diff --git a/src/leo/class01/BSAwesome.java b/src/leo/class01/BSAwesome.java
index 4bf6e8f..b3550df 100644
--- a/src/leo/class01/BSAwesome.java
+++ b/src/leo/class01/BSAwesome.java
@@ -133,6 +133,32 @@ public class BSAwesome {
 
     }
 
+    public static int BSAwesome3(int[] arr) {
+        if (arr.length == 0 || arr == null) {
+            return -1;
+        }
+        if (arr.length == 1 || arr[0] < arr[1]) {
+            return 0;
+        }
+        if (arr[arr.length - 1] < arr[arr.length - 2]) {
+            return arr.length - 1;
+        }
+
+        int L = 0;
+        int R = arr.length - 1;
+        int mid = 0;
+        while (L < R) {
+            mid = L + ((R - L) >> 1);
+            if (arr[mid] > arr[mid + 1]) {
+                L = mid + 1;
+            } else if (arr[mid] > arr[mid - 1]) {
+                R = mid - 1;
+            }else {
+                return mid;
+            }
+        }
+        return -1;
+    }
 
 
     public static int verifyBSAwesome(int[] arr, int index) {
@@ -172,7 +198,7 @@ public class BSAwesome {
         boolean succeed = true;
         for (int i = 0; i < testTime; i++) {
             int[] arr = ArrayUtil.randomAdjacentNotEqualArray(maxSize, range);
-            final int index = BSAwesome2(arr);
+            final int index = BSAwesome3(arr);
             final int verifyIndex = verifyBSAwesome(arr,index);
             if (index != verifyIndex) {
                 succeed = false;
diff --git a/src/leo/class01/BSExist.java b/src/leo/class01/BSExist.java
index 01fcf01..09ece85 100644
--- a/src/leo/class01/BSExist.java
+++ b/src/leo/class01/BSExist.java
@@ -109,6 +109,27 @@ public class BSExist {
     }
 
 
+    public static boolean exist5(int[] arr, int value) {
+        if (arr.length <= 0 || arr == null) {
+            return false;
+        }
+        int L = 0;
+        int R = arr.length - 1;
+        int mid = 0;
+        while (L < R) {
+            mid = L + ((R - L) >> 1);
+            if (arr[mid] > value) {
+                R = mid - 1;
+            } else if (arr[mid] < value) {
+                L = mid + 1;
+            }else{
+                return true;
+            }
+        }
+        return arr[L] == value;
+    }
+
+
     /**
      * 功能描述 : test
      * @author Leo
@@ -137,7 +158,7 @@ public class BSExist {
             int[] sortArr = ArrayUtil.randomSortArray(maxSize, range);
             int value = (int) ((range + 1) * Math.random() - (range + 1) * Math.random());
 
-            if (exist4(sortArr, value) != exist(sortArr, value)) {
+            if (exist5(sortArr, value) != exist(sortArr, value)) {
                 succeed = false;
                 ArrayUtil.printArr(sortArr);
                 break;
diff --git a/src/leo/class01/BSNear.java b/src/leo/class01/BSNear.java
index 5bb7cee..ebee2d3 100644
--- a/src/leo/class01/BSNear.java
+++ b/src/leo/class01/BSNear.java
@@ -105,6 +105,27 @@ public class BSNear {
     }
 
 
+    public static int BSNearLeft5(int[] arr, int value) {
+        if (arr.length <= 0 || arr == null) {
+            return -1;
+        }
+        int L = 0;
+        int R = arr.length - 1;
+        int mid = 0;
+        int index = -1;
+        while (L <= R) {
+            mid = L + ((R - L) >> 1);
+            if (arr[mid] >= value) {
+                index = mid;
+                R = mid - 1;
+            }else{
+                L = mid + 1;
+            }
+        }
+        return index;
+    }
+
+
     /**
      * 功能描述 : 在有序数组中找出>=某个数最左侧的位置(for test)
      * @author Leo
@@ -202,6 +223,27 @@ public class BSNear {
         return index;
     }
 
+
+    public static int BSNearRight4(int[] arr, int value) {
+        int index = -1;
+        if (arr.length <= 0 || arr == null) {
+            return index;
+        }
+        int L = 0;
+        int R = arr.length - 1;
+        int mid = 0;
+        while (L <= R) {
+            mid = L + ((R - L) >> 1);
+            if (arr[mid] <= value) {
+                index = mid;
+                L = mid + 1;
+            }else{
+                R = mid - 1;
+            }
+        }
+        return index;
+    }
+
     public static int forTestBSNearRight(int[] arr, int value) {
         int index = -1;
         if (arr == null || arr.length == 0) {
@@ -224,7 +266,7 @@ public class BSNear {
         for (int i = 0; i < testTime; i++) {
             int[] sortArr = ArrayUtil.randomSortArray(maxSize, range);
             int value = (int) ((range + 1) * Math.random() - (range + 1) * Math.random());
-            final int res1 = BSNearLeft4(sortArr, value);
+           /* final int res1 = BSNearLeft5(sortArr, value);
             final int res2 = forTestBSNearLeft(sortArr, value);
             if (res1 != res2) {
                 success = false;
@@ -232,8 +274,8 @@ public class BSNear {
                 System.out.println("BSNearLeft=" + res1);
                 System.out.println("forTestBSNearLeft=" + res2);
                 break;
-            }
-            /*final int res3 = BSNearRight(sortArr, value);
+            }*/
+            final int res3 = BSNearRight4(sortArr, value);
             final int res4 = forTestBSNearRight(sortArr, value);
             if (res3 != res4) {
                 success = false;
@@ -241,7 +283,7 @@ public class BSNear {
                 System.out.println("BSNearRight=" + res3);
                 System.out.println("forTestBSNearRight=" + res4);
                 break;
-            }*/
+            }
         }
         System.out.println(success ? "Nice!!" : "Fucking Fucked!");
     }
diff --git a/src/leo/class01/BubbleSort.java b/src/leo/class01/BubbleSort.java
index dddb215..3c27c6e 100644
--- a/src/leo/class01/BubbleSort.java
+++ b/src/leo/class01/BubbleSort.java
@@ -101,6 +101,32 @@ public class BubbleSort {
         }
     }
 
+    public static void bubbleSort7(int[] arr) {
+        if (arr.length == 0 || arr == null) {
+            return;
+        }
+        for (int i = arr.length - 1; i > 0; i--) {
+            for (int j = 0; j < i; j++) {
+                if (arr[j] > arr[j + 1]) {
+                    swap(arr, j, j + 1);
+                }
+            }
+        }
+    }
+
+    public static void bubbleSort8(int[] arr) {
+        if (arr.length == 0 || arr == null) {
+            return;
+        }
+        for (int i = arr.length - 1; i > 0; i--) {
+            for (int j = 0; j < i; j++) {
+                if (arr[j] > arr[j + 1]) {
+                    swap(arr, j, j + 1);
+                }
+            }
+        }
+    }
+
     /**
      * 功能描述 : 交换
      * @author Leo
@@ -131,7 +157,7 @@ public class BubbleSort {
         for (int i = 0; i < testOfTime; i++) {
             int[] arr = ArrayUtil.randomArray(maxSize, range);
             int[] anotherArr = ArrayUtil.copyArray(arr);
-            bubbleSort6(arr);
+            bubbleSort8(arr);
             Arrays.sort(anotherArr);
             if (!ArrayUtil.isEqual(arr, anotherArr)) {
                 succeed = false;
diff --git a/src/leo/class01/EvenTimesOddTimes.java b/src/leo/class01/EvenTimesOddTimes.java
index 96e1569..39b11bd 100644
--- a/src/leo/class01/EvenTimesOddTimes.java
+++ b/src/leo/class01/EvenTimesOddTimes.java
@@ -32,6 +32,14 @@ public class EvenTimesOddTimes {
         System.out.println(eor);
     }
 
+    public static void printOdd2(int[] arr) {
+        int eor = 0;
+        for (int i = 0; i < arr.length; i++) {
+            eor ^= arr[i];
+        }
+        System.out.println(eor);
+    }
+
 
     /**
      * 功能描述 : 有两种数出现了奇数次,找出他
@@ -74,4 +82,25 @@ public class EvenTimesOddTimes {
 
     }
 
+    public static void printOddTwo3(int[] arr) {
+        int eor = 0;
+        for (int i = 0; i < arr.length; i++) {
+            eor ^= arr[i];
+        }
+
+        int rightOnly = eor & (-eor);
+
+        int eorOther = 0;
+        for (int i = 0; i < arr.length; i++) {
+
+            if ((rightOnly & arr[i]) != 0) {
+                eorOther ^= arr[i];
+            }
+        }
+        System.out.println(eor + "   " + (eor ^ eorOther));
+
+    }
+
+
+
 }
diff --git a/src/leo/class01/InsertionSort.java b/src/leo/class01/InsertionSort.java
index 9814034..df909f5 100644
--- a/src/leo/class01/InsertionSort.java
+++ b/src/leo/class01/InsertionSort.java
@@ -90,6 +90,30 @@ public class InsertionSort {
         }
     }
 
+
+    public static void insertionSort6(int[] arr) {
+        if (arr == null || arr.length < 0) {
+            return;
+        }
+        for (int i = 1; i < arr.length; i++) {
+            for (int j = i - 1; j >= 0 && arr[j] > arr[j + 1]; j--) {
+                swap(arr, j, j + 1);
+            }
+        }
+    }
+
+
+    public static void insertionSort7(int[] arr) {
+        if (arr == null || arr.length < 0) {
+            return;
+        }
+        for (int i = 1; i < arr.length; i++) {
+            for (int j = i - 1; j >= 0 && arr[j] > arr[j + 1]; j--) {
+                swap(arr, j, j + 1);
+            }
+        }
+    }
+
     private static void swap(int[] arr, int i, int j) {
         if (arr == null
                 || arr.length < 2
@@ -114,7 +138,7 @@ public class InsertionSort {
         for (int i = 0; i < testOfTime; i++) {
             int[] arr = ArrayUtil.randomArray(maxSize, range);
             int[] anotherArr = ArrayUtil.copyArray(arr);
-            insertionSort5(arr);
+            insertionSort7(arr);
             Arrays.sort(anotherArr);
             if (!ArrayUtil.isEqual(arr, anotherArr)) {
                 succeed = false;
diff --git a/src/leo/class01/KM.java b/src/leo/class01/KM.java
new file mode 100644
index 0000000..66f0a9c
--- /dev/null
+++ b/src/leo/class01/KM.java
@@ -0,0 +1,135 @@
+package leo.class01;
+
+import java.util.HashMap;
+import java.util.HashSet;
+
+/**
+ * @author Leo
+ * @ClassName KM
+ * @DATE 2020/11/15 6:48 下午
+ * @Description arr中只有一种数出现了K次,其他数出了M次,k<m,找出出现K次的数.
+ * & 遇0则0; | 遇1则1;
+ */
+public class KM {
+
+    public static int testForOnlyKTimes(int[] arr, int k, int m) {
+        HashMap<Integer, Integer> map = new HashMap<>(8);
+        for (int num : arr) {
+            if (map.containsKey(num)) {
+                map.put(num, map.get(num) + 1);
+            }else {
+                map.put(num, 1);
+            }
+        }
+        for (int num : map.keySet()) {
+            if (map.get(num) == k) {
+                return num;
+            }
+        }
+
+        return -1;
+    }
+
+    public static int onlyKTimes(int[] arr, int k, int m) {
+
+        //准备32位的数组,用于记录arr中所有出现数的每一位出现1的次数
+        int[] t = new int[32];
+
+        for (int num : arr) {
+            for (int i = 0; i < t.length; i++) {
+                t[i] += (num >> i) & 1;
+            }
+        }
+        int ans = 0;
+        for (int i = 0; i < t.length; i++) {
+            //如果t的某一位取模m不等0;说明出现k次数的位上有1
+            if (t[i] % m != 0) {
+                ans |= (1 << i);
+            }
+        }
+        return ans;
+
+    }
+
+
+    public static void main(String[] args) {
+        int maxKinds = 8;
+        int range = 50;
+        int testTimes = 1000;
+        int max = 9;
+        System.out.println("开始");
+        for (int i = 0; i < testTimes; i++) {
+            int a = (int) (max * Math.random() + 1);
+            int b = (int) (max * Math.random() + 1);
+            int k = Math.min(a, b);
+            int m = Math.max(a, b);
+            if (k == m) {
+                m++;
+            }
+            int[] arr = randomArray(maxKinds, range, k, m);
+
+            int ans = onlyKTimes(arr, k, m);
+            int ans2 = testForOnlyKTimes(arr, k, m);
+            if (ans != ans2) {
+                System.out.println("出错了!!");
+                break;
+            }
+        }
+        System.out.println("结束");
+    }
+
+    /**
+     * 功能描述 :
+     * @author Leo
+     * @date 2020/11/15 8:01 下午
+     * @param maxKinds 最多几种数
+     * @param range 范围
+     * @param k k出现的次数
+     * @param m m出现的次数
+     * @throw
+     * @return int[]
+     */
+    private static int[] randomArray(int maxKinds, int range, int k, int m) {
+        //一共几种数,必须大于2
+        int numKinds = (int) (maxKinds * Math.random() + 2);
+        //出现k的数
+        int kValue = randomInt(range);
+        //arr长度
+        int[] arr = new int[k + (numKinds - 1) * m];
+
+
+        int index = 0;
+        for (; index < k; index++) {
+            arr[index] = kValue;
+        }
+        numKinds--;
+        HashSet<Integer> set = new HashSet<>();
+        set.add(kValue);
+        while (numKinds != 0) {
+            int curNum;
+            do {
+                curNum = randomInt(range);
+            } while (set.contains(curNum));
+            set.add(curNum);
+            numKinds--;
+            for (int i = 0; i < m; i++) {
+                arr[index++] = curNum;
+            }
+
+        }
+        for (int i = 0; i < arr.length; i++) {
+            int j = (int) (arr.length * Math.random());
+            int temp = arr[i];
+            arr[i] = arr[j];
+            arr[j] = temp;
+        }
+        return arr;
+    }
+
+
+    private static int randomInt(int range) {
+        return (int) ((range * Math.random() + 1) - (range * Math.random() + 1));
+    }
+
+
+}
diff --git a/src/leo/class01/SelectionSort.java b/src/leo/class01/SelectionSort.java
index bb196e2..48a5a96 100644
--- a/src/leo/class01/SelectionSort.java
+++ b/src/leo/class01/SelectionSort.java
@@ -122,6 +122,33 @@ public class SelectionSort {
         }
     }
 
+    public static void selectionSort8(int[] arr) {
+        if (arr == null || arr.length < 0) {
+            return;
+        }
+        for (int i = 0; i < arr.length-1; i++) {
+            for (int j = i+1; j < arr.length; j++) {
+                if (arr[i] > arr[j ]) {
+                    swap(arr, i, j );
+                }
+            }
+
+        }
+    }
+
+    public static void selectionSort9(int[] arr) {
+        if (arr == null || arr.length <=1) {
+            return;
+        }
+        for (int i = 0; i < arr.length-1; i++) {
+            for (int j = i + 1; j < arr.length; j++) {
+                if (arr[i] > arr[j]) {
+                    swap(arr, i, j);
+                }
+            }
+        }
+    }
+
 
     /**
      * 功能描述 : 交换
@@ -153,7 +180,7 @@ public class SelectionSort {
         for (int i = 0; i < testOfTime; i++) {
             int[] arr = ArrayUtil.randomArray(maxSize, range);
             int[] anotherArr = ArrayUtil.copyArray(arr);
-            selectionSort7(arr);
+            selectionSort9(arr);
             Arrays.sort(anotherArr);
             if (!ArrayUtil.isEqual(arr, anotherArr)) {
                 succeed = false;