Acwing-----算法提高课第二章搜索（四）

1112. 迷宫

• 链接：https://www.acwing.com/problem/content/1114/

#include <iostream>
#include <cstring>
#include <algorithm>

using namespace std;
const int N = 110;
int n, xa,xb, ya, yb;
char g[N][N];
bool st[N][N];
int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};

bool dfs(int x, int y) {
    if (g[x][y] == '#') return false;
    if (x == xb && y == yb) return true;
    
    st[x][y] = true;
    for (int i = 0; i < 4; ++i) {
        int a = x + dx[i], b = y + dy[i];
        if (a < 0 || a >= n || b < 0 || b >= n) continue;
        if (st[a][b]) continue;
        
        if (dfs(a, b)) return true;
    }
    return false;
}

int main() {
    int T;
    cin >> T;
    while (T--) {
        cin >> n;
        for (int i = 0; i < n; ++i) cin >> g[i];
        memset(st, 0, sizeof st);
        cin >> xa >> ya >> xb >> yb;
        if (dfs(xa, ya)) cout << "YES" << endl;
        else cout << "NO" << endl;
    }
    return 0;
}

1113. 红与黑

• 链接：https://www.acwing.com/problem/content/1115/

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

const int N = 25;
int n, m;
char g[N][N];
bool st[N][N];
int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};

int dfs(int x, int y) {
    int cnt = 1;
    st[x][y] = true;
    
    for (int i = 0; i < 4; ++i) {
        int a = x + dx[i], b = y + dy[i];
        if (a < 0 || a >= n || b < 0 || b >= m) continue;
        if (g[a][b] != '.') continue;
        if (st[a][b]) continue;
        
        cnt += dfs(a, b);
    }
    return cnt;
}

int main() {
    while (cin >> m >> n, n || m) {
        for (int i = 0; i < n; ++i) cin >> g[i];
        int x, y;
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < m; ++j) {
                if (g[i][j] == '@') {
                    x = i;
                    y = j;
                }
            }
        }
        memset(st, 0, sizeof st);
        cout << dfs(x, y) << endl;
    }
    return 0;
}

1116. 马走日

• 链接：https://www.acwing.com/problem/content/1118/

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

const int N = 15;
int n, m, ans;
bool st[N][N];
int dx[8] = {-2, -1, 1, 2, 2, 1, -1, -2};
int dy[8] = {1, 2, 2, 1, -1, -2, -2, -1};

void dfs(int x, int y, int cnt) {
    if (cnt == m * n) {
        ans ++;
        return;
    }
    st[x][y] = true;
    
    for (int i = 0; i < 8; ++i) {
        int a = x + dx[i], b = y + dy[i];
        if (a < 0 || a >= n || b < 0 || b >= m) continue;
        if (st[a][b]) continue;
        dfs(a, b, cnt + 1);
    }
    st[x][y] = false;
}

int main() {
    int T;
    cin >> T;
    while (T--) {
        int x, y;
        cin >> n >> m >> x >> y;
        ans = 0;
        dfs(x, y, 1);
        cout << ans << endl;
    }
    return 0;
}

1117. 单词接龙

• 链接：https://www.acwing.com/problem/content/1119/

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

const int N = 21;
int n, ans;
string word[N];
int g[N][N];
int used[N];

void dfs(string dragon, int last) {
    ans = max((int)dragon.size(), ans);
    used[last]++;
    
    for (int i = 0; i < n; ++i) {
        if (g[last][i] && used[i] < 2) {
            dfs(dragon + word[i].substr(g[last][i]), i);
        }
    }
    
    used[last]--;
}

int main() {
    cin >> n;
    for (int i = 0; i < n; ++i) cin >> word[i];
    char start;
    cin >> start;
    
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            string a = word[i], b =  word[j];
            for (int k = 1; k < min(a.size(), b.size()); ++k) {
                if (a.substr(a.size() - k, k) == b.substr(0, k)) {
                    g[i][j] = k;
                    break;
                }
            }
        }
    }
    for (int i = 0; i < n; ++i) {
        if (word[i][0] == start) {
            dfs(word[i], i);
        }
    }
    cout << ans << endl;
    return 0;
}

1118. 分成互质组

• 链接：https://www.acwing.com/problem/content/1120/

#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
const int N = 10;

int n, p[N], group[N][N], ans = N;
bool st[N];

int gcd(int a, int b) {
    return b ? gcd(b, a % b) : a;
}

bool check(int group[], int gc, int idx) {
    for (int i = 0; i < gc; ++i) {
        if (gcd(p[group[i]], p[idx]) > 1) return false;
    }
    return true;
}

void dfs(int u, int gc, int tc, int start) {
    if (u >= ans) return;
    if (tc == n) ans = u;
    bool flag = true;
    for (int i = start; i < n; ++i) {
        if (!st[i] && check(group[u], gc, i)) {
            st[i] = true;
            group[u][gc] = i;
            dfs(u, gc + 1, tc + 1, i + 1);
            st[i] = false;
            flag = false;
        }
    }    
    if (flag) dfs(u + 1, 0, tc, 0);
} 

int main() {
    cin >> n;
    for (int i = 0; i < n; ++i) cin >> p[i];
    dfs(1, 0, 0, 0);
    
    cout << ans << endl;
    return 0;
}