ccf csp-201612-4-压缩编码（区间dp）

• 区间DP模板：三层循环
  循环1 --------- 枚举区间长度
  循环2 --------- --------- 枚举区间开始位置（同时计算出区间结束位置）
  循环3 --------- --------- --------- 枚举区间分割点k，并结合状态转移方程进行DP
• 本题还可用四边形优化，即：s(i,j-1)<=s(i,j)<=s(i+1,j) （s(i,j)=k）

未用四边形优化代码

#include<iostream>
#include<cstdio>
#include<climits>
using namespace std;
const int N = 1001;
int sum[N],t[N];
int dp[N][N],p[N][N];
int main()
{
	int n;
	scanf("%d", &n);
	sum[0] = 0;
	fill(dp[0], dp[0]+N*N, INT_MAX);
	for(int i = 1; i <= n; i++){
		scanf("%d", &t[i]);
		sum[i] = sum[i-1] + t[i];
		dp[i][i] = 0;
		//p[i][i] = i;
	}
	for(int len = 2; len <= n; len++){
		for(int i = 1; i <= n; i++){
			int j = i+len-1;
			if(j > n) continue;
			//for(int k = p[i][j-1]; k <= p[i+1][j]; k++){
			for(int k = i; k < j; k++){
				int tmp = dp[i][k]+dp[k+1][j]+sum[j]-sum[i-1];
				if(dp[i][j] > tmp){
					dp[i][j] = tmp;
					//p[i][j] = k;
				}
			}
		}
	}
	printf("%d", dp[1][n]);
	return 0;
}

用了四边形优化后代码

#include<iostream>
#include<cstdio>
#include<climits>
#include<cstring>
using namespace std;
const int N = 1001;
const int INT_MAX2 = 0x7F7F7F7F;
int sum[N],t[N];
int dp[N][N],p[N][N];
int main()
{
	int n;
	scanf("%d", &n);
	sum[0] = 0;
	memset(dp, INT_MAX2, sizeof(dp));
	//fill(dp[0], dp[0]+N*N, INT_MAX);
	for(int i = 1; i <= n; i++){
		scanf("%d", &t[i]);
		sum[i] = sum[i-1] + t[i];
		dp[i][i] = 0;
		p[i][i] = i;
	}
	for(int len = 2; len <= n; len++){
		for(int i = 1; i <= n; i++){
			int j = i+len-1;
			if(j > n) continue;
			for(int k = p[i][j-1]; k <= p[i+1][j]; k++){
				int tmp = dp[i][k]+dp[k+1][j]+sum[j]-sum[i-1];
				if(dp[i][j] > tmp){
					dp[i][j] = tmp;
					p[i][j] = k;
				}
			}
		}
	}
	printf("%d", dp[1][n]);
	return 0;
}