《算法基础》 DFS

《算法基础》 DFS

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1.排列数字

#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;

const int N = 10;
int path[N];
int vis[N];
int n;

void dfs(int u)
{
    if (u == n) {
        for (int i = 0; i < n; i ++) cout << path[i] << " ";
        cout << endl;
        return ;
    }
    for (int i = 1; i <= n; i ++) {
        if (!vis[i]) {
            path[u] = i;
            vis[i] = 1;
            dfs(u + 1);
            vis[i] = 0;
            path[u] = 0;
        }
    }
}

int main()
{
    cin >> n;
    
    dfs(0);
    
    return 0;
}

2. n皇后

#include <iostream>
#include <algorithm>
using namespace std;

const int N = 20;
char map[N][N];
int col[N], dg[N], udg[N];
int n;

void dfs(int u)
{
    if (u == n) {
        for (int i = 0; i < n; i++) cout << map[i] << endl;
        cout << endl;
        return ;
    }
    for (int i = 0; i < n; i ++) {
        if (!col[i] && !dg[u + i] && !udg[n + i - u]) {
            map[u][i] = 'Q';
            col[i] = dg[u + i] = udg[n + i - u] = 1;
            dfs(u + 1);
            map[u][i] = '.';
            col[i] = dg[u + i] = udg[n + i - u] = 0;
        }
    }
}

int main()
{
    cin >> n;
    
    for (int i = 0; i < n; i ++) {
        for (int j = 0; j < n; j ++) {
            map[i][j] = '.';
        }
    }
    
    dfs(0);
    
    return 0;
}
}

3.n皇后原始

#include <iostream>
#include <algorithm>
using namespace std;

const int N = 20;
char map[N][N];
int row[N], col[N], dg[N], udg[N];
int n;

void dfs(int x, int y, int s)   //在(x, y)处 已经放了几个皇后了
{
	if (y >= n) {
		y = 0;
		x ++;
	}
	if (x == n) {       //不管有没有成功 都要return;
		if (s == n) {
			for (int i = 0; i < n; i ++) cout << map[i] << endl;
			cout << endl;
		}
		return ;
	}
	//在 (x, y) 处不放皇后
	dfs(x, y + 1, s);
	
	//在 (x, y) 处放皇后
	if (!row[x] && !col[y] && !dg[x + y] && !udg[x - y + n]) {
		map[x][y] = 'Q';
		row[x] = col[y] = dg[x + y] = udg[x - y + n] = 1;
		dfs(x, y + 1, s + 1);
		row[x] = col[y] = dg[x + y] = udg[x - y + n] = 0;
		map[x][y] = '.';
	}
}

int main()
{
	cin >> n;
	
	for (int i = 0; i < n; i ++)
		for (int j = 0; j < n; j ++)
			map[i][j] = '.';

	dfs(0, 0, 0);

 	return 0;
}