利用歸併排序解決小數和問題

小數和

題目描述

在一個數組中，每一個數左邊比當前數小的數累加起來，叫做這個數組的小和。求一個數組 的小和。
例子:
[1,3,4,2,5] 1左邊比1小的數，沒有; 3左邊比3小的數，1; 4左邊比4小的數，1、3; 2左邊比2小的數，1; 5左邊比5小的數，1、3、4、2; 所以小和爲1+1+3+1+1+3+4+2=16。

代碼

#include <iostream>
#include <vector>
using namespace std;

class Solution {
public:
    // 小和問題
    int merge(vector<int>& example, int left, int mid, int right) {
        vector<int> tmp;
        int p1 = left, p2 = mid + 1;
        int res = 0;
        while (p1 <= mid && p2 <= right) {
            if (example[p1] < example[p2]) {
                res += (right - p2 + 1) * example[p1];
                tmp.push_back(example[p1]);
                p1++;
            } else {
                tmp.push_back(example[p2]);
                p2++;
            }
        }
        while (p1 <= mid) {
            for (int i = p1; i <= mid; i++) {
                tmp.push_back(example[i]);
                p1++;
            }
        }
        while (p2 <= right) {
            for (int i = p2; i <= right; i++) {
                tmp.push_back(example[i]);
                p2++;
            }
        }
        for (int i = 0; i < tmp.size(); i++) {
            example[left+i] = tmp[i];
        }
        return res;
    }
    int mergeSort(vector<int>& example, int left, int right) {
        if (left == right) {
            return 0;
        }
        int mid = left + ((right - left) >> 1);
        return mergeSort(example, left, mid) + mergeSort(example, mid + 1, right) + merge(example, left, mid, right);
    }
    int smallSum(vector<int>& example) {
        if (example.empty() || example.size() == 1) {
            return 0;
        }
        return mergeSort(example, 0, example.size() - 1);
    }
};

int main()
{
    vector<int> example = {1, 3, 4, 2, 5};
    // 16
    cout << "排序前的數組爲: ";
    for (int i = 0; i < example.size() - 1; i++) {
        cout << example[i] << ", ";
    }
    cout << example[example.size()-1] << endl;
    cout << "----------------------------" << endl;
    Solution su;
    int t = su.smallSum(example);
    cout << "排序後的數組爲: ";
    for (int i = 0; i < example.size() - 1; i++) {
        cout << example[i] << ", ";
    }
    cout << example[example.size()-1] << endl;
    cout << t << endl;
    return 0;
}