HDU 4786 Fibonacci Tree

Fibonacci Tree

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 5502    Accepted Submission(s): 1711

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, ... )

 

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).

 

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

#include<cstdio>
#include<algorithm>
#include<iostream>
using namespace std;
const int N = 200000 + 10;
struct node{
	int u, v, d;
}p[N];
int n, m;
int pre[N], Fib[50];
bool cmp(node a, node b){
	return a.d < b.d;
}
bool cmp1(node a, node b){
	return a.d > b.d;
}
int Find(int x){
	if(x != pre[x]) pre[x] = Find(pre[x]);
	return pre[x];
}
join(int x, int y){
	int t1, t2;
	t1 = Find(x);
	t2 = Find(y);
	if(t1 != t2) pre[t1] = t2;
}
void init(){
	for(int i = 1; i <= n; i++){
		pre[i] = i;
	}
}
int main(){
	Fib[0] = 1, Fib[1] = 1;
	for(int i = 2; i <= 45; i++){
		Fib[i] = Fib[i - 1] + Fib[i - 2];
	}
	int T, iCase = 1;
	scanf("%d", &T);
	while(T--){
		scanf("%d%d", &n ,&m);
		init();
		for(int i = 1; i <= m; i++){
			scanf("%d%d%d", &p[i].u, &p[i].v, &p[i].d);
			join(p[i].u, p[i].v);
		}
		printf("Case #%d: ", iCase++);
		bool flag = true;
		for(int i = 1; i <= n; i++){
			if(Find(1) != Find(i)){
				flag = false;
			}
		}
		if(!flag){
			printf("No\n");
			continue;
		}
		init();
		int cnt = 0, cnt1 = 0, size = 0;
		sort(p + 1, p + 1 + m, cmp);
		for(int i = 1; i <= m; i++){
			if(Find(p[i].u) != Find(p[i].v)){
				cnt += p[i].d;
				join(p[i].u, p[i].v);
				size++;
				if(size == n - 1) break;
			}
		}
		init();
		size = 0;
		sort(p + 1, p + 1 + m, cmp1);
		for(int i = 1; i <= m; i++){
			if(Find(p[i].u) != Find(p[i].v)){
				cnt1 += p[i].d;
				join(p[i].u, p[i].v);
				size++;
				if(size == n - 1) break;
			}
		}
		bool flag1 = true;
		for(int i = 1; i <= 45; i++){
			if(Fib[i] >= cnt && Fib[i] <= cnt1){
				flag1 = false;
				break;
			}
		}
		if(!flag1) printf("Yes\n");
		else printf("No\n");
	}
	return 0;
}