这是神题，n <= 1000，如果是极限数据普通的n^3区间DP怎么可能过？可偏偏就过了。

刘汝佳大哥的训练指南上面说的存在nlgn的算法解决矩阵链乘问题，可是百度都找不到。。。。

AC代码

#include <cstdio>
#include <cmath>
#include <algorithm>
#include <cstring>
#include <utility>
#include <string>
#include <iostream>
#include <map>
#include <set>
#include <vector>
#include <queue>
#include <stack>
using namespace std;
#pragma comment(linker, "/STACK:1024000000,1024000000")
#define eps 1e-10
#define inf 0x3f3f3f3f
#define PI pair<int, int>
typedef long long LL;
const int maxn = 1000 + 5;
const LL INF = 1e15;
LL d[maxn][maxn];
int n, w[maxn];
LL solve() {
	//初始化边界
	for(int i = 0; i < n; ++i) d[i][i] = 0;
	for(int l = 2; l <= n; ++l) {
		for(int i = 0; i <= n-l; ++i) {
			int j = i + l - 1;
			d[i][j] = INF;
			LL m = w[i] * w[j+1], h; //优化常数
			for(int k = i; k < j; ++k) {
				h = d[i][k] + d[k+1][j] + w[k+1]*m;
				if(h < d[i][j]) d[i][j] = h;
			}
		}
	}
	return d[0][n-1];
}
int main() {
	while(scanf("%d", &n) == 1) {
		for(int i = 0; i <= n; ++i) scanf("%d", &w[i]);
		printf("%lld\n", solve());
	}

	return 0;
}

如有不当之处欢迎指出！