UVA 10003 cuting sticks 切木棍 （区间dp）

区间dp，切割dp[i][j]的花费和切法无关（无后效性）

dp[i][j]表示区间i,j的花费，于是只要枚举切割方法就行了，区间就划分成更小的区间了。O(n^3)

四边形不等式尚待学习

#include<bits/stdc++.h> //变量不要取成ignore left之类
using namespace std;
const int maxn = 51;
int cut[maxn];
int dp[maxn][maxn];
const int INF = 0x3fffffff;
int main()
{
    //freopen("in.txt","r",stdin);
    int L,n;
    while(scanf("%d",&L),L){
        scanf("%d",&n);
        cut[0] = 0; cut[n+1] = L;
        for(int i = 1; i <= n; i++) scanf("%d",cut+i);
        for(int i = 0; i <= n; i++) dp[i][i+1] = 0;

        for(int d = 1; d <= n; d++){
            for(int i = 0,mi = n-d; i <= mi; i++){
                int j = i+d+1;
                dp[i][j] = INF;
                for(int k = i+1; k < j; k++){
                    dp[i][j] = min(dp[i][j],dp[i][k]+dp[k][j]);
                }
                dp[i][j] += cut[j]-cut[i];
            }
        }
        printf("The minimum cutting is %d.
",dp[0][n+1]);
    }
    return 0;
}