值的更新结构里");
+		System.out.println("dp3的优化用到了窗口内最小值的更新结构");
 	}
 
 }
diff --git a/src/class26/Code01_FibonacciProblem.java b/src/class26/Code01_FibonacciProblem.java
new file mode 100644
index 0000000..e2376e5
--- /dev/null
+++ b/src/class26/Code01_FibonacciProblem.java
@@ -0,0 +1,186 @@
+package class26;
+
+public class Code01_FibonacciProblem {
+
+	public static int f1(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		if (n == 1 || n == 2) {
+			return 1;
+		}
+		return f1(n - 1) + f1(n - 2);
+	}
+
+	public static int f2(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		if (n == 1 || n == 2) {
+			return 1;
+		}
+		int res = 1;
+		int pre = 1;
+		int tmp = 0;
+		for (int i = 3; i <= n; i++) {
+			tmp = res;
+			res = res + pre;
+			pre = tmp;
+		}
+		return res;
+	}
+
+	public static int f3(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		if (n == 1 || n == 2) {
+			return 1;
+		}
+		// [ 1 ,1 ]
+		// [ 1, 0 ]
+		int[][] base = { 
+				{ 1, 1 }, 
+				{ 1, 0 } 
+				};
+		int[][] res = matrixPower(base, n - 2);
+		return res[0][0] + res[1][0];
+	}
+
+	public static int[][] matrixPower(int[][] m, int p) {
+		int[][] res = new int[m.length][m[0].length];
+		for (int i = 0; i < res.length; i++) {
+			res[i][i] = 1;
+		}
+		
+		// res = 矩阵中的1
+		int[][] tmp = m;// 矩阵1次方
+		for (; p != 0; p >>= 1) {
+			if ((p & 1) != 0) {
+				res = muliMatrix(res, tmp);
+			}
+			tmp = muliMatrix(tmp, tmp);
+		}
+		return res;
+	}
+
+	// 两个矩阵乘完之后的结果返回
+	public static int[][] muliMatrix(int[][] m1, int[][] m2) {
+		int[][] res = new int[m1.length][m2[0].length];
+		for (int i = 0; i < m1.length; i++) {
+			for (int j = 0; j < m2[0].length; j++) {
+				for (int k = 0; k < m2.length; k++) {
+					res[i][j] += m1[i][k] * m2[k][j];
+				}
+			}
+		}
+		return res;
+	}
+
+	public static int s1(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		if (n == 1 || n == 2) {
+			return n;
+		}
+		return s1(n - 1) + s1(n - 2);
+	}
+
+	public static int s2(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		if (n == 1 || n == 2) {
+			return n;
+		}
+		int res = 2;
+		int pre = 1;
+		int tmp = 0;
+		for (int i = 3; i <= n; i++) {
+			tmp = res;
+			res = res + pre;
+			pre = tmp;
+		}
+		return res;
+	}
+
+	public static int s3(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		if (n == 1 || n == 2) {
+			return n;
+		}
+		int[][] base = { { 1, 1 }, { 1, 0 } };
+		int[][] res = matrixPower(base, n - 2);
+		return 2 * res[0][0] + res[1][0];
+	}
+
+	public static int c1(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		if (n == 1 || n == 2 || n == 3) {
+			return n;
+		}
+		return c1(n - 1) + c1(n - 3);
+	}
+
+	public static int c2(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		if (n == 1 || n == 2 || n == 3) {
+			return n;
+		}
+		int res = 3;
+		int pre = 2;
+		int prepre = 1;
+		int tmp1 = 0;
+		int tmp2 = 0;
+		for (int i = 4; i <= n; i++) {
+			tmp1 = res;
+			tmp2 = pre;
+			res = res + prepre;
+			pre = tmp1;
+			prepre = tmp2;
+		}
+		return res;
+	}
+
+	public static int c3(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		if (n == 1 || n == 2 || n == 3) {
+			return n;
+		}
+		int[][] base = { 
+				{ 1, 1, 0 }, 
+				{ 0, 0, 1 }, 
+				{ 1, 0, 0 } };
+		int[][] res = matrixPower(base, n - 3);
+		return 3 * res[0][0] + 2 * res[1][0] + res[2][0];
+	}
+
+	public static void main(String[] args) {
+		int n = 19;
+		System.out.println(f1(n));
+		System.out.println(f2(n));
+		System.out.println(f3(n));
+		System.out.println("===");
+
+		System.out.println(s1(n));
+		System.out.println(s2(n));
+		System.out.println(s3(n));
+		System.out.println("===");
+
+		System.out.println(c1(n));
+		System.out.println(c2(n));
+		System.out.println(c3(n));
+		System.out.println("===");
+
+	}
+
+}
diff --git a/src/class26/Code02_ZeroLeftOneStringNumber.java b/src/class26/Code02_ZeroLeftOneStringNumber.java
new file mode 100644
index 0000000..00ca6fc
--- /dev/null
+++ b/src/class26/Code02_ZeroLeftOneStringNumber.java
@@ -0,0 +1,109 @@
+package class26;
+
+public class Code02_ZeroLeftOneStringNumber {
+
+	public static int getNum1(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		return process(1, n);
+	}
+
+	public static int process(int i, int n) {
+		if (i == n - 1) {
+			return 2;
+		}
+		if (i == n) {
+			return 1;
+		}
+		return process(i + 1, n) + process(i + 2, n);
+	}
+
+	public static int getNum2(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		if (n == 1) {
+			return 1;
+		}
+		int pre = 1;
+		int cur = 1;
+		int tmp = 0;
+		for (int i = 2; i < n + 1; i++) {
+			tmp = cur;
+			cur += pre;
+			pre = tmp;
+		}
+		return cur;
+	}
+
+	public static int getNum3(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		if (n == 1 || n == 2) {
+			return n;
+		}
+		int[][] base = { { 1, 1 }, { 1, 0 } };
+		int[][] res = matrixPower(base, n - 2);
+		return 2 * res[0][0] + res[1][0];
+	}
+	
+	
+	
+	
+	
+	
+	public static int fi(int n) {
+		if (n < 1) {
+			return 0;
+		}
+		if (n == 1 || n == 2) {
+			return 1;
+		}
+		int[][] base = { { 1, 1 }, 
+				         { 1, 0 } };
+		int[][] res = matrixPower(base, n - 2);
+		return res[0][0] + res[1][0];
+	}
+
+	
+	
+	
+	public static int[][] matrixPower(int[][] m, int p) {
+		int[][] res = new int[m.length][m[0].length];
+		for (int i = 0; i < res.length; i++) {
+			res[i][i] = 1;
+		}
+		int[][] tmp = m;
+		for (; p != 0; p >>= 1) {
+			if ((p & 1) != 0) {
+				res = muliMatrix(res, tmp);
+			}
+			tmp = muliMatrix(tmp, tmp);
+		}
+		return res;
+	}
+
+	public static int[][] muliMatrix(int[][] m1, int[][] m2) {
+		int[][] res = new int[m1.length][m2[0].length];
+		for (int i = 0; i < m1.length; i++) {
+			for (int j = 0; j < m2[0].length; j++) {
+				for (int k = 0; k < m2.length; k++) {
+					res[i][j] += m1[i][k] * m2[k][j];
+				}
+			}
+		}
+		return res;
+	}
+
+	public static void main(String[] args) {
+		for (int i = 0; i != 20; i++) {
+			System.out.println(getNum1(i));
+			System.out.println(getNum2(i));
+			System.out.println(getNum3(i));
+			System.out.println("===================");
+		}
+
+	}
+}
diff --git a/src/class27/Code01_FindMinKth.java b/src/class27/Code01_FindMinKth.java
new file mode 100644
index 0000000..2ca14b7
--- /dev/null
+++ b/src/class27/Code01_FindMinKth.java
@@ -0,0 +1,174 @@
+package class27;
+
+import java.util.Comparator;
+import java.util.PriorityQueue;
+
+public class Code01_FindMinKth {
+
+	public static class MaxHeapComparator implements Comparator<Integer> {
+
+		@Override
+		public int compare(Integer o1, Integer o2) {
+			return o2 - o1;
+		}
+
+	}
+
+	// 利用大根堆，时间复杂度O(N*logK)
+	public static int minKth1(int[] arr, int k) {
+		PriorityQueue<Integer> maxHeap = new PriorityQueue<>(new MaxHeapComparator());
+		for (int i = 0; i < k; i++) {
+			maxHeap.add(arr[i]);
+		}
+		for (int i = k; i < arr.length; i++) {
+			if (arr[i] < maxHeap.peek()) {
+				maxHeap.poll();
+				maxHeap.add(arr[i]);
+			}
+		}
+		return maxHeap.peek();
+	}
+
+	// 改写快排，时间复杂度O(N)
+	public static int minKth2(int[] array, int k) {
+		int[] arr = copyArray(array);
+		return process2(arr, 0, arr.length - 1, k - 1);
+	}
+
+	public static int[] copyArray(int[] arr) {
+		int[] ans = new int[arr.length];
+		for (int i = 0; i != ans.length; i++) {
+			ans[i] = arr[i];
+		}
+		return ans;
+	}
+
+	// arr 第k小的数
+	// process2(arr, 0, N-1, k-1)
+	// arr[L..R]  范围上，如果排序的话(不是真的去排序)，找位于index的数
+	// index [L..R]
+	public static int process2(int[] arr, int L, int R, int index) {
+		if (L == R) { // L = =R ==INDEX
+			return arr[L];
+		}
+		// 不止一个数  L +  [0, R -L]
+		int pivot = arr[L + (int) (Math.random() * (R - L + 1))];
+		
+		// range[0] range[1]
+		//  L   ..... R     pivot 
+		//  0         1000     70...800
+		int[] range = partition(arr, L, R, pivot);
+		if (index >= range[0] && index <= range[1]) {
+			return arr[index];
+		} else if (index < range[0]) {
+			return process2(arr, L, range[0] - 1, index);
+		} else {
+			return process2(arr, range[1] + 1, R, index);
+		}
+	}
+
+	public static int[] partition(int[] arr, int L, int R, int pivot) {
+		int less = L - 1;
+		int more = R + 1;
+		int cur = L;
+		while (cur < more) {
+			if (arr[cur] < pivot) {
+				swap(arr, ++less, cur++);
+			} else if (arr[cur] > pivot) {
+				swap(arr, cur, --more);
+			} else {
+				cur++;
+			}
+		}
+		return new int[] { less + 1, more - 1 };
+	}
+
+	public static void swap(int[] arr, int i1, int i2) {
+		int tmp = arr[i1];
+		arr[i1] = arr[i2];
+		arr[i2] = tmp;
+	}
+
+	// 利用bfprt算法，时间复杂度O(N)
+	public static int minKth3(int[] array, int k) {
+		int[] arr = copyArray(array);
+		return bfprt(arr, 0, arr.length - 1, k - 1);
+	}
+
+	// arr[L..R]  如果排序的话，位于index位置的数，是什么，返回
+	public static int bfprt(int[] arr, int L, int R, int index) {
+		if (L == R) {
+			return arr[L];
+		}
+		int pivot = medianOfMedians(arr, L, R);
+		int[] range = partition(arr, L, R, pivot);
+		if (index >= range[0] && index <= range[1]) {
+			return arr[index];
+		} else if (index < range[0]) {
+			return bfprt(arr, L, range[0] - 1, index);
+		} else {
+			return bfprt(arr, range[1] + 1, R, index);
+		}
+	}
+
+	// arr[L...R]  五个数一组
+	// 每个小组内部排序
+	// 每个小组中位数领出来，组成marr
+	// marr中的中位数，返回
+	public static int medianOfMedians(int[] arr, int L, int R) {
+		int size = R - L + 1;
+		int offset = size % 5 == 0 ? 0 : 1;
+		int[] mArr = new int[size / 5 + offset];
+		for (int team = 0; team < mArr.length; team++) {
+			int teamFirst = L + team * 5;
+			// L ... L + 4
+			// L +5 ... L +9
+			// L +10....L+14
+			mArr[team] = getMedian(arr, teamFirst, Math.min(R, teamFirst + 4));
+		}
+		// marr中，找到中位数
+		// marr(0, marr.len - 1,  mArr.length / 2 )
+		return bfprt(mArr, 0, mArr.length - 1, mArr.length / 2);
+	}
+
+	public static int getMedian(int[] arr, int L, int R) {
+		insertionSort(arr, L, R);
+		return arr[(L + R) / 2];
+	}
+
+	public static void insertionSort(int[] arr, int L, int R) {
+		for (int i = L + 1; i <= R; i++) {
+			for (int j = i - 1; j >= L && arr[j] > arr[j + 1]; j--) {
+				swap(arr, j, j + 1);
+			}
+		}
+	}
+
+	// for test
+	public static int[] generateRandomArray(int maxSize, int maxValue) {
+		int[] arr = new int[(int) (Math.random() * maxSize) + 1];
+		for (int i = 0; i < arr.length; i++) {
+			arr[i] = (int) (Math.random() * (maxValue + 1));
+		}
+		return arr;
+	}
+
+	public static void main(String[] args) {
+		int testTime = 1000000;
+		int maxSize = 100;
+		int maxValue = 100;
+		System.out.println("test begin");
+		for (int i = 0; i < testTime; i++) {
+			int[] arr = generateRandomArray(maxSize, maxValue);
+			int k = (int) (Math.random() * arr.length) + 1;
+			int ans1 = minKth1(arr, k);
+			int ans2 = minKth2(arr, k);
+			int ans3 = minKth3(arr, k);
+			if (ans1 != ans2 || ans2 != ans3) {
+				System.out.println("Oops!");
+			}
+		}
+		System.out.println("test finish");
+	}
+
+}
diff --git a/src/class27/Code02_MaxTopK.java b/src/class27/Code02_MaxTopK.java
new file mode 100644
index 0000000..87746c8
--- /dev/null
+++ b/src/class27/Code02_MaxTopK.java
@@ -0,0 +1,223 @@
+package class27;
+
+import java.util.Arrays;
+
+public class Code02_MaxTopK {
+
+	// 时间复杂度O(N*logN)
+	// 排序+收集
+	public static int[] maxTopK1(int[] arr, int k) {
+		if (arr == null || arr.length == 0) {
+			return new int[0];
+		}
+		int N = arr.length;
+		k = Math.min(N, k);
+		Arrays.sort(arr);
+		int[] ans = new int[k];
+		for (int i = N - 1, j = 0; j < k; i--, j++) {
+			ans[j] = arr[i];
+		}
+		return ans;
+	}
+
+	// 方法二，时间复杂度O(N + K*logN)
+	// 解释：堆
+	public static int[] maxTopK2(int[] arr, int k) {
+		if (arr == null || arr.length == 0) {
+			return new int[0];
+		}
+		int N = arr.length;
+		k = Math.min(N, k);
+		// 从底向上建堆，时间复杂度O(N)
+		for (int i = N - 1; i >= 0; i--) {
+			heapify(arr, i, N);
+		}
+		// 只把前K个数放在arr末尾，然后收集，O(K*logN)
+		int heapSize = N;
+		swap(arr, 0, --heapSize);
+		int count = 1;
+		while (heapSize > 0 && count < k) {
+			heapify(arr, 0, heapSize);
+			swap(arr, 0, --heapSize);
+			count++;
+		}
+		int[] ans = new int[k];
+		for (int i = N - 1, j = 0; j < k; i--, j++) {
+			ans[j] = arr[i];
+		}
+		return ans;
+	}
+
+	public static void heapInsert(int[] arr, int index) {
+		while (arr[index] > arr[(index - 1) / 2]) {
+			swap(arr, index, (index - 1) / 2);
+			index = (index - 1) / 2;
+		}
+	}
+
+	public static void heapify(int[] arr, int index, int heapSize) {
+		int left = index * 2 + 1;
+		while (left < heapSize) {
+			int largest = left + 1 < heapSize && arr[left + 1] > arr[left] ? left + 1 : left;
+			largest = arr[largest] > arr[index] ? largest : index;
+			if (largest == index) {
+				break;
+			}
+			swap(arr, largest, index);
+			index = largest;
+			left = index * 2 + 1;
+		}
+	}
+
+	public static void swap(int[] arr, int i, int j) {
+		int tmp = arr[i];
+		arr[i] = arr[j];
+		arr[j] = tmp;
+	}
+
+	// 方法三，时间复杂度O(n + k * logk)
+	public static int[] maxTopK3(int[] arr, int k) {
+		if (arr == null || arr.length == 0) {
+			return new int[0];
+		}
+		int N = arr.length;
+		k = Math.min(N, k);
+		// O(N)
+		int num = minKth(arr, N - k);
+		int[] ans = new int[k];
+		int index = 0;
+		for (int i = 0; i < N; i++) {
+			if (arr[i] > num) {
+				ans[index++] = arr[i];
+			}
+		}
+		for (; index < k; index++) {
+			ans[index] = num;
+		}
+		// O(k*logk)
+		Arrays.sort(ans);
+		for (int L = 0, R = k - 1; L < R; L++, R--) {
+			swap(ans, L, R);
+		}
+		return ans;
+	}
+
+	// 时间复杂度O(N)
+	public static int minKth(int[] arr, int index) {
+		int L = 0;
+		int R = arr.length - 1;
+		int pivot = 0;
+		int[] range = null;
+		while (L < R) {
+			pivot = arr[L + (int) (Math.random() * (R - L + 1))];
+			range = partition(arr, L, R, pivot);
+			if (index < range[0]) {
+				R = range[0] - 1;
+			} else if (index > range[1]) {
+				L = range[1] + 1;
+			} else {
+				return pivot;
+			}
+		}
+		return arr[L];
+	}
+
+	public static int[] partition(int[] arr, int L, int R, int pivot) {
+		int less = L - 1;
+		int more = R + 1;
+		int cur = L;
+		while (cur < more) {
+			if (arr[cur] < pivot) {
+				swap(arr, ++less, cur++);
+			} else if (arr[cur] > pivot) {
+				swap(arr, cur, --more);
+			} else {
+				cur++;
+			}
+		}
+		return new int[] { less + 1, more - 1 };
+	}
+
+	// for test
+	public static int[] generateRandomArray(int maxSize, int maxValue) {
+		int[] arr = new int[(int) ((maxSize + 1) * Math.random())];
+		for (int i = 0; i < arr.length; i++) {
+			// [-? , +?]
+			arr[i] = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());
+		}
+		return arr;
+	}
+
+	// for test
+	public static int[] copyArray(int[] arr) {
+		if (arr == null) {
+			return null;
+		}
+		int[] res = new int[arr.length];
+		for (int i = 0; i < arr.length; i++) {
+			res[i] = arr[i];
+		}
+		return res;
+	}
+
+	// for test
+	public static boolean isEqual(int[] arr1, int[] arr2) {
+		if ((arr1 == null && arr2 != null) || (arr1 != null && arr2 == null)) {
+			return false;
+		}
+		if (arr1 == null && arr2 == null) {
+			return true;
+		}
+		if (arr1.length != arr2.length) {
+			return false;
+		}
+		for (int i = 0; i < arr1.length; i++) {
+			if (arr1[i] != arr2[i]) {
+				return false;
+			}
+		}
+		return true;
+	}
+
+	// for test
+	public static void printArray(int[] arr) {
+		if (arr == null) {
+			return;
+		}
+		for (int i = 0; i < arr.length; i++) {
+			System.out.print(arr[i] + " ");
+		}
+		System.out.println();
+	}
+
+	// 生成随机数组测试
+	public static void main(String[] args) {
+		int testTime = 500000;
+		int maxSize = 100;
+		int maxValue = 100;
+		boolean pass = true;
+		System.out.println("测试开始，没有打印出错信息说明测试通过");
+		for (int i = 0; i < testTime; i++) {
+			int k = (int) (Math.random() * maxSize) + 1;
+			int[] arr = generateRandomArray(maxSize, maxValue);
+
+			int[] arr1 = copyArray(arr);
+			int[] arr2 = copyArray(arr);
+			int[] arr3 = copyArray(arr);
+
+			int[] ans1 = maxTopK1(arr1, k);
+			int[] ans2 = maxTopK2(arr2, k);
+			int[] ans3 = maxTopK3(arr3, k);
+			if (!isEqual(ans1, ans2) || !isEqual(ans1, ans3)) {
+				pass = false;
+				System.out.println("出错了！");
+				printArray(ans1);
+				printArray(ans2);
+				printArray(ans3);
+				break;
+			}
+		}
+		System.out.println("测试结束了，测试了" + testTime + "组，是否所有测试用例都通过？" + (pass ? "是" : "否"));
+	}
+
+}
diff --git a/src/class27/Code03_ReservoirSampling.java b/src/class27/Code03_ReservoirSampling.java
new file mode 100644
index 0000000..b187659
--- /dev/null
+++ b/src/class27/Code03_ReservoirSampling.java
@@ -0,0 +1,63 @@
+package class27;
+
+public class Code03_ReservoirSampling {
+
+	public static class RandomBox {
+		private int[] bag;
+		private int N;
+		private int count;
+
+		public RandomBox(int capacity) {
+			bag = new int[capacity];
+			N = capacity;
+			count = 0;
+		}
+
+		private int rand(int max) {
+			return (int) (Math.random() * max) + 1;
+		}
+
+		public void add(int num) {
+			count++;
+			if (count <= N) {
+				bag[count - 1] = num;
+			} else {
+				if (rand(count) <= N) {
+					bag[rand(N) - 1] = num;
+				}
+			}
+		}
+
+		public int[] choices() {
+			int[] ans = new int[N];
+			for (int i = 0; i < N; i++) {
+				ans[i] = bag[i];
+			}
+			return ans;
+		}
+
+	}
+
+	public static void main(String[] args) {
+		System.out.println("hello");
+		int all = 100;
+		int choose = 10;
+		int testTimes = 50000;
+		int[] counts = new int[all + 1];
+		for (int i = 0; i < testTimes; i++) {
+			RandomBox box = new RandomBox(choose);
+			for (int num = 1; num <= all; num++) {
+				box.add(num);
+			}
+			int[] ans = box.choices();
+			for (int j = 0; j < ans.length; j++) {
+				counts[ans[j]]++;
+			}
+		}
+
+		for (int i = 0; i < counts.length; i++) {
+			System.out.println(i + " times : " + counts[i]);
+		}
+
+	}
+}
diff --git a/src/class28/Code01_KMP.java b/src/class28/Code01_KMP.java
new file mode 100644
index 0000000..400cf5b
--- /dev/null
+++ b/src/class28/Code01_KMP.java
@@ -0,0 +1,77 @@
+package class28;
+
+public class Code01_KMP {
+    // O(N)
+	public static int getIndexOf(String s, String m) {
+		if (s == null || m == null || m.length() < 1 || s.length() < m.length()) {
+			return -1;
+		}
+		char[] str = s.toCharArray();
+		char[] match = m.toCharArray();
+		int x = 0; // str中当前比对到的位置
+		int y = 0; // match中当前比对到的位置
+		// M  M <= N   O(M)
+		int[] next = getNextArray(match); // next[i]  match中i之前的字符串match[0..i-1]
+		// O(N)
+		while (x < str.length && y < match.length) {
+			if (str[x] == match[y]) {
+				x++;
+				y++;
+			} else if (next[y] == -1) { // y == 0
+				x++;
+			} else {
+				y = next[y];
+			}
+		}
+		return y == match.length ? x - y : -1;
+	}
+
+	// M   O(M)
+	public static int[] getNextArray(char[] match) {
+		if (match.length == 1) {
+			return new int[] { -1 };
+		}
+		int[] next = new int[match.length];
+		next[0] = -1;
+		next[1] = 0;
+		int i = 2;
+		// cn代表，cn位置的字符，是当前和i-1位置比较的字符
+		int cn = 0;
+		while (i < next.length) {
+			if (match[i - 1] == match[cn]) { // 跳出来的时候
+				next[i++] = ++cn;
+			} else if (cn > 0) {
+				cn = next[cn];
+			} else {
+				next[i++] = 0;
+			}
+		}
+		return next;
+	}
+
+	// for test
+	public static String getRandomString(int possibilities, int size) {
+		char[] ans = new char[(int) (Math.random() * size) + 1];
+		for (int i = 0; i < ans.length; i++) {
+			ans[i] = (char) ((int) (Math.random() * possibilities) + 'a');
+		}
+		return String.valueOf(ans);
+	}
+
+	public static void main(String[] args) {
+		int possibilities = 5;
+		int strSize = 20;
+		int matchSize = 5;
+		int testTimes = 5000000;
+		System.out.println("test begin");
+		for (int i = 0; i < testTimes; i++) {
+			String str = getRandomString(possibilities, strSize);
+			String match = getRandomString(possibilities, matchSize);
+			if (getIndexOf(str, match) != str.indexOf(match)) {
+				System.out.println("Oops!");
+			}
+		}
+		System.out.println("test finish");
+	}
+
+}
diff --git a/src/class28/Code02_TreeEqual.java b/src/class28/Code02_TreeEqual.java
new file mode 100644
index 0000000..e03d696
--- /dev/null
+++ b/src/class28/Code02_TreeEqual.java
@@ -0,0 +1,177 @@
+package class28;
+
+import java.util.ArrayList;
+
+public class Code02_TreeEqual {
+
+	public static class Node {
+		public int value;
+		public Node left;
+		public Node right;
+
+		public Node(int v) {
+			value = v;
+		}
+	}
+
+	// big做头节点的树，其中是否有某棵子树的结构，是和small为头的树，完全一样的
+	public static boolean containsTree1(Node big, Node small) {
+		if (small == null) {
+			return true;
+		}
+		// small != null
+		if (big == null) {
+			return false;
+		}
+		// big！=null  small!=null
+		if (isSameValueStructure(big, small)) {
+			return true;
+		}
+		return containsTree1(big.left, small) || containsTree1(big.right, small);
+	}
+
+	// head1为头的树，是否在结构对应上，完全和head2一样
+	public static boolean isSameValueStructure(Node head1, Node head2) {
+		if (head1 == null && head2 != null) {
+			return false;
+		}
+		if (head1 != null && head2 == null) {
+			return false;
+		}
+		if (head1 == null && head2 == null) {
+			return true;
+		}
+		if (head1.value != head2.value) {
+			return false;
+		}
+		// head1.value == head2.value
+		return isSameValueStructure(head1.left, head2.left) 
+				&& isSameValueStructure(head1.right, head2.right);
+	}
+
+	public static boolean containsTree2(Node big, Node small) {
+		if (small == null) {
+			return true;
+		}
+		if (big == null) {
+			return false;
+		}
+		ArrayList<String> b = preSerial(big);
+		ArrayList<String> s = preSerial(small);
+		String[] str = new String[b.size()];
+		for (int i = 0; i < str.length; i++) {
+			str[i] = b.get(i);
+		}
+
+		String[] match = new String[s.size()];
+		for (int i = 0; i < match.length; i++) {
+			match[i] = s.get(i);
+		}
+		return getIndexOf(str, match) != -1;
+	}
+
+	public static ArrayList<String> preSerial(Node head) {
+		ArrayList<String> ans = new ArrayList<>();
+		pres(head, ans);
+		return ans;
+	}
+
+	public static void pres(Node head, ArrayList<String> ans) {
+		if (head == null) {
+			ans.add(null);
+		} else {
+			ans.add(String.valueOf(head.value));
+			pres(head.left, ans);
+			pres(head.right, ans);
+		}
+	}
+
+	public static int getIndexOf(String[] str1, String[] str2) {
+		if (str1 == null || str2 == null || str1.length < 1 || str1.length < str2.length) {
+			return -1;
+		}
+		int x = 0;
+		int y = 0;
+		int[] next = getNextArray(str2);
+		while (x < str1.length && y < str2.length) {
+			if (isEqual(str1[x], str2[y])) {
+				x++;
+				y++;
+			} else if (next[y] == -1) {
+				x++;
+			} else {
+				y = next[y];
+			}
+		}
+		return y == str2.length ? x - y : -1;
+	}
+
+	public static int[] getNextArray(String[] ms) {
+		if (ms.length == 1) {
+			return new int[] { -1 };
+		}
+		int[] next = new int[ms.length];
+		next[0] = -1;
+		next[1] = 0;
+		int i = 2;
+		int cn = 0;
+		while (i < next.length) {
+			if (isEqual(ms[i - 1], ms[cn])) {
+				next[i++] = ++cn;
+			} else if (cn > 0) {
+				cn = next[cn];
+			} else {
+				next[i++] = 0;
+			}
+		}
+		return next;
+	}
+
+	public static boolean isEqual(String a, String b) {
+		if (a == null && b == null) {
+			return true;
+		} else {
+			if (a == null || b == null) {
+				return false;
+			} else {
+				return a.equals(b);
+			}
+		}
+	}
+
+	// for test
+	public static Node generateRandomBST(int maxLevel, int maxValue) {
+		return generate(1, maxLevel, maxValue);
+	}
+
+	// for test
+	public static Node generate(int level, int maxLevel, int maxValue) {
+		if (level > maxLevel || Math.random() < 0.5) {
+			return null;
+		}
+		Node head = new Node((int) (Math.random() * maxValue));
+		head.left = generate(level + 1, maxLevel, maxValue);
+		head.right = generate(level + 1, maxLevel, maxValue);
+		return head;
+	}
+
+	public static void main(String[] args) {
+		int bigTreeLevel = 7;
+		int smallTreeLevel = 4;
+		int nodeMaxValue = 5;
+		int testTimes = 100000;
+		System.out.println("test begin");
+		for (int i = 0; i < testTimes; i++) {
+			Node big = generateRandomBST(bigTreeLevel, nodeMaxValue);
+			Node small = generateRandomBST(smallTreeLevel, nodeMaxValue);
+			boolean ans1 = containsTree1(big, small);
+			boolean ans2 = containsTree2(big, small);
+			if (ans1 != ans2) {
+				System.out.println("Oops!");
+			}
+		}
+		System.out.println("test finish!");
+
+	}
+
+}
diff --git a/src/class28/Code03_IsRotation.java b/src/class28/Code03_IsRotation.java
new file mode 100644
index 0000000..f11fd28
--- /dev/null
+++ b/src/class28/Code03_IsRotation.java
@@ -0,0 +1,64 @@
+package class28;
+
+public class Code03_IsRotation {
+
+	public static boolean isRotation(String a, String b) {
+		if (a == null || b == null || a.length() != b.length()) {
+			return false;
+		}
+		String b2 = b + b;
+		return getIndexOf(b2, a) != -1;
+	}
+
+	// KMP Algorithm
+	public static int getIndexOf(String s, String m) {
+		if (s.length() < m.length()) {
+			return -1;
+		}
+		char[] ss = s.toCharArray();
+		char[] ms = m.toCharArray();
+		int si = 0;
+		int mi = 0;
+		int[] next = getNextArray(ms);
+		while (si < ss.length && mi < ms.length) {
+			if (ss[si] == ms[mi]) {
+				si++;
+				mi++;
+			} else if (next[mi] == -1) {
+				si++;
+			} else {
+				mi = next[mi];
+			}
+		}
+		return mi == ms.length ? si - mi : -1;
+	}
+
+	public static int[] getNextArray(char[] ms) {
+		if (ms.length == 1) {
+			return new int[] { -1 };
+		}
+		int[] next = new int[ms.length];
+		next[0] = -1;
+		next[1] = 0;
+		int pos = 2;
+		int cn = 0;
+		while (pos < next.length) {
+			if (ms[pos - 1] == ms[cn]) {
+				next[pos++] = ++cn;
+			} else if (cn > 0) {
+				cn = next[cn];
+			} else {
+				next[pos++] = 0;
+			}
+		}
+		return next;
+	}
+
+	public static void main(String[] args) {
+		String str1 = "yunzuocheng";
+		String str2 = "zuochengyun";
+		System.out.println(isRotation(str1, str2));
+
+	}
+
+}
diff --git a/src/class29/Code01_Manacher.java b/src/class29/Code01_Manacher.java
new file mode 100644
index 0000000..74c8d42
--- /dev/null
+++ b/src/class29/Code01_Manacher.java
@@ -0,0 +1,89 @@
+package class29;
+
+public class Code01_Manacher {
+
+	public static int manacher(String s) {
+		if (s == null || s.length() == 0) {
+			return 0;
+		}
+		// "12132" -> "#1#2#1#3#2#"
+		char[] str = manacherString(s);
+		// 回文半径的大小
+		int[] pArr = new int[str.length];
+		int C = -1;
+		// 讲述中：R代表最右的扩成功的位置。coding：最右的扩成功位置的，再下一个位置
+		int R = -1;
+		int max = Integer.MIN_VALUE;
+		for (int i = 0; i < str.length; i++) {
+			// R第一个违规的位置，i>= R
+			// i位置扩出来的答案，i位置扩的区域，至少是多大。
+			pArr[i] = R > i ? Math.min(pArr[2 * C - i], R - i) : 1;
+			while (i + pArr[i] < str.length && i - pArr[i] > -1) {
+				if (str[i + pArr[i]] == str[i - pArr[i]])
+					pArr[i]++;
+				else {
+					break;
+				}
+			}
+			if (i + pArr[i] > R) {
+				R = i + pArr[i];
+				C = i;
+			}
+			max = Math.max(max, pArr[i]);
+		}
+		return max - 1;
+	}
+
+	public static char[] manacherString(String str) {
+		char[] charArr = str.toCharArray();
+		char[] res = new char[str.length() * 2 + 1];
+		int index = 0;
+		for (int i = 0; i != res.length; i++) {
+			res[i] = (i & 1) == 0 ? '#' : charArr[index++];
+		}
+		return res;
+	}
+
+	// for test
+	public static int right(String s) {
+		if (s == null || s.length() == 0) {
+			return 0;
+		}
+		char[] str = manacherString(s);
+		int max = 0;
+		for (int i = 0; i < str.length; i++) {
+			int L = i - 1;
+			int R = i + 1;
+			while (L >= 0 && R < str.length && str[L] == str[R]) {
+				L--;
+				R++;
+			}
+			max = Math.max(max, R - L - 1);
+		}
+		return max / 2;
+	}
+
+	// for test
+	public static String getRandomString(int possibilities, int size) {
+		char[] ans = new char[(int) (Math.random() * size) + 1];
+		for (int i = 0; i < ans.length; i++) {
+			ans[i] = (char) ((int) (Math.random() * possibilities) + 'a');
+		}
+		return String.valueOf(ans);
+	}
+
+	public static void main(String[] args) {
+		int possibilities = 5;
+		int strSize = 20;
+		int testTimes = 5000000;
+		System.out.println("test begin");
+		for (int i = 0; i < testTimes; i++) {
+			String str = getRandomString(possibilities, strSize);
+			if (manacher(str) != right(str)) {
+				System.out.println("Oops!");
+			}
+		}
+		System.out.println("test finish");
+	}
+
+}
diff --git a/src/class29/Code02_AddShortestEnd.java b/src/class29/Code02_AddShortestEnd.java
new file mode 100644
index 0000000..81f3e20
--- /dev/null
+++ b/src/class29/Code02_AddShortestEnd.java
@@ -0,0 +1,54 @@
+package class29;
+
+public class Code02_AddShortestEnd {
+
+	public static String shortestEnd(String s) {
+		if (s == null || s.length() == 0) {
+			return null;
+		}
+		char[] str = manacherString(s);
+		int[] pArr = new int[str.length];
+		int C = -1;
+		int R = -1;
+		int maxContainsEnd = -1;
+		for (int i = 0; i != str.length; i++) {
+			pArr[i] = R > i ? Math.min(pArr[2 * C - i], R - i) : 1;
+			while (i + pArr[i] < str.length && i - pArr[i] > -1) {
+				if (str[i + pArr[i]] == str[i - pArr[i]])
+					pArr[i]++;
+				else {
+					break;
+				}
+			}
+			if (i + pArr[i] > R) {
+				R = i + pArr[i];
+				C = i;
+			}
+			if (R == str.length) {
+				maxContainsEnd = pArr[i];
+				break;
+			}
+		}
+		char[] res = new char[s.length() - maxContainsEnd + 1];
+		for (int i = 0; i < res.length; i++) {
+			res[res.length - 1 - i] = str[i * 2 + 1];
+		}
+		return String.valueOf(res);
+	}
+
+	public static char[] manacherString(String str) {
+		char[] charArr = str.toCharArray();
+		char[] res = new char[str.length() * 2 + 1];
+		int index = 0;
+		for (int i = 0; i != res.length; i++) {
+			res[i] = (i & 1) == 0 ? '#' : charArr[index++];
+		}
+		return res;
+	}
+
+	public static void main(String[] args) {
+		String str1 = "abcd123321";
+		System.out.println(shortestEnd(str1));
+	}
+
+}
diff --git a/src/class30/Code01_MorrisTraversal.java b/src/class30/Code01_MorrisTraversal.java
new file mode 100644
index 0000000..7206332
--- /dev/null
+++ b/src/class30/Code01_MorrisTraversal.java
@@ -0,0 +1,223 @@
+package class30;
+
+public class Code01_MorrisTraversal {
+
+	public static class Node {
+		public int value;
+		Node left;
+		Node right;
+
+		public Node(int data) {
+			this.value = data;
+		}
+	}
+
+	public static void morris(Node head) {
+		if (head == null) {
+			return;
+		}
+		Node cur = head;
+		Node mostRight = null;
+		while (cur != null) {
+			// cur有没有左树
+			mostRight = cur.left;
+			if (mostRight != null) { // 有左树的情况下
+				// 找到cur左树上，真实的最右
+				while (mostRight.right != null && mostRight.right != cur) {
+					mostRight = mostRight.right;
+				}
+				// 从while中出来，mostRight一定是cur左树上的最右节点
+				// mostRight
+				if (mostRight.right == null) {
+					mostRight.right = cur;
+					cur = cur.left;
+					continue;
+				} else { // mostRight.right != null -> mostRight.right == cur
+					mostRight.right = null;
+				}
+			}
+			cur = cur.right;
+		}
+	}
+
+	public static void morrisIn(Node head) {
+		if (head == null) {
+			return;
+		}
+		Node cur = head;
+		Node mostRight = null;
+		while (cur != null) {
+			mostRight = cur.left;
+			if (mostRight != null) {
+				while (mostRight.right != null && mostRight.right != cur) {
+					mostRight = mostRight.right;
+				}
+				if (mostRight.right == null) {
+					mostRight.right = cur;
+					cur = cur.left;
+					continue;
+				} else {
+					mostRight.right = null;
+				}
+			}
+			System.out.print(cur.value + " ");
+			cur = cur.right;
+		}
+		System.out.println();
+	}
+
+	public static void morrisPre(Node head) {
+		if (head == null) {
+			return;
+		}
+		Node cur1 = head;
+		Node cur2 = null;
+		while (cur1 != null) {
+			cur2 = cur1.left;
+			if (cur2 != null) {
+				while (cur2.right != null && cur2.right != cur1) {
+					cur2 = cur2.right;
+				}
+				if (cur2.right == null) {
+					cur2.right = cur1;
+					System.out.print(cur1.value + " ");
+					cur1 = cur1.left;
+					continue;
+				} else {
+					cur2.right = null;
+				}
+			} else {
+				System.out.print(cur1.value + " ");
+			}
+			cur1 = cur1.right;
+		}
+		System.out.println();
+	}
+
+	public static void morrisPos(Node head) {
+		if (head == null) {
+			return;
+		}
+		Node cur = head;
+		Node mostRight = null;
+		while (cur != null) {
+			mostRight = cur.left;
+			if (mostRight != null) {
+				while (mostRight.right != null && mostRight.right != cur) {
+					mostRight = mostRight.right;
+				}
+				if (mostRight.right == null) {
+					mostRight.right = cur;
+					cur = cur.left;
+					continue;
+				} else {
+					mostRight.right = null;
+					printEdge(cur.left);
+				}
+			}
+			cur = cur.right;
+		}
+		printEdge(head);
+		System.out.println();
+	}
+
+	public static void printEdge(Node head) {
+		Node tail = reverseEdge(head);
+		Node cur = tail;
+		while (cur != null) {
+			System.out.print(cur.value + " ");
+			cur = cur.right;
+		}
+		reverseEdge(tail);
+	}
+
+	public static Node reverseEdge(Node from) {
+		Node pre = null;
+		Node next = null;
+		while (from != null) {
+			next = from.right;
+			from.right = pre;
+			pre = from;
+			from = next;
+		}
+		return pre;
+	}
+
+	// for test -- print tree
+	public static void printTree(Node head) {
+		System.out.println("Binary Tree:");
+		printInOrder(head, 0, "H", 17);
+		System.out.println();
+	}
+
+	public static void printInOrder(Node head, int height, String to, int len) {
+		if (head == null) {
+			return;
+		}
+		printInOrder(head.right, height + 1, "v", len);
+		String val = to + head.value + to;
+		int lenM = val.length();
+		int lenL = (len - lenM) / 2;
+		int lenR = len - lenM - lenL;
+		val = getSpace(lenL) + val + getSpace(lenR);
+		System.out.println(getSpace(height * len) + val);
+		printInOrder(head.left, height + 1, "^", len);
+	}
+
+	public static String getSpace(int num) {
+		String space = " ";
+		StringBuffer buf = new StringBuffer("");
+		for (int i = 0; i < num; i++) {
+			buf.append(space);
+		}
+		return buf.toString();
+	}
+
+	public static boolean isBST(Node head) {
+		if (head == null) {
+			return true;
+		}
+		Node cur = head;
+		Node mostRight = null;
+		Integer pre = null;
+		boolean ans = true;
+		while (cur != null) {
+			mostRight = cur.left;
+			if (mostRight != null) {
+				while (mostRight.right != null && mostRight.right != cur) {
+					mostRight = mostRight.right;
+				}
+				if (mostRight.right == null) {
+					mostRight.right = cur;
+					cur = cur.left;
+					continue;
+				} else {
+					mostRight.right = null;
+				}
+			}
+			if (pre != null && pre >= cur.value) {
+				ans = false;
+			}
+			pre = cur.value;
+			cur = cur.right;
+		}
+		return ans;
+	}
+
+	public static void main(String[] args) {
+		Node head = new Node(4);
+		head.left = new Node(2);
+		head.right = new Node(6);
+		head.left.left = new Node(1);
+		head.left.right = new Node(3);
+		head.right.left = new Node(5);
+		head.right.right = new Node(7);
+		printTree(head);
+		morrisIn(head);
+		morrisPre(head);
+		morrisPos(head);
+		printTree(head);
+
+	}
+
+}
diff --git a/src/class30/Code05_MinHeight.java b/src/class30/Code05_MinHeight.java
new file mode 100644
index 0000000..c328760
--- /dev/null
+++ b/src/class30/Code05_MinHeight.java
@@ -0,0 +1,117 @@
+package class30;
+
+public class Code05_MinHeight {
+
+	public static class Node {
+		public int val;
+		public Node left;
+		public Node right;
+
+		public Node(int x) {
+			val = x;
+		}
+	}
+
+	public static int minHeight1(Node head) {
+		if (head == null) {
+			return 0;
+		}
+		return p(head);
+	}
+
+	public static int p(Node x) {
+		if (x.left == null && x.right == null) {
+			return 1;
+		}
+		// 左右子树起码有一个不为空
+		int leftH = Integer.MAX_VALUE;
+		if (x.left != null) {
+			leftH = p(x.left);
+		}
+		int rightH = Integer.MAX_VALUE;
+		if (x.right != null) {
+			rightH = p(x.right);
+		}
+		return 1 + Math.min(leftH, rightH);
+	}
+
+	// 根据morris遍历改写
+	public static int minHeight2(Node head) {
+		if (head == null) {
+			return 0;
+		}
+		Node cur = head;
+		Node mostRight = null;
+		int curLevel = 0;
+		int minHeight = Integer.MAX_VALUE;
+		while (cur != null) {
+			mostRight = cur.left;
+			if (mostRight != null) {
+				int rightBoardSize = 1;
+				while (mostRight.right != null && mostRight.right != cur) {
+					rightBoardSize++;
+					mostRight = mostRight.right;
+				}
+				if (mostRight.right == null) { // 第一次到达
+					curLevel++;
+					mostRight.right = cur;
+					cur = cur.left;
+					continue;
+				} else { // 第二次到达
+					if (mostRight.left == null) {
+						minHeight = Math.min(minHeight, curLevel);
+					}
+					curLevel -= rightBoardSize;
+					mostRight.right = null;
+				}
+			} else { // 只有一次到达
+				curLevel++;
+			}
+			cur = cur.right;
+		}
+		int finalRight = 1;
+		cur = head;
+		while (cur.right != null) {
+			finalRight++;
+			cur = cur.right;
+		}
+		if (cur.left == null && cur.right == null) {
+			minHeight = Math.min(minHeight, finalRight);
+		}
+		return minHeight;
+	}
+
+	// for test
+	public static Node generateRandomBST(int maxLevel, int maxValue) {
+		return generate(1, maxLevel, maxValue);
+	}
+
+	// for test
+	public static Node generate(int level, int maxLevel, int maxValue) {
+		if (level > maxLevel || Math.random() < 0.5) {
+			return null;
+		}
+		Node head = new Node((int) (Math.random() * maxValue));
+		head.left = generate(level + 1, maxLevel, maxValue);
+		head.right = generate(level + 1, maxLevel, maxValue);
+		return head;
+	}
+
+	public static void main(String[] args) {
+		int treeLevel = 7;
+		int nodeMaxValue = 5;
+		int testTimes = 100000;
+		System.out.println("test begin");
+		for (int i = 0; i < testTimes; i++) {
+			Node head = generateRandomBST(treeLevel, nodeMaxValue);
+			int ans1 = minHeight1(head);
+			int ans2 = minHeight2(head);
+			if (ans1 != ans2) {
+				System.out.println("Oops!");
+			}
+		}
+		System.out.println("test finish!");
+
+	}
+
+}
diff --git a/src/class31/Code01_SegmentTree.java b/src/class31/Code01_SegmentTree.java
new file mode 100644
index 0000000..80e1b26
--- /dev/null
+++ b/src/class31/Code01_SegmentTree.java
@@ -0,0 +1,251 @@
+package class31;
+
+public class Code01_SegmentTree {
+
+	public static class SegmentTree {
+		// arr[]为原序列的信息从0开始，但在arr里是从1开始的
+		// sum[]模拟线段树维护区间和
+		// lazy[]为累加懒惰标记
+		// change[]为更新的值
+		// update[]为更新慵懒标记
+		private int MAXN;
+		private int[] arr;
+		private int[] sum;
+		private int[] lazy;
+		private int[] change;
+		private boolean[] update;
+
+		public SegmentTree(int[] origin) {
+			MAXN = origin.length + 1;
+			arr = new int[MAXN]; // arr[0] 不用  从1开始使用
+			for (int i = 1; i < MAXN; i++) {
+				arr[i] = origin[i - 1];
+			}
+			sum = new int[MAXN << 2]; // 用来支持脑补概念中，某一个范围的累加和信息
+			
+			lazy = new int[MAXN << 2]; // 用来支持脑补概念中，某一个范围沒有往下傳遞的纍加任務
+			change = new int[MAXN << 2]; // 用来支持脑补概念中，某一个范围有没有更新操作的任务
+			update = new boolean[MAXN << 2]; // 用来支持脑补概念中，某一个范围更新任务，更新成了什么
+		}
+
+		private void pushUp(int rt) {
+			sum[rt] = sum[rt << 1] + sum[rt << 1 | 1];
+		}
+
+		// 之前的，所有懒增加，和懒更新，从父范围，发给左右两个子范围
+		// 分发策略是什么
+		// ln表示左子树元素结点个数，rn表示右子树结点个数
+		private void pushDown(int rt, int ln, int rn) {
+			if (update[rt]) {
+				update[rt << 1] = true;
+				update[rt << 1 | 1] = true;
+				change[rt << 1] = change[rt];
+				change[rt << 1 | 1] = change[rt];
+				lazy[rt << 1] = 0;
+				lazy[rt << 1 | 1] = 0;
+				sum[rt << 1] = change[rt] * ln;
+				sum[rt << 1 | 1] = change[rt] * rn;
+				update[rt] = false;
+			}
+			if (lazy[rt] != 0) {
+				lazy[rt << 1] += lazy[rt];
+				sum[rt << 1] += lazy[rt] * ln;
+				lazy[rt << 1 | 1] += lazy[rt];
+				sum[rt << 1 | 1] += lazy[rt] * rn;
+				lazy[rt] = 0;
+			}
+		}
+
+		// 在初始化阶段，先把sum数组，填好
+		// 在arr[l~r]范围上，去build，1~N，
+		// rt :  这个范围在sum中的下标
+		public void build(int l, int r, int rt) {
+			if (l == r) {
+				sum[rt] = arr[l];
+				return;
+			}
+			int mid = (l + r) >> 1;
+			build(l, mid, rt << 1);
+			build(mid + 1, r, rt << 1 | 1);
+			pushUp(rt);
+		}
+
+		public void update(int L, int R, int C, int l, int r, int rt) {
+			if (L <= l && r <= R) {
+				update[rt] = true;
+				change[rt] = C;
+				sum[rt] = C * (r - l + 1);
+				lazy[rt] = 0;
+				return;
+			}
+			// 当前任务躲不掉，无法懒更新，要往下发
+			int mid = (l + r) >> 1;
+			pushDown(rt, mid - l + 1, r - mid);
+			if (L <= mid) {
+				update(L, R, C, l, mid, rt << 1);
+			}
+			if (R > mid) {
+				update(L, R, C, mid + 1, r, rt << 1 | 1);
+			}
+			pushUp(rt);
+		}
+
+		// L..R -> 任务范围 ,所有的值累加上C
+		// l,r -> 表达的范围
+		// rt  去哪找l，r范围上的信息
+		public void add(
+				int L, int R, int C,
+				int l, int r, 
+				int rt) {
+			// 任务的范围彻底覆盖了，当前表达的范围
+			if (L <= l && r <= R) {
+				sum[rt] += C * (r - l + 1);
+				lazy[rt] += C;
+				return;
+			}
+			// 任务并没有把l...r全包住
+			// 要把当前任务往下发
+			// 任务  L, R  没有把本身表达范围 l,r 彻底包住
+			int mid = (l + r) >> 1; // l..mid  (rt << 1)   mid+1...r(rt << 1 | 1)
+			// 下发之前所有攒的懒任务
+			pushDown(rt, mid - l + 1, r - mid);
+			// 左孩子是否需要接到任务
+			if (L <= mid) {
+				add(L, R, C, l, mid, rt << 1);
+			}
+			// 右孩子是否需要接到任务
+			if (R > mid) {
+				add(L, R, C, mid + 1, r, rt << 1 | 1);
+			}
+			// 左右孩子做完任务后，我更新我的sum信息
+			pushUp(rt);
+		}
+
+		//   1~6 累加和是多少？ 1~8   rt
+		public long query(int L, int R, int l, int r, int rt) {
+			if (L <= l && r <= R) {
+				return sum[rt];
+			}
+			int mid = (l + r) >> 1;
+			pushDown(rt, mid - l + 1, r - mid);
+			long ans = 0;
+			if (L <= mid) {
+				ans += query(L, R, l, mid, rt << 1);
+			}
+			if (R > mid) {
+				ans += query(L, R, mid + 1, r, rt << 1 | 1);
+			}
+			return ans;
+		}
+
+	}
+
+	public static class Right {
+		public int[] arr;
+
+		public Right(int[] origin) {
+			arr = new int[origin.length + 1];
+			for (int i = 0; i < origin.length; i++) {
+				arr[i + 1] = origin[i];
+			}
+		}
+
+		public void update(int L, int R, int C) {
+			for (int i = L; i <= R; i++) {
+				arr[i] = C;
+			}
+		}
+
+		public void add(int L, int R, int C) {
+			for (int i = L; i <= R; i++) {
+				arr[i] += C;
+			}
+		}
+
+		public long query(int L, int R) {
+			long ans = 0;
+			for (int i = L; i <= R; i++) {
+				ans += arr[i];
+			}
+			return ans;
+		}
+
+	}
+
+	public static int[] genarateRandomArray(int len, int max) {
+		int size = (int) (Math.random() * len) + 1;
+		int[] origin = new int[size];
+		for (int i = 0; i < size; i++) {
+			origin[i] = (int) (Math.random() * max) - (int) (Math.random() * max);
+		}
+		return origin;
+	}
+
+	public static boolean test() {
+		int len = 100;
+		int max = 1000;
+		int testTimes = 5000;
+		int addOrUpdateTimes = 1000;
+		int queryTimes = 500;
+		for (int i = 0; i < testTimes; i++) {
+			int[] origin = genarateRandomArray(len, max);
+			SegmentTree seg = new SegmentTree(origin);
+			int S = 1;
+			int N = origin.length;
+			int root = 1;
+			seg.build(S, N, root);
+			Right rig = new Right(origin);
+			for (int j = 0; j < addOrUpdateTimes; j++) {
+				int num1 = (int) (Math.random() * N) + 1;
+				int num2 = (int) (Math.random() * N) + 1;
+				int L = Math.min(num1, num2);
+				int R = Math.max(num1, num2);
+				int C = (int) (Math.random() * max) - (int) (Math.random() * max);
+				if (Math.random() < 0.5) {
+					seg.add(L, R, C, S, N, root);
+					rig.add(L, R, C);
+				} else {
+					seg.update(L, R, C, S, N, root);
+					rig.update(L, R, C);
+				}
+			}
+			for (int k = 0; k < queryTimes; k++) {
+				int num1 = (int) (Math.random() * N) + 1;
+				int num2 = (int) (Math.random() * N) + 1;
+				int L = Math.min(num1, num2);
+				int R = Math.max(num1, num2);
+				long ans1 = seg.query(L, R, S, N, root);
+				long ans2 = rig.query(L, R);
+				if (ans1 != ans2) {
+					return false;
+				}
+			}
+		}
+		return true;
+	}
+
+	public static void main(String[] args) {
+		int[] origin = { 2, 1, 1, 2, 3, 4, 5 };
+		SegmentTree seg = new SegmentTree(origin);
+		int S = 1; // 整个区间的开始位置，规定从1开始，不从0开始 -> 固定
+		int N = origin.length; // 整个区间的结束位置，规定能到N，不是N-1 -> 固定
+		int root = 1; // 整棵树的头节点位置，规定是1，不是0 -> 固定
+		int L = 2; // 操作区间的开始位置 -> 可变
+		int R = 5; // 操作区间的结束位置 -> 可变
+		int C = 4; // 要加的数字或者要更新的数字 -> 可变
+		// 区间生成，必须在[S,N]整个范围上build
+		seg.build(S, N, root);
+		// 区间修改，可以改变L、R和C的值，其他值不可改变
+		seg.add(L, R, C, S, N, root);
+		// 区间更新，可以改变L、R和C的值，其他值不可改变
+		seg.update(L, R, C, S, N, root);
+		// 区间查询，可以改变L和R的值，其他值不可改变
+		long sum = seg.query(L, R, S, N, root);
+		System.out.println(sum);
+
+		System.out.println("对数器测试开始...");
+		System.out.println("测试结果 : " + (test() ? "通过" : "未通过"));
+
+	}
+
+}
diff --git a/src/class31/Code02_FallingSquares.java b/src/class31/Code02_FallingSquares.java
new file mode 100644
index 0000000..fb85a67
--- /dev/null
+++ b/src/class31/Code02_FallingSquares.java
@@ -0,0 +1,116 @@
+package class31;
+
+import java.util.ArrayList;
+import java.util.HashMap;
+import java.util.List;
+import java.util.TreeSet;
+
+public class Code02_FallingSquares {
+
+	public static class SegmentTree {
+		private int[] max;
+		private int[] change;
+		private boolean[] update;
+
+		public SegmentTree(int size) {
+			int N = size + 1;
+			max = new int[N << 2];
+			
+			change = new int[N << 2];
+			update = new boolean[N << 2];
+		}
+
+		private void pushUp(int rt) {
+			max[rt] = Math.max(max[rt << 1], max[rt << 1 | 1]);
+		}
+
+		// ln表示左子树元素结点个数，rn表示右子树结点个数
+		private void pushDown(int rt, int ln, int rn) {
+			if (update[rt]) {
+				update[rt << 1] = true;
+				update[rt << 1 | 1] = true;
+				change[rt << 1] = change[rt];
+				change[rt << 1 | 1] = change[rt];
+				max[rt << 1] = change[rt];
+				max[rt << 1 | 1] = change[rt];
+				update[rt] = false;
+			}
+		}
+
+		public void update(int L, int R, int C, int l, int r, int rt) {
+			if (L <= l && r <= R) {
+				update[rt] = true;
+				change[rt] = C;
+				max[rt] = C;
+				return;
+			}
+			int mid = (l + r) >> 1;
+			pushDown(rt, mid - l + 1, r - mid);
+			if (L <= mid) {
+				update(L, R, C, l, mid, rt << 1);
+			}
+			if (R > mid) {
+				update(L, R, C, mid + 1, r, rt << 1 | 1);
+			}
+			pushUp(rt);
+		}
+
+		public int query(int L, int R, int l, int r, int rt) {
+			if (L <= l && r <= R) {
+				return max[rt];
+			}
+			int mid = (l + r) >> 1;
+			pushDown(rt, mid - l + 1, r - mid);
+			int left = 0;
+			int right = 0;
+			if (L <= mid) {
+				left = query(L, R, l, mid, rt << 1);
+			}
+			if (R > mid) {
+				right = query(L, R, mid + 1, r, rt << 1 | 1);
+			}
+			return Math.max(left, right);
+		}
+
+	}
+
+	// positions
+	// [2,7] -> 2 , 8
+	// [3, 10] -> 3, 12
+	//
+	//
+	public HashMap<Integer, Integer> index(int[][] positions) {
+		TreeSet<Integer> pos = new TreeSet<>();
+		for (int[] arr : positions) {
+			pos.add(arr[0]);
+			pos.add(arr[0] + arr[1] - 1);
+		}
+		HashMap<Integer, Integer> map = new HashMap<>();
+		int count = 0;
+		for (Integer index : pos) {
+			map.put(index, ++count);
+		}
+		return map;
+	}
+
+	public List<Integer> fallingSquares(int[][] positions) {
+		HashMap<Integer, Integer> map = index(positions);
+		// 100   -> 1    306 ->   2   403 -> 3
+		// [100,403]   1~3 
+		int N = map.size(); // 1 ~ 	N
+		SegmentTree segmentTree = new SegmentTree(N);
+		int max = 0;
+		List<Integer> res = new ArrayList<>();
+		// 每落一个正方形，收集一下，所有东西组成的图像，最高高度是什么
+		for (int[] arr : positions) {
+			int L = map.get(arr[0]);
+			int R = map.get(arr[0] + arr[1] - 1);
+			int height = segmentTree.query(L, R, 1, N, 1) + arr[1];
+			max = Math.max(max, height);
+			res.add(max);
+			segmentTree.update(L, R, height, 1, N, 1);
+		}
+		return res;
+	}
+
+}