模板判断二分图

Posted 2020-09-10 蒟蒻zht的博客

给你一个无向图， 让你判断这是不是一个二分图。

二分图的标准：可以把这个图的点分成两堆，试每条边都连接这两个堆里的点，而一个堆里的点不能相连。

无向图G为二分图的充分必要条件是，G至少有两个顶点, 且其所有回路的长度均为偶数。（？？？什么意思？？？）

语文不好，看图吧。

 

就这个意思。

而现在然你自己判断该怎么判断。

——看代码就能看懂（dfs版）

 1 #include <cstdio>
 2 #include <cstring>
 3 
 4 int n, e, cnt;
 5 int head[1001], next[1001], to[1001], color[1001];
 6 
 7 void add(int x, int y)
 8 {
 9     to[cnt] = y;
10     next[cnt] = head[x];
11     head[x] = cnt++;
12 }
13 
14 bool dfs(int u, int c)
15 {
16     int i, v;
17     color[u] = c;
18     for(i = head[u]; i != -1; i = next[i])
19     {
20         v = to[i];
21         if(color[v] == c) return 0;
22         if(color[v] == 0 && !dfs(v, -c)) return 0;
23     }
24     return 1;
25 }
26 
27 bool solve()
28 {
29     int i;
30     for(i = 1; i <= n; i++)
31      if(color[i] == 0 && !dfs(i, 1))
32       return 0;
33     return 1;
34 }
35 
36 int main()
37 {
38     int i, x, y;
39     scanf("%d %d", &n, &e);
40     memset(head, -1, sizeof(head));
41     for(i = 1; i <= e; i++)
42     {
43         scanf("%d %d", &x, &y);
44         add(x, y);
45         add(y, x);
46     }
47     if(solve()) printf("YES");
48     else printf("NO");
49     return 0;
50 }

View Code

 

——bfs版

 1 # include <iostream>
 2 # include <cstdio>
 3 # include <cstring>
 4 # include <string>
 5 # include <cmath>
 6 # include <vector>
 7 # include <map>
 8 # include <queue>
 9 # include <cstdlib>
10 # define MAXN 2333
11 using namespace std;
12 
13 inline void File() {
14 #ifdef DEBUG
15     freopen("in.txt", "r", stdin);
16 #else
17     //freopen();
18     //freopen();
19 #endif
20 }
21 
22 inline int get_num() {
23     int k = 0, f = 1;
24     char c = getchar();
25     for(; !isdigit(c); c = getchar()) if(c == \'-\') f = -1;
26     for(; isdigit(c); c = getchar()) k = k * 10 + c - \'0\';
27     return k * f;
28 }
29 
30 int n, m, cnt;
31 int head[MAXN], next[MAXN], to[MAXN], color[MAXN];
32 queue <int> q;
33 
34 inline void add(int x, int y)
35 {
36     to[cnt] = y;
37     next[cnt] = head[x];
38     head[x] = cnt++;
39 }
40 
41 int main()
42 {
43     int i, j, x, y, u, v;
44     n = get_num();
45     m = get_num();
46     memset(head, -1, sizeof(head));
47     for(i = 1; i <= m; i++)
48     {
49         x = get_num();
50         y = get_num();
51         add(x, y);
52         add(y, x);
53     }
54     memset(color, -1, sizeof(color));
55     q.push(1);
56     color[1] = 0;
57     while(!q.empty())
58     {
59         u = q.front();
60         q.pop();
61         for(i = head[u]; i != -1; i = next[i])
62         {
63             v = to[i];
64             if(color[v] == color[u])
65             {
66                 printf("WRONG!");
67                 return 0;
68             }
69             if(color[v] == -1)
70             {
71                 color[v] = color[u] ^ 1;
72                 q.push(v);
73             }
74         }
75     }
76     return 0;
77 }

View Code

 

——并查集

 1 # include <iostream>
 2 # include <cstdio>
 3 # include <cstring>
 4 # include <string>
 5 # include <cmath>
 6 # include <vector>
 7 # include <map>
 8 # include <queue>
 9 # include <cstdlib>
10 # define MAXN 233
11 using namespace std;
12 
13 inline void File() {
14 #ifdef DEBUG
15     freopen("in.txt", "r", stdin);
16 #else
17     //freopen();
18     //freopen();
19 #endif
20 }
21 
22 inline int get_num() {
23     int k = 0, f = 1;
24     char c = getchar();
25     for(; !isdigit(c); c = getchar()) if(c == \'-\') f = -1;
26     for(; isdigit(c); c = getchar()) k = k * 10 + c - \'0\';
27     return k * f;
28 }
29 
30 int n, m;
31 int f[MAXN];
32 
33 inline int find(int x)
34 {
35     return x == f[x] ? x : f[x] = find(f[x]);
36 }
37 
38 int main()
39 {
40     int i, j, x, y, fx, fy;
41     n = get_num();
42     m = get_num();
43     for(i = 1; i <= n * 2; i++) f[i] = i;
44     for(i = 1; i <= m; i++)
45     {
46         x = get_num();
47         y = get_num();
48         fx = find(2 * x - 1);
49         fy = find(2 * y);
50         //一个染白则另一个染黑 
51         f[fx] = fy;
52         fx = find(2 * x);
53         fy = find(2 * y - 1);
54         //一个染黑则另一个染白 
55         f[fx] = fy;
56     }
57     for(i = 1; i <= n; i++)
58         if(find(i * 2) == find(i * 2 - 1))
59         {
60             printf("WRONG!");
61             return 0;
62         }
63     return 0;
64 }

View Code