回想法——Ural 1073 Square Country

回溯法——Ural 1073 Square Country

1073. Square CountryTime 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 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.

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

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

Sampleinputoutput

344

3

搜索过程图示

#include <iostream>#include <cstdio>#include <cstring>#include <cmath>using namespace std;#define MAX 250int 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;}