N皇后问题 回溯递归算法 C++实现1

运行结果

代码如下

#include <bits/stdc++.h>
using namespace std;
const int MAX = 1024;
const char *LINE32 = "--------------------------------";
const bool PRINT_DETAILS = false; 
long long n, cnt = 0;// n表示皇后数量，cnt表示方案数量 
int queen[MAX+1];// queen[5]值为7时表示的含义：第五行第七列放置皇后 

void print() {
    cout << LINE32 << endl;
    cout << "第" << cnt << "个方案: " << endl;
    for (int i = 1; i <= n; i++) {
        if (i != 1) {
            cout << ", ";
        }
        cout << "(" << i << "," << queen[i] << ")";
    } 
    cout << endl;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            if (queen[i] != j) {
                cout << 'x';
            } else {
                cout << 'Q';
            }
        }
        cout << endl;
    }
}

bool check(int row, int col) {// 检查是否可以在（row，col）这个坐标放置皇后 
    for (int placed = 1; placed < row; placed++) {
        if (queen[placed]==col || abs(row-placed)==abs(col-queen[placed])) {
            return false;
        }
    }
    return true;
}
void place(int row) {// 在第row行上放置皇后 
    if (row > n) {
        cnt++;
        if (PRINT_DETAILS) {
            print();
        }
    } else {
        for (int col = 1; col <= n; col++) {
            if (check(row, col)) {
                queen[row] = col;
                place(row+1);
            } 
        }
    }
}

int main() {
    // input
    cout << "输入皇后个数: "; 
    cin >> n;
    // compute
    clock_t begin = clock(); 
    place(1);
    clock_t end = clock(); 
    // output
    cout << LINE32 << endl;
    cout << n << "皇后问题一共有" << cnt << "种解决方案" << endl; 
    cout << LINE32 << endl;
    cout << "回溯递归算法实现1 解决" << n << "皇后问题耗时" << /*end-begin << "打点" <<*/(double)(end-begin)/CLOCKS_PER_SEC  << "s" << endl;
    return 0;
}
// 14 8~10s