陣列中每個數的左邊所有比這個數小的數累加起來，為這個陣列的小和。當然可以每個數遍歷所有左邊的數，複雜度為O(N^2)。這是一個典型的歸併排序的應用，整個陣列的小和為左邊組內的小和加右邊組內的小和加整體組間的小和。那麼複雜度為O(N*log(N))。

程式碼

// 歸併排序

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");
    }
}