最优矩阵链乘

poj1651

状态转移方程：f(i, j) = min { f(i, k) + f(k+1, j) + P(i-1)P(k)P(j) }, i <= k < j

 

#include<iostream>
#include<algorithm>
#include<math.h>
#include<string.h>
#include<stdio.h>
#include<string>
using namespace std;
const int maxn = 5000 + 10;
const int INF = 0x3f3f3f3f;
int p[maxn];
int n;
int d[maxn][maxn];
void dp() {
	n--;
	for (int i = 0; i <= n; i++)d[i][i] = 0;
	for (int len = 2; len <= n; len++) {
		for (int i = 1; i <= n - len + 1;i++) {
			int j = i + len - 1;
			for (int k = i; k < j; k++) {
				d[i][j] = min(d[i][j], d[i][k] + d[k+1][j] + p[i - 1] * p[k] * p[j]);
			}
		}
	}
	cout << d[1][n] << endl;
}
int dp2(int i,int j) {
	if (d[i][j] !=INF)return d[i][j];
	if (i == j)return 0;
	for (int k = i; k <= j; k++) {
		d[i][j] = min(d[i][j], dp2(i, k) + dp2(k + 1, j) + p[i - 1] * p[k] * p[j]);
	}
	return d[i][j];
}
int main()
{
	while (cin >> n && n) {
		memset(d, 0x3f, sizeof(d));
		for (int i = 0; i < n; i++)cin >> p[i];
		if (n-1 == 1)cout << p[0] * p[1] << endl;
		else {
			dp();
			//cout << dp2(1, n-1) << endl;
		}
		
	}
	return 0;
}