[CF808D] Array Division

[CF808D] Array Division

Description

给你一组数，问是否可以最多移动一个数，使得这一串数可以分成两个部分，每一部分所有数的和相等。

Solution

要么是一个前缀里抽调一个数，要么是一个前缀再加上剩下部分的一个数

#include <bits/stdc++.h>
using namespace std;

#define int long long

signed main()
{
    ios::sync_with_stdio(false);

    int n;
    cin >> n;

    vector<int> a(n + 2);
    for (int i = 1; i <= n; i++)
        cin >> a[i];

    multiset<int> s_left, s_right;
    for (int i = 1; i <= n; i++)
        s_right.insert(a[i]);

    int sum = 0;
    for (int i = 1; i <= n; i++)
        sum += a[i];

    if (sum & 1)
    {
        cout << "NO" << endl;
        return 0;
    }

    int presum = 0;

    for (int i = 1; i <= n; i++)
    {
        s_left.insert(a[i]);
        s_right.erase(s_right.find(a[i]));
        presum += a[i];
        if (presum * 2 == sum)
        {
            cout << "YES" << endl;
            return 0;
        }
        else if (presum * 2 < sum)
        {
            if (s_right.find(sum / 2 - presum) != s_right.end())
            {
                cout << "YES" << endl;
                return 0;
            }
        }
        else
        {
            if (s_left.find(-sum / 2 + presum) != s_left.end())
            {
                cout << "YES" << endl;
                return 0;
            }
        }
    }
    cout << "NO" << endl;
}