Zuma CodeForces - 608D（记忆化搜索）

Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color c i. The goal of the game is to destroy all the gemstones in the line as quickly as possible.

In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?

Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.

Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.

The second line contains n space-separated integers, the i-th of which is c i (1 ≤ c i ≤ n) — the color of the i-th gemstone in a line.

Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.

Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.

In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.

In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1.
思路：很明显的dp题目，dp题目也可以用记忆化搜索来做。
我们令dp[l][r]代表删除l~r所需要花费的最小时间。
状态转移方程为：dp[l][r]=min(dp[l][r],dp[l][i]+dp[i+1][r]).
但是如果说a[l]==a[r]的话，那么dp[l][r]=min(dp[l][r],dp[l+1][r-1]).这种情况需要多考虑一步。
代码如下：

#include<bits/stdc++.h>
#define ll long long
#define inf 0x3f3f3f3f
using namespace std;

const int maxx=5e2+10;
int dp[maxx][maxx];
int a[maxx];
int n;

inline int dfs(int l,int r)
{
	if(dp[l][r]!=-1) return dp[l][r];
	if(l==r) return dp[l][r]=1;
	if(l+1==r) return dp[l][r]=(a[l]==a[r]?1:2);
	int sum=inf;
	if(a[l]==a[r]) sum=dfs(l+1,r-1);
	for(int i=l;i<r;i++) sum=min(sum,dfs(l,i)+dfs(i+1,r));
	return dp[l][r]=sum;
}

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	memset(dp,-1,sizeof(dp));
	cout<<dfs(1,n)<<endl;
	return 0;
}

努力加油a啊，(^o)/~

标签：gemstones,int,608D,CodeForces,Zuma,color,destroy,line,dp
来源： https://blog.csdn.net/starlet_kiss/article/details/105991990