回溯法——Ural 1073 Square Country

1073. Square Country

Time Limit: 1.0 second
Memory Limit: 16 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  a ² 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

搜索过程图示

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>

using namespace std;

#define MAX 250

int minn; //最小数量

int ConstructCandidates(int *c, int r)
{
	int f = (int)sqrt((double)r);
	int i;
	for (i = 0; f > 0; i++, f--)
	{
		c[i] = f;
	}
	return i;
}

bool Backtrack(int k, int r)
{
	if (r == 0)
	{
		if (k < minn)
		{
			minn = k;
		}
	}
	else
	{
		int c[MAX];
		int nc = ConstructCandidates(c, r);

		int i;
		for (i = 0; i < nc; i++)
		{
			if (k+1 < minn)
			{
				if (!Backtrack(k+1, r-(c[i]*c[i])))
				{
					return true; //结束本层
				}
			}
			else
			{
				return false; //本层所有候选值都不会产生更优解
			}
		}
	}
	return true;
}

int main(void)
{
	int n;
	while (scanf("%d", &n) != EOF)
	{
		minn = 99999999;
		Backtrack(0, n);
		printf("%d\n", minn);
	}
	return 0;
}