认识O(NlogN)的排序

参考视频：一周刷爆LeetCode，算法大神左神（左程云）耗时100天打造算法与数据结构基础到高级全家桶教程，直击BTAJ等一线大厂必问算法面试题真题详解（马士兵）点击观看

文章目录

中点
归并排序
快速排序
- 例子

中点

int mid = (L + R) / 2;
int mid = L + (R - L) / 2;(防止溢出)
int mid = L + ((R - L) >> 1);

复制代码

>> 1 相当于除以2，但位运算比算术运算更快
注意括号必须加，因为移位运算符优先级低于加法

使用递归方法求一个数组L到R的最大值

java 复制代码

public class Main {
    public static void main(String[] args) {
        //使用递归方法求数组中L到R的最大值
        int[] arr = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
        System.out.println(getMax(arr, 0, arr.length - 1));
    }
    public static int getMax(int[] arr, int L, int R) {
        if (L == R) {
            return arr[L];
        }
        int mid = L + ((R - L) >> 1);
        int leftMax = getMax(arr, L, mid);
        int rightMax = getMax(arr, mid + 1, R);
        return Math.max(leftMax, rightMax);
    }
}

归并排序

java 复制代码

public class Main {
    public static void main(String[] args) {
        //归并排序
        int[] arr = {8, 4, 5, 7, 1, 3, 6, 2};
        mergeSort(arr, 0, arr.length - 1);
    }
    public static void mergeSort(int[] arr, int left, int right) {
        int mid = (left + right) / 2;
        mergeSort(arr, left, mid);
        mergeSort(arr, mid + 1, right);
        merge(arr, left, mid, right);
    }
    public static void merge(int[] arr, int left, int mid, int right) {
        int[] temp = new int[right - left + 1];
        int i = left, j = mid + 1, k = 0;
        while (i <= mid && j <= right) {
            if (arr[i] <= arr[j]) {
                temp[k++] = arr[i++];
            } else {
                temp[k++] = arr[j++];
            }
        }
        while (i <= mid) {
            temp[k++] = arr[i++];
        }
        while (j <= right) {
            temp[k++] = arr[j++];
        }
        for (int m = 0; m < k; m++) {
            arr[left + m] = temp[m];
        }
        System.out.println("归并：");
        for (int n = left; n <= right; n++) {
            System.out.print(arr[n] + " ");
        }
    }
}

java 复制代码

public class Main {
    public static void main(String[] args) {
        //归并排序求解小和问题
        int[] arr = {8, 4, 5, 7, 1, 3, 6, 2};
        int sum = mergeSort(arr, 0, arr.length - 1);
        System.out.println(sum);
    }
    public static int mergeSort(int[] arr, int left, int right) {
        if (left == right) {
            return 0;
        }
        int mid = (left + right) / 2;
        return mergeSort(arr, left, mid)+
        mergeSort(arr, mid + 1, right)+
        merge(arr, left, mid, right);
    }
    public static int merge(int[] arr, int left, int mid, int right) {
        int[] temp = new int[right - left + 1];
        int i = left, j = mid + 1, k = 0;
        int res = 0;
        while (i <= mid && j <= right) {
            res+=arr[i] < arr[j] ? arr[i] * (right - j + 1) : 0;
            if (arr[i] <= arr[j]) {
                temp[k++] = arr[i++];
            } else {
                temp[k++] = arr[j++];
            }
        }
        while (i <= mid) {
            temp[k++] = arr[i++];
        }
        while (j <= right) {
            temp[k++] = arr[j++];
        }
        for (int m = 0; m < k; m++) {
            arr[left + m] = temp[m];
        }
        System.out.println("归并：");
        for (int n = left; n <= right; n++) {
            System.out.print(arr[n] + " ");
        }
        System.out.println();
        return res;
    }
    //8, 4, 5, 7, 1, 3, 6, 2
    //4+9+1+13+1=28
}

快速排序

例子

情况1：左边是小于等于num的数右边是大于num的数

情况2：左边是小于num的数中间是等于num的数右边是大于num的数