SmallSum

[Question]

在一个数组中，将每一个比当前数小的左边的数累加起来称作这个数组的小和(small Sum)。求该数组的小和。

[Example]

int[] array = new int[] {1, 3, 4, 2, 5};
smallSum = 1 + (1 + 3) + 1 + (1 + 3 + 4 + 2) //==> smallSum = 16
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[Idea]

将小和问题转换为右边有多少个数比它大（基于MergeSort）
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[Source code]

public class code02_SmallSum {
    public static void main(String[] args) {
        System.out.println(smallSum(new int[]{1, 3, 4, 2, 5}));
    }

    public static int smallSum(int[] array) {
        if (array == null || array.length < 2) {
            return 0;
        }
        return process(array, 0, array.length - 1);
    }

    public static int process(int[] array, int L, int R) {
        if (L == R) {
            return 0;
        }
        int middle = L + ((R - L) >> 1);
        return process(array, L, middle) + process(array, middle + 1, R) + merge(array, L, middle, R);
    }

    public static int merge(int[] array, int L, int middle, int R) {
        int[] tmp = new int[R - L + 1];
        int i = 0;
        int p1 = L;
        int p2 = middle + 1;
        int sum = 0;
        while (p1 <= middle && p2 <= R) {
            sum += array[p1] < array[p2] ? array[p1] * (R - p2 + 1) : 0;
            tmp[i++] = array[p1] < array[p2] ? array[p1++] : array[p2++];
        }
        while (p1 <= middle) {
            tmp[i++] = array[p1++];
        }
        while (p2 <= R) {
            tmp[i++] = array[p2++];
        }
        System.arraycopy(tmp, 0, array, L, tmp.length);
        return sum;
    }
}
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