图论 List

题目

#A 小 K 的农场 (Unaccepted)
    #B 信息传递 (Unaccepted)
    #C 最短路计数 (Accepted)
    #D 通往奥格瑞玛的道路 (Accepted)

#E 公路修建 (Unaccepted)

#F 货车运输 (Unaccepted)

#G 图的m着色问题  (Unaccepted)

---

1. DFS & BFS

// 八皇后
// Au: GG

#include <cstdio>
#include <cmath>
using namespace std;
int v[15], n, ans = 0;
bool f[15];

void dfs(int i) {
    if (i > n) {
        ans++;
        if (ans <= 3) {
            for (int j = 1; j <= n; j++) {
                printf("%d ", v[j]);
            }
            printf("\n");
        }
        return;
    }
    for (int k = 1; k <= n; k++) {
        if (f[k]) continue;
        bool pd = true;
        for (int j = 1; j < i; j++)
            if (v[j] == k || abs(i - j) == abs(v[j] - k)) pd = false;
        if (pd) {
            v[i] = k;
            f[k] = true;
            dfs(i + 1);
            f[k] = false;
            v[i] = 0;
        }
    }
}

int main() {
    scanf("%d", &n);
    dfs(1);
    printf("%d", ans);
    return 0;
}

// 马的遍历
// Au: GG

#include <iostream>
#include <algorithm>
#include <queue>
#include <cmath>
#include <cstring>
#include <cstdio>
#include <cstdlib>
using namespace std;

int n, m;
int dx[8] = { -2, -1, 1, 2, 2, 1, -1, -2};
int dy[8] = {1, 2, 2, 1, -1, -2, -2, -1};
int map[400 + 3][400 + 3];
struct bbc {
    int x, y, n;
} s;
queue<bbc> q;

int main() {
    memset(map, -1, sizeof(map));
    scanf("%d%d%d%d", &n, &m, &s.x, &s.y);
    map[s.x][s.y] = 0;
    q.push(s);

    while (!q.empty()) {
        bbc a;
        for (int i = 0; i < 8; i++) {
            a = q.front();
            int bx = a.x + dx[i];
            int by = a.y + dy[i];
            if (bx < 1 || bx > n || by < 1 || by > m || map[bx][by] != -1)
                continue;
            a.x = bx;
            a.y = by;
            a.n++;
            q.push(a);
            map[bx][by] = a.n;
        }
        q.pop();
    }

    for (int k = 1; k <= n; k++) {
        for (int r = 1; r <= m; r++)
            printf("%-5d", map[k][r]);
        printf("\n");
    }
    return 0;
}

/* Luogu P1126 机器人搬重物
 * Au: GG
 */
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <queue>
#include <iostream>
#include <algorithm>
using namespace std;
const int N = 53;
int n, m, g[N][N], endx, endy;
bool d[N][N][4];

struct status {
    int x, y, t;
    char d;
} sta;
queue<status> q;

char ltd(char dir) {
    if (dir == 'N') return 'W';
    else if (dir == 'W') return 'S';
    else if (dir == 'S') return 'E';
    else return dir = 'N';
}

char rtd(char dir) {
    if (dir == 'N') return 'E';
    else if (dir == 'E') return 'S';
    else if (dir == 'S') return 'W';
    else return 'N';
}

int did(char dir) {
    if (dir == 'N') return 0;
    else if (dir == 'E') return 1;
    else if (dir == 'S') return 2;
    else return 3;
}

int main() {
    int h;
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++) {
            scanf("%d", &h);
            if (h) {
                g[i][j] = -1;
                g[i + 1][j] = -1;
                g[i][j + 1] = -1;
                g[i + 1][j + 1] = -1;
            }
        }

    scanf("%d%d%d%d %c", &sta.x, &sta.y, &endx, &endy, &sta.d);
    sta.x++; sta.y++; endx++; endy++;
    sta.t = 0; d[sta.x][sta.y][did(sta.d)] = true;

    q.push(sta);
    while (!q.empty()) {
        status a = q.front(), b;
        q.pop();

        if (a.x == endx && a.y == endy) {
            printf("%d\n", a.t); return 0;
        }
        d[a.x][a.y][did(a.d)] = true;
        // printf("Status a(%d, %d, %c) = %d\n", a.x, a.y, a.d, a.t);

        // Creep & Walk & Run
        for (int step = 1; step <= 3; step++) {
            if (a.d == 'N') {
                b.x = a.x - step; b.y = a.y;
            } else if (a.d == 'S') {
                b.x = a.x + step; b.y = a.y;
            } else if (a.d == 'W') {
                b.x = a.x; b.y = a.y - step;
            } else {
                b.x = a.x; b.y = a.y + step;
            }
            b.d = a.d; b.t = a.t + 1;
            if (g[b.x][b.y] == 0 && !d[b.x][b.y][did(b.d)]) {
                if (b.x > 1 && b.x < n + 1 && b.y > 1 && b.y < m + 1)
                    q.push(b);
                else break;
            } else break;
        }

        // Left
        b.x = a.x; b.y = a.y; b.t = a.t + 1;
        b.d = ltd(a.d);
        if (!d[b.x][b.y][did(b.d)])
            if (b.x > 1 && b.x < n + 1 && b.y > 1 && b.y < m + 1)
                q.push(b);

        // Right
        b.x = a.x; b.y = a.y; b.t = a.t + 1;
        b.d = rtd(a.d);
        if (!d[b.x][b.y][did(b.d)])
            if (b.x > 1 && b.x < n + 1 && b.y > 1 && b.y < m + 1)
                q.push(b);
    }

    printf("-1\n");
    return 0;
}
/*
9 10
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 1 0
0 0 0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 1 0
7 2 2 7 S
*/

/*
问题（估计是致命问题）给你一个图（点阵，不是块阵）
0 0 0 0 0 0 0
0 S 1 T 1 0 0
机器人在S处面向右方，根据你82-97行的前进代码，机器人可以到达T处，但是事实上并不能到达，所以题目数据的图（点阵）如下
 0 0 0 0 0 0-1-1 0 0 0
 0 0 0 0 0 0-1-1-1-1 0
 0 0 V-1-1 V 0 T-1-1 0
 0 0-1-1-1 0 0 0 0 0 0
 0 0-1-1 0 0-1-1 0 0 0
 0 0 V 0 0-1-1-1 0 0 0
 0 0 0-1-1-1-1 0 0 0 0
 0 0 S-1-1-1 0 0 0 0 0
-1-1 0 0 0 0 0 0-1-1 0
-1-1 0 0 0 0 0 0-1-1 0
7步的行径路径给你了

左转（面向右边）
左转（面向上方）
walk
run（这步其实不能走，但是按照你的代码是可以走的）
右转（面向右边）
run（这步其实也不能走，但是按照你的代码也是可以走的）
walk

以上七步S是起点V是途经点T是终点

连这个错误你都犯，你可以去面壁一天了。。。（什么时候可以穿墙了。。。）
还有，让zzh去面壁半天，连这么简单的错误都看不出来。
我先走了
——8：45 by dph
*/

/* P1118 [USACO06FEB]数字三角形Backward Digit Su…
 * Au: GG
 */
#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <algorithm>
using namespace std;
const int N = 15;
int n, sum, tri[N][N], d[N];
bool v[N];

void triangle() { // triangle table
    for (int i = 1; i <= n; i++) tri[i][1] = tri[i][i] = 1;
    for (int i = 2; i <= n; i++)
        for (int j = 2; j < i; j++)
            tri[i][j] = tri[i - 1][j] + tri[i - 1][j - 1];

    // for (int i = 1; i <= n; i++) {
    //     for (int j = 1; j <= i; j++)
    //         printf("%d ", tri[i][j]);
    //     printf("\n");
    // }
}

bool dfs(int f, int s) {
    // printf("dfs(%d, %d, d = %d)\n", f, s, d[f - 1]);
    if (f > n) {
        if (s == sum) return true;
        else return false;
    }
    for (int i = 1; i <= n; i++)
        if (!v[i] && s + i * tri[n][f] <= sum) {
            v[i] = true; d[f] = i;
            if (dfs(f + 1, s + i * tri[n][f])) return true;
            v[i] = false;
        }
    return false;
}

int main() {
    scanf("%d%d", &n, &sum);
    triangle();

    if (dfs(1, 0)) {
        for (int i = 1; i <= n; i++) printf("%d ", d[i]);
    }

    return 0;
}

/* Luogu P1141 01迷宫
 * Au: GG
 */
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <queue>
#include <iostream>
#include <algorithm>
using namespace std;
const int N = 1000 + 5;
int n, m, g[N][N]; int vis[N][N], vs, vcnt[100000 + 5];
int dx[] = {0, -1, 1, 0}, dy[] = {-1, 0, 0, 1};

struct point {
    int x, y;
};

int read() {
    char a = getchar();
    while (a != '0' && a != '1') a = getchar();
    return a - '0';
}

bool check(point i) {
    if (i.x < 1 || i.x > n) return false;
    if (i.y < 1 || i.y > n) return false;
    return true;
}

int bfs(int u, int v) {
    if (vis[u][v]) return vcnt[vis[u][v]]; 

    int cnt = 0; vs++;
    queue<point> q;
    point a, b; a.x = u, a.y = v;
    q.push(a);

    while (!q.empty()) {
        a = q.front();
        q.pop(); if (vis[a.x][a.y]) continue;
        vis[a.x][a.y] = vs; cnt++;

        for (int i = 0; i < 4; i++) {
            b.x = a.x + dx[i];
            b.y = a.y + dy[i];
            if (check(b) && (g[b.x][b.y] != g[a.x][a.y]) && !vis[b.x][b.y]) q.push(b);
        }
    }

    return vcnt[vs] = cnt;
}

int main() {
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            g[i][j] = read();
        }
    }

    int xx, yy;
    while (m--) {
        scanf("%d%d", &xx, &yy);
        printf("%d\n", bfs(xx, yy));
    }

    return 0;
}

2. 最小生成树

// 最小生成树
// Au: GG

#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <queue>
#include <algorithm>
using namespace std;

int n, m, f[5000 + 3], sum;
struct edge {
    int x, y, w;
    bool operator < (const edge &a) const {
        return w > a.w;
    }
} temp;
priority_queue<edge> G;

int find(int x) {
    return (f[x] == x) ? x : f[x] = find(f[x]);
}
void join(int x, int y) {
    f[find(y)] = find(x);
}

int main() {
    int x, y, z, flag = 0;
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= m; i++) {
        scanf("%d%d%d", &x, &y, &z);
        temp.x = x; temp.y = y; temp.w = z; G.push(temp);
    }
    for (int i = 1; i <= n; i++) f[i] = i;
    while (!G.empty()) {
        temp = G.top(); G.pop();
        if (find(temp.x) != find(temp.y)) join(temp.x, temp.y), sum += temp.w, flag++;
    }
    if (flag < n - 1) printf("orz\n");
    else printf("%d\n", sum);
    return 0;
}

3. 并查集

/* 并查集
 * Au: GG
 */
#include <cstdio>
#include <cstring>
#include <cmath>
using namespace std;
const int maxn = 10000 + 3;
int n, m, z, x, y, f[maxn];
int find(int x) {
    return (f[x] == x) ? x : f[x] = find(f[x]);
}
inline void join(int x, int y) {
    f[find(y)] = find(x);
}
int main() {
    scanf("%d%d", &n, &m);
    while (n--) f[n] = n;
    while (m--) {
        scanf("%d%d%d", &z, &x, &y);
        if (z == 1) {
            join(x, y);
        } else {
            if (find(x) == find(y)) printf("Y\n");
            else printf("N\n");
        }
    }
    return 0;
}