POJ 3362 Square

原创于 2021-02-21 17:43:11 发布 · 113 阅读

CC 4.0 BY-SA版权

本文介绍了一种使用C++编程解决的木棍拼接问题，通过深度优先搜索(DFS)判断能否用给定的木棍组合出边长为整数倍的等边三角形。核心算法包括剪枝和路径搜索，适用于计算机科学竞赛或算法学习。

#include <iostream>
#include <map>
#include <cstdio>
#include <algorithm>
#include <queue>
#include <cstring>

using namespace std;

const int MAXN = 25;
bool visit[MAXN];
int sticks[MAXN];
int m;
int side;                               //边长

bool DFS(int sum, int number, int position) {       //sum:当前拼凑的木棍长度, number:已拼凑成边长的数量, position:当前木棍的编号
    if (number == 3) {
        return true;
    }
    int sample = 0;                     //剪枝(3)
    for (int i = position; i < m; i++) {            //木棍长度已排序，无需从头开始寻找木棍
        if (visit[i] || sum + sticks[i] > side || sticks[i] == sample) {
            continue;
        }
        visit[i] = true;
        if (sum + sticks[i] == side) {
            if (DFS(0, number + 1, 0)) {
                return true;
            } else {
                sample = sticks[i];     //记录失败棍子的长度
            }
        } else {
            if (DFS(sum + sticks[i], number, i + 1)) {
                return true;
            } else {
                sample = sticks[i];
            }
        }
        visit[i] = false;
    }
    return false;
}

int main() {
    int n;
    cin >> n;
    while (n--) {
        int length = 0;
        cin >> m;
        for (int i = 0; i < m; i++) {
            cin >> sticks[i];
            length += sticks[i];
        }
        memset(visit, false, sizeof(visit));
        if (length % 4 != 0) {
            cout << "no" << endl;
            continue;
        }
        side = length / 4;
        sort(sticks, sticks + m, less<int>());
        if (sticks[0] > side) {
            cout << "no" << endl;
            continue;
        }
        if (DFS(0, 0, 0)) {
            cout << "yes" << endl;
        } else {
            cout << "no" << endl;
        }
    }
    return 0;
}