首页 > 代码库 > HDU 4786(最小生成树 kruskal)
HDU 4786(最小生成树 kruskal)
题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=4786
Problem Description
Coach Pang is interested in Fibonacci numbers while Uncle Yang wants him to do some research on Spanning Tree. So Coach Pang decides to solve the following problem:
Consider a bidirectional graph G with N vertices and M edges. All edges are painted into either white or black. Can we find a Spanning Tree with some positive Fibonacci number of white edges?
(Fibonacci number is defined as 1, 2, 3, 5, 8, ... )
Consider a bidirectional graph G with N vertices and M edges. All edges are painted into either white or black. Can we find a Spanning Tree with some positive Fibonacci number of white edges?
(Fibonacci number is defined as 1, 2, 3, 5, 8, ... )
Input
The first line of the input contains an integer T, the number of test cases.
For each test case, the first line contains two integers N(1 <= N <= 105) and M(0 <= M <= 105).
Then M lines follow, each contains three integers u, v (1 <= u,v <= N, u<> v) and c (0 <= c <= 1), indicating an edge between u and v with a color c (1 for white and 0 for black).
For each test case, the first line contains two integers N(1 <= N <= 105) and M(0 <= M <= 105).
Then M lines follow, each contains three integers u, v (1 <= u,v <= N, u<> v) and c (0 <= c <= 1), indicating an edge between u and v with a color c (1 for white and 0 for black).
Output
For each test case, output a line “Case #x: s”. x is the case number and s is either “Yes” or “No” (without quotes) representing the answer to the problem.
Sample Input
2 4 4 1 2 1 2 3 1 3 4 1 1 4 0 5 6 1 2 1 1 3 1 1 4 1 1 5 1 3 5 1 4 2 1
Sample Output
Case #1: Yes Case #2: No
Source
2013 Asia Chengdu Regional Contest
题意:
N个顶点,M条边,每条边或为白色或为黑色( 1 or 0 ),
问有没有用是斐波那契数的数目的白色边构成一棵生成树。
PS:
其实说是并查集更靠谱一点的酱紫!
首先判断整个图是否是连通的,若不连通则直接输出No。
接下来首先仅讨论白边,不要黑边,看最多能加入多少条白边,使得不存在环。这样我们得到了能加入白边的最大值max。(就是所有生成树里白边数量的最大值)。
接下来同理仅讨论黑边,这样我们可以得到可加入白边的最小值min,(也可以认为是所有生成树中白边的最小值)。
然后我们只要判断这两个值之间是否存在斐波那契数就行了。
代码如下:
#include <cstdio> #include <cstring> #include <algorithm> #include <iostream> using namespace std; const int maxn = 100017; struct node { int u, v; int c; } a[maxn]; int f[maxn], Fib[maxn]; int n, m; int findd(int x) { return x==f[x] ? x : f[x]=findd(f[x]); } int kruskal(int sign) { int k = 0; //sort(a,a+m,cmp); for(int i = 0; i <= n; i++) { f[i] = i; } for(int i = 1; i <= m; i++) { if(a[i].c != sign) { int f1 = findd(a[i].u); int f2 = findd(a[i].v); if(f1 != f2) { f[f1] = f2; k++; } } } return k; } void init() { Fib[0] = 1, Fib[1] = 2; for(int i = 2; ; i++) { Fib[i] = Fib[i-1]+Fib[i-2]; if(Fib[i] > maxn) break; } } int main() { int t; int cas = 0; init(); scanf("%d",&t); while(t--) { scanf("%d%d",&n,&m); for(int i = 1; i <= m; i++) { scanf("%d%d%d",&a[i].u,&a[i].v,&a[i].c); } int ans = kruskal(2); if(ans != n-1)//不能形成树 { printf("Case #%d: No\n",++cas); continue; } int maxx = kruskal(0); int minn = n-1-kruskal(1); int flag = 0; for(int i = 0; ; i++) { if(Fib[i] >=minn && Fib[i]<=maxx) { flag = 1; break; } if(Fib[i] > maxx) { break; } } if(flag) { printf("Case #%d: Yes\n",++cas); } else { printf("Case #%d: No\n",++cas); } } return 0; }
HDU 4786(最小生成树 kruskal)
声明:以上内容来自用户投稿及互联网公开渠道收集整理发布,本网站不拥有所有权,未作人工编辑处理,也不承担相关法律责任,若内容有误或涉及侵权可进行投诉: 投诉/举报 工作人员会在5个工作日内联系你,一经查实,本站将立刻删除涉嫌侵权内容。