小和问题和逆序对问题

       数组中每个数的左边所有比这个数小的数累加起来，为这个数组的小和。当然可以每个数遍历所有左边的数，复杂度为O(N^2)。这是一个典型的归并排序的应用，整个数组的小和为左边组内的小和加右边组内的小和加整体组间的小和。那么复杂度为O(N*log(N))。

代码

// 归并排序

import java.util.Arrays;

public class SmallSum {

    public static int smallSum(int[] arr) {
        return mergeSort(arr,0, arr.length-1);
    }

    public static int mergeSort(int[] arr, int l, int r) {
        if (l == r) {
            return 0;
        }
        int mid = l + ((r - l) >> 1);
        return mergeSort(arr, l, mid) + mergeSort(arr,mid+1,r) + merge(arr, l, mid, r);
    }

    public static int merge(int[] arr, int l, int mid, int r) {
        int[] help = new int[r-l+1];
        int p1 = l;
        int p2 = mid+1;
        int i = 0;
        int res = 0;
        while(p1 <= mid && p2 <= r) {
            res += arr[p1] < arr[p2] ? arr[p1] * (r-p2+1) : 0;
            help[i++] = arr[p1] < arr[p2] ? arr[p1++] : arr[p2++];
        }
        while(p1 <= mid) {
            help[i++] = arr[p1++];
        }
        while(p2 <= r) {
            help[i++] = arr[p2++];
        }
        for (i=0; i < help.length; ++i) {
            arr[l+i] = help[i];
        }
        return res;
    }

    public static void printArray(int[] arr) {
        for(int i=0; i<arr.length; ++i) {
            System.out.print(arr[i] + " ");
        }
        System.out.println();
    }

    public static int comparator(int[] arr) {
        int res = 0;
        for (int i=0; i<arr.length; ++i) {
            for(int j=0; j<i; j++) {
                res += arr[j] < arr[i] ? arr[j] : 0;
            }
        }
        return res;
    }

    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;
    }

    public static boolean isEqual(int[] arr1, int[] arr2) {
        if (arr1.length != arr2.length) {
            return false;
        }
        for(int i=0; i<arr1.length; ++i) {
            if (arr1[i] != arr2[i]) {
                return false;
            }
        }
        return true;
    }

    public static int[] copyArray(int[] arr) {
        int[] res = new int[arr.length];
        for(int i=0; i<res.length; ++i) {
            res[i] = arr[i];
        }
        return res;
    }

    public static void main(String[] args) {
        int testTime = 20;
        int maxSize = 100;
        int maxValue = 100;
        boolean succeed = true;
        for (int i=0; i < testTime; ++i) {
            int[] arr1 = generateRandomArray(maxSize, maxValue);
            int[] arr2 = copyArray(arr1);
            int res1 = smallSum(arr1);
            int res2 = comparator(arr2);
            if (res1 != res2) {
                succeed = false;
                printArray(arr1);
                printArray(arr2);
                break;
            }
        }

        System.out.println(succeed ? "Nice" : "Bad");
    }
}