[算法] 八皇后——回溯问题

#include <iostream>
#include <cmath>

using namespace std;

int count = 0;

void show(int* mark, const int n) {
    cout << "case " << count << ":" << endl;
    for (int i = 0; i < n; i ++)
        cout << mark[i] << " ";
    cout << endl;
    for (int i = 0; i < n; i ++) {
        for (int j = 0; j < n; j ++) {
            if (j == mark[i])
                cout << '@';
            else
                cout << '-';
        }
        cout << endl;
    }
}

bool isCorrectPosition(int* mark, const int n, const int row, const int col) {
    for (int i = 0; i < n; i ++) {
        if (mark[i] != -1 && (abs(i - row) == abs(mark[i] - col) || i == row || mark[i] == col))
            return false;
    }
    return true;
}


void BackTrack(int *mark, const int n, const int index) {
    if (index >= n) {
        count++;
        show(mark, n);
        return;
    }
        

    for (int j = 0; j < n; j ++) {
        if (isCorrectPosition(mark, n, index, j)) {
            mark[index] = j;
            BackTrack(mark, n, index + 1);
            mark[index] = -1;
        }
    }
}

int main() {
    int n = 8;
    cin >> n;
    int* mark = new int [n];
    for (int i = 0; i < n; i ++)
        mark[i] = -1;
    count = 0;
    BackTrack(mark, n, 0);
    delete mark;
    
    return 0;
}

 

 

//非递归
void iterativeBackTrack(int* mark, const int n) {
    int currentLayer = 0;
    while (currentLayer >= 0) {

        int temp_col = mark[currentLayer] + 1;
        mark[currentLayer] = -1;
        while (!isCorrectPosition(mark, n, currentLayer, temp_col) && temp_col < n) {
            temp_col++;
        }
        if (temp_col >= n) {
            mark[currentLayer] = -1;
            currentLayer--;
        }
        else {
            mark[currentLayer] = temp_col;
            currentLayer++;
            if (currentLayer >= n) {
                count++;
                show(mark, n);
                currentLayer--;
            }
        }
    }
}