CODEVS-1048 区间dp入门 石子合并

题意：有n堆石子排成一列，每堆石子有一个重量w[i], 每次合并可以合并相邻的两堆石子，一次合并的代价为两堆石子的重量和w[i]+w[i+1]。问安排怎样的合并顺序，能够使得总合并代价达到最小。

引用：https://blog.csdn.net/qq_34374664/article/details/54745702（简单石子合并讲解）

code:

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#include<string>
#include<cstring>
#pragma warning(disable:4996)

using namespace std;
typedef long long ll;
const int MAX = 105;
const int INF = 0x7fffff;
int sum[MAX][MAX];
int w[MAX];
int dp[MAX][MAX];
int n;
int main()
{
	while (scanf("%d", &n) != EOF)
	{
		for (int i = 1; i <= n; i++)
		{
			scanf("%d",&w[i]);
			sum[i][i] = w[i];
		}
		for (int i = 1; i <= n; i++)
			for (int j = i; j <= n; j++)
			{
				dp[i][j] = i == j ? 0 : INF;
			}
		int len;
		for (int len = 1; len < n; len++)//控制区间长度
		{
			for (int i = 1; i + len <= n; i++)
			{
				int j = i + len;
				for (int k = i; k < j; k++)
				{
					sum[i][j] = sum[i][k] + sum[k + 1][j];
					dp[i][j] = min(dp[i][j], dp[i][k] + dp[k + 1][j] + sum[i][j]);
				}
			}
		}
		printf("%d\n",dp[1][n]);
	}
}