DFS & BFS

DFS & BFS

（1）深度优先搜索

题意：求全排列。

#include <bits/stdc++.h>
using namespace std;

const char nl = '
';
const int N = 25;

int n;
int path[N];
bool st[N];

void dfs(int u){
    if (u == n){
        for (int i = 0; i < n; ++i) cout << path[i] << ' ';
        cout << nl;
        return ;
    }
    for (int i = 1; i <= n; ++i){
        if (!st[i]){
            path[u] = i;
            st[i] = true;
            dfs(u + 1);
            st[i] = false;
        }
    }
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    cin >> n;
    dfs(0);

    return 0;
}

题意：n-皇后问题。

#include <bits/stdc++.h>
using namespace std;

const char nl = '
';
const int N = 55;

int n;
char g[N][N];
bool col[N], dg[N], udg[N];

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

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

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

    dfs(0);

    return 0;
}

（2）广度优先搜索

题意：迷宫问题，从左上角走到右下角。

#include <bits/stdc++.h>
using namespace std;

typedef pair<int, int> PII;

const char nl = '
';
const int N = 110;

int n, m;
int g[N][N], d[N][N];

int dx[4] = {0, -1, 0, 1};
int dy[4] = {-1, 0, 1, 0};

void bfs(){
    queue<PII> q;
    q.push({0, 0});
    d[0][0] = 0;

    while (!q.empty()) {
        auto t = q.front();
        q.pop();

        int x = t.first, y = t.second;
        for (int i = 0; i < 4; ++i) {
            int tx = x + dx[i], ty = y + dy[i];
            if (0 <= tx && tx < n && 0 <= ty && ty < m && d[tx][ty] == -1) {
                d[tx][ty] = d[x][y] + 1;
                q.push({tx, ty});
            }
        }
    }
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    cin >> n >> m;
    for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) d[i][j] = -1;
    for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) cin >> g[i][j];

    bfs();

    cout << d[n - 1][m - 1] << nl;

    return 0;
}

/*

5 5
0 1 0 0 0
0 1 0 1 0
0 0 0 0 0
0 1 1 1 0
0 0 0 1 0

8

*/