interviewstreet – even tree

題目來源：https://www.interviewstreet.com/challenges/dashboard/#problem/4fffc24df25cd

解題報告：

這道題求一顆樹，最多可以去掉幾條邊，使得被分割成的每顆單獨的樹的節點個數都是偶數。題目蠻有意思，難度適宜。

首先，將輸入轉換為樹的格式，對每個節點，保留它的父親節點和兒子節點的編號。

然後遍曆樹的每個節點，得到以該節點為根的樹的節點個數（包括該節點）

對一個節點R，設它有兒子節點A，如果以A為根的樹的節點個數有偶數個，則代表R與A這條邊可以被去除，否則不可以。這樣依次尋找每個節點，看它與它兒子的邊是否可以被去除，最後得到最多可以刪去多少條邊。

/* Enter your code here. Read input from STDIN. Print output to STDOUT */#include <iostream>#include <queue>using namespace std;int sum[101]; //以i為根的樹的節點個數int s[101][101]; //s[i][j]=1代表j為i的兒子int p[101];int adj[101][101];int k;int getSum(int index){    if (sum[index] != 0)        return sum[index];    int sm = 0;    for (int i = 0; i <= 100; i++)    {        if(s[index][i] == 1)        {            sm += getSum(i);        }    }    sm++;    sum[index] = sm;    return sm;}void findResult(int root){    for (int i = 0; i <= 100; i++)    {        if (s[root][i] == 1)        {            if(getSum(i) % 2 == 0)            {                k++;             } findResult(i);        }    }}int main(){    int N, M;    int root;    cin >> N >> M;    //initialization    k = 0;    for(int i = 0; i <= 100; i++)    {        sum[i] = 0;        p[i] = -1;        for (int j = 0; j <= 100; j++)        {            s[i][j] = 0;            adj[i][j] = 0;        }        }    for (int i = 0; i < M; i++)    {        int node1, node2;        cin >> node1 >> node2;        if (i == 0)            root = node1;        adj[node1][node2] = 1;        adj[node2][node1] = 1;    }    queue<int> q;    q.push(root);    while(!q.empty())    {        int node = q.front();        q.pop();        for (int i = 0; i <= 100; i++)        {            if (adj[node][i] == 1 && i!=p[node])            {                p[i] = node;                s[node][i] = 1;                q.push(i);            }        }    }    findResult(root);    cout << k << endl;    }

附錄：

You are given a tree (a simple connected graph with no cycles).You have to remove as many edges from the tree as possible to obtain a forest with the condition that : Each connected
component of the forest contains even number of vertices

Your task is to calculate the number of removed edges in such a forest.

Input:
The first line of input contains two integers N and M. N is the number of vertices and M is the number of edges. 2 <= N <= 100. 
Next M lines contains two integers u_{i and vi which
specifies an edge of the tree. (1-based index)}

Output:
Print a single integer which is the answer

Sample Input 

10 92 13 14 35 26 17 28 69 810 8  Sample Output :2  Explanation : On removing the edges (1, 3) and (1, 6), we can get the desired result.Original tree: 

Decomposed tree:

Note: The tree in the input will be such that it can always be decomposed into components containing even number of nodes.