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algorithmbasic2020
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add class

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pull/6/head
左程云 5 years ago
parent 0106bd9d69
commit 745f7e0535
16 changed files with 1932 additions and 6 deletions
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7
src/class24/Code01_SlidingWindowMaxArray.java
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@ -9,11 +9,12 @@ public class Code01_SlidingWindowMaxArray {
if (arr == null || w < 1 || arr.length < w) { if (arr == null || w < 1 || arr.length < w) {
return null; 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 index = 0;
int L = 0; int L = 0;
int R = w - 1; int R = w - 1;
while (R < arr.length) { while (R < N) {
int max = arr[L]; int max = arr[L];
for (int i = L + 1; i <= R; i++) { for (int i = L + 1; i <= R; i++) {
max = Math.max(max, arr[i]); max = Math.max(max, arr[i]);
@ -30,6 +31,8 @@ public class Code01_SlidingWindowMaxArray {
if (arr == null || w < 1 || arr.length < w) { if (arr == null || w < 1 || arr.length < w) {
return null; return null;
} }
// qmax 窗口最大值的更新结构
// 放下标
LinkedList<Integer> qmax = new LinkedList<Integer>(); LinkedList<Integer> qmax = new LinkedList<Integer>();
int[] res = new int[arr.length - w + 1]; int[] res = new int[arr.length - w + 1];
int index = 0; int index = 0;

8
src/class24/Code04_MinCoinsOnePaper.java
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@ -110,10 +110,8 @@ public class Code04_MinCoinsOnePaper {
return dp[0][aim]; 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) // 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) { public static int dp3(int[] arr, int aim) {
if (aim == 0) { if (aim == 0) {
return 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 // 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 i = N - 1; i >= 0; i--) {
for (int mod = 0; mod < Math.min(aim + 1, c[i]); mod++) { 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<>(); LinkedList<Integer> w = new LinkedList<>();
w.add(mod); w.add(mod);
dp[i][mod] = dp[i + 1][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("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");
} }
} }

186
src/class26/Code01_FibonacciProblem.java
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@ -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("===");
}
}

109
src/class26/Code02_ZeroLeftOneStringNumber.java
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@ -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("===================");
}
}
}

174
src/class27/Code01_FindMinKth.java
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@ -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");
}
}

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src/class27/Code02_MaxTopK.java
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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"));
}
}

63
src/class27/Code03_ReservoirSampling.java
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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]);
}
}
}

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src/class28/Code01_KMP.java
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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");
}
}

177
src/class28/Code02_TreeEqual.java
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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!");
}
}

64
src/class28/Code03_IsRotation.java
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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));
}
}

89
src/class29/Code01_Manacher.java
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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");
}
}

54
src/class29/Code02_AddShortestEnd.java
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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));
}
}

223
src/class30/Code01_MorrisTraversal.java
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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);
}
}

117
src/class30/Code05_MinHeight.java
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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!");
}
}

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src/class31/Code01_SegmentTree.java
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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"));
}
}

116
src/class31/Code02_FallingSquares.java
Unescape View File

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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;
}
}
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