ural 1073.Square Country（动态规划）

1073. Square Country

Time limit: 1.0 second
Memory limit: 64 MB

There live square people in a square country. Everything in this country is square also. Thus, the Square Parliament has passed a law about a land. According to the law each citizen of the country has a right to buy land. A land is sold in squares, surely. Moreover, a length of a square side must be a positive integer amount of meters. Buying a square of land with a side a one pays a² quadrics (a local currency) and gets a square certificate of a landowner.

One citizen of the country has decided to invest all of his N quadrics into the land. He can, surely, do it, buying square pieces 1 × 1 meters. At the same time the citizen has requested to minimize an amount of pieces he buys: "It will be easier for me to pay taxes," — he has said. He has bought the land successfully.

Your task is to find out a number of certificates he has gotten.

Input

The only line contains a positive integer N ≤ 60 000 , that is a number of quadrics that the citizen has invested.

Output

The only line contains a number of certificates that he has gotten.

Sample

input	output
344	3

 题意：

 在一个正方形的国度里住着正方形的人.在这个国家里,所有的东西都是正方形的.该国的国会通过了一项关于土地的法律,依照法律,该国的国民有买土地的权利,当然,土地的买卖也是按照正方形进行.而且,买卖的土地的边长必须是整米数,每买一块土地,必须付款(用当地的钱币),每买一块地,买主会得到一份土地所有者的证明.一个市民打算把他的钱投资到土地上,因为都只能买边长为整数的正方形地,他希望土地的块数最小.他认为:"这使我在交税时,更方便",他终于购地成功. 你的任务是找出他购地的块数,以便发给他地主证书.

输入包含一个自然数N,N<=60000,表示他能买多少方土地

思路，递归方程dp[i]={dp[k]|k=i-j*j,1<=j*j<=i}

AC代码：

 

#include<iostream>
#include<cstdio>


using namespace std;
int dp[60010]={0};

int main()
{
    int i,j;
    int sgin=0;
    int n;
    cin>>n;
    for(i=1;i<=n;i++){
        j=1;
        sgin=60010;
        while(j*j<=i){
            if(dp[i-j*j]<sgin)
                sgin=dp[i-j*j];
            j++;
        }
        dp[i]=sgin+1;
    }
    cout<<dp[n]<<endl;
    return 0;
}