Hdu4786

Fibonacci Tree

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2340 Accepted Submission(s): 748


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

Source 2013 Asia Chengdu Regional Contest




題意：問構成的生成樹其中是否存在黑色邊（邊為1）數為斐波那契數 思路：求出生成樹中最小包含的黑色邊數，和最多黑色邊數，如果有斐波那契數在兩者之間，則可以構成，因為黑白邊可以搭配使用

#include 
#include 
#include 
#include 
using namespace std;
int n,m;
int fibo[50];
int f[100010];
struct node
{
    int u,v,c;
} s[100010];

bool cmp1(node x , node y)
{
    return x.c < y.c;
}

bool cmp2(node x, node y)
{
    return  x.c > y.c;
}

int find(int x)
{
    return x == f[x] ? x : f[x] = find(f[x]);
}

void Union(int x ,int y)
{
    int fx = find(x);
    int fy = find(y);

    if(fx != fy)
    {
        f[fx] = fy;
    }
}

int main()
{
#ifdef xxz
    freopen("in.txt","r",stdin);
#endif
    fibo[1] = 1;
    fibo[2] = 2;
    for(int i = 3; ; i++)
    {
        fibo[i] = fibo[i-1] + fibo[i-2];
        if(fibo[i] >= 100000) break;
    }

    int T,Case = 1;;
    scanf("%d",&T);

    while(T--)
    {


        scanf("%d%d",&n,&m);
        for(int i = 1; i <= n; i++) f[i] = i;

        for(int i = 0; i < m; i++)
        {

            scanf("%d%d%d",&s[i].u,&s[i].v,&s[i].c);
            Union(s[i].u,s[i].v);
        }
        int cent = 0;
        int bl = 0, bh = 0;
        int root = 0,size = 0;

        for(int i = 1; i <= n; i++)
        {
            if(f[i] == i)
            {
                cent++;
                root = i;
            }
        }

        printf("Case #%d: ",Case++);
        if(cent >= 2) cout<<"No"<= bl && fibo[i] <= bh)
                {
                    flag = 1;
                    break;
                }
            }
            if(flag) printf("Yes\n");
            else printf("No\n");

        }


    }
}