数组平均分割

题意：

将一个数组分成两堆，使两堆的和的差值尽可能小。

思路：

dp。

实现：

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

int splitToMin(int a[], int n, int b[], int c[])
{
    int sum = accumulate(a, a + n, 0);
    int dp[15][1005];
    memset(dp, 0, sizeof dp);
    for (int i = 1; i <= n; i++)
    {
        for (int j = sum >> 1; j >= a[i - 1]; j--)
        {
            dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - a[i - 1]] + a[i - 1]);
        }
    }
    int tot = dp[n][sum >> 1], ans[15];
    memset(ans, 0, sizeof ans);
    for (int i = n; i >= 1; i--)
    {
        if (dp[i][tot] > dp[i - 1][tot])
        {
            tot -= a[i - 1];
            ans[i - 1] = 1;
        }
    }
    int x = 0, y = 0;
    for (int i = 0; i < n; i++)
    {
        if (ans[i]) b[x++] = a[i];
        else c[y++] = a[i];
    }
    return abs(sum - 2 * dp[n][sum >> 1]);
}

int main()
{
    int a[] = {61, 82, 100, 61, 61};
    int b[10], c[10];
    memset(b, 0, sizeof b); memset(c, 0, sizeof c);
    cout << splitToMin(a, 5, b, c) << endl;
    for (int i = 0; i < 5; i++) cout << b[i] << " ";
    cout << endl;
    for (int i = 0; i < 5; i++) cout << c[i] << " ";
    cout << endl;
    return 0;
}