CodeForces - 607B 

Zuma

description:

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 ci. 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 ci (1 ≤ ci ≤ 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.

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题目大意：
给出一个数字序列，每次删除一个回文子序列，问最少做几次删除操作可以全部删完。

解题思路：
1.采用区间dp的做法，用 f[i][j] 记录从第i个数到第j个数最少需要删除的次数。
2.根据回文的性质，如果a[i] = a[j] 的话，f[i][j] = f[i+1][j-1] 。

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源代码：

#include<iostream>
#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<math.h>
using namespace std;

int n;
int a[505];
int f[505][505];


int dfs(int i,int j){
    if(f[i][j]!=-1)
      return f[i][j];
    if(i>=j)
      return f[i][j]=1;
    f[i][j] = 1e9;
    if(a[i]==a[j]) 
        f[i][j] = dfs(i+1,j-1);
    for(int x=i;x<j;x++)   
        f[i][j] = min(f[i][j],dfs(i,x)+dfs(x+1,j));

    return f[i][j];
} 

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