1044 Shopping in Mars

Shopping in Mars is quite a different experience. The Mars people pay by chained diamonds. Each diamond has a value (in Mars dollars M$). When making the payment, the chain can be cut at any position for only once and some of the diamonds are taken off the chain one by one. Once a diamond is off the chain, it cannot be taken back. For example, if we have a chain of 8 diamonds with values M$3, 2, 1, 5, 4, 6, 8, 7, and we must pay M$15. We may have 3 options:

1. Cut the chain between 4 and 6, and take off the diamonds from the position 1 to 5 (with values 3+2+1+5+4=15).
2. Cut before 5 or after 6, and take off the diamonds from the position 4 to 6 (with values 5+4+6=15).
3. Cut before 8, and take off the diamonds from the position 7 to 8 (with values 8+7=15).

Now given the chain of diamond values and the amount that a customer has to pay, you are supposed to list all the paying options for the customer.

If it is impossible to pay the exact amount, you must suggest solutions with minimum lost.

Input Specification:

Each input file contains one test case. For each case, the first line contains 2 numbers: N (≤), the total number of diamonds on the chain, and M (≤), the amount that the customer has to pay. Then the next line contains N positive numbers D​1​​⋯D​N​​ (D​i​​≤10​3​​ for all ,) which are the values of the diamonds. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print i-j in a line for each pair of i ≤ j such that Di + ... + Dj = M. Note that if there are more than one solution, all the solutions must be printed in increasing order of i.

If there is no solution, output i-j for pairs of i ≤ j such that Di + ... + Dj > with (Di + ... + Dj −) minimized. Again all the solutions must be printed in increasing order of i.

It is guaranteed that the total value of diamonds is sufficient to pay the given amount.

Sample Input 1:

16 15
3 2 1 5 4 6 8 7 16 10 15 11 9 12 14 13

 

Sample Output 1:

1-5
4-6
7-8
11-11

 

Sample Input 2:

5 13
2 4 5 7 9

 

Sample Output 2:

2-4
4-5

题意：

　　给出一出数字要求找出一个子串，是这个子串的和等于m， 若这样的子串不存在，则输出比m大的最小子串。

思路：

　　刚开始想的使用暴力来求解，但是提交的时候会超时。正解应该是使用二分查找，因为前缀和是有序的所以满足二分查找的条件。

Code：

#include <bits/stdc++.h>

using namespace std;

int n, m;
vector<int> sum;

void BS(int i, int& j, int& tempSum) {
    int left = i, right = n;
    while (left < right) {
        int mid = (left + right) / 2;
        if (sum[mid] - sum[i - 1] >= m)
            right = mid;
        else
            left = mid + 1;
    }
    j = right;
    tempSum = sum[j] - sum[i - 1];
}

int main() {
    cin >> n >> m;
    sum.resize(n + 1, 0);
    for (int i = 1; i <= n; ++i) {
        cin >> sum[i];
        sum[i] += sum[i - 1];
    }
    int minans = sum[n];
    vector<pair<int, int> > res;
    for (int i = 1; i <= n; ++i) {
        int j, tempSum;
        BS(i, j, tempSum);
        if (tempSum > minans) continue;
        if (tempSum >= m) {
            if (tempSum < minans) {
                res.clear();
                minans = tempSum;
            }
            res.push_back({i, j});
        }
    }

    for (auto it : res) cout << it.first << "-" << it.second << endl;

    return 0;
}

参考：

　　https://www.liuchuo.net/archives/2939