【算法设计与分析】回溯—n皇后问题

强烈推荐的教程：算法与数据结构，回溯法求解八皇后，最经典的递归问题_哔哩哔哩_bilibili

#include<iostream>
#include<vector>
using namespace std;
long long t;


//put_queen函数用来改变attack矩阵
void put_queen(int k,int i,vector<vector<int>> &attack){ //k是第几行，i是第几列
    t++;
    cout<<t<<' ';
    int n=attack.size();
    for(int j=0;j<n;j++){
        attack[k][j]=1; 
        attack[j][i]=1;
    }
    int x=k,y=i;
    while(x>0&&y>0){
        x--;
        y--;
        attack[x][y]=1;
    }
    x=k;
    y=i;
    while(x>0&&y<n-1){
        x--;
        y++;
        attack[x][y]=1;
    }
    x=k;
    y=i;
    while(x<n-1&&y>0){
        x++;
        y--;
        attack[x][y]=1;
    }
    x=k;
    y=i;
    while(x<n-1&&y<n-1){
        x++;
        y++;
        attack[x][y]=1;
    }
    //打印attack矩阵
 /*   cout<<"attack matrix:"<<endl;
    for(int i=0;i<n;i++){
        for(int j=0;j<n;j++){
            cout<<attack[i][j]<<" ";
        }
        cout<<endl;
    } */
}

void backtrack(int k,int n,vector<string> &queen,vector<vector<int>> &attack,vector<vector<string>> &solve){
    if(k==n){
        solve.push_back(queen);
        return;
    }
    for(int i=0;i<n;i++){
        if(attack[k][i]==0){
            vector<vector<int>> temp=attack;
            queen[k][i]='Q';
            put_queen(k,i,attack);
            backtrack(k+1,n,queen,attack,solve);
            attack=temp;
            queen[k][i]='.';
        }
    }
}


vector<vector<string>> solveNQueens(int n) {
    vector<vector<string>> solve;
    vector<vector<int>> attack;
    vector<string> queen;
    for(int i=0;i<n;i++){
        attack.push_back(vector<int>());
        for(int j=0;j<n;j++){
            attack[i].push_back(0);
        }
        queen.push_back("");
        queen[i].append(n,'.');
    }
    backtrack(0,n,queen,attack,solve);
    return solve;
}

int main(){
    int n;
    cout<<"input n:";
    cin>>n;
    vector<vector<string>> result;
    result=solveNQueens(n);
    for(int i=0;i<result.size();i++){
        for(int j=0;j<result[i].size();j++){
            cout<<result[i][j]<<endl;
        }
        cout<<endl;
    }
    cout<<"total solutions:"<<result.size()<<endl;
    return 0;
}