codeforces 782c Andryusha and Colored Balloons

Andryusha goes through a park each day. The squares and paths between them look boring to Andryusha, so he decided to decorate them.

The park consists of n squares connected with (n - 1) bidirectional paths in such a way that any square is reachable from any other using these paths. Andryusha decided to hang a colored balloon at each of the squares. The baloons' colors are described by positive integers, starting from 1. In order to make the park varicolored, Andryusha wants to choose the colors in a special way. More PRecisely, he wants to use such colors that if a, b and c are distinct squares that a and b have a direct path between them, and b and c have a direct path between them, then balloon colors on these three squares are distinct.

Andryusha wants to use as little different colors as possible. Help him to choose the colors!

The first line contains single integer n (3 ≤ n ≤ 2·105) — the number of squares in the park.

Each of the next (n - 1) lines contains two integers x and y (1 ≤ x, y ≤ n) — the indices of two squares directly connected by a path.

It is guaranteed that any square is reachable from any other using the paths.

In the first line print single integer k — the minimum number of colors Andryusha has to use.

In the second line print n integers, the i-th of them should be equal to the balloon color on the i-th square. Each of these numbers should be within range from 1 to k.

32 31 3output
31 3 2 input
52 35 34 31 3output
51 3 2 5 4 input
52 13 24 35 4output
31 2 3 1 2 Note
In the first sample the park consists of three squares: 1 → 3 → 2. Thus, the balloon colors have to be distinct.
Illustration for the first sample.
In the second example there are following triples of consequently connected squares:
1 → 3 → 21 → 3 → 41 → 3 → 52 → 3 → 42 → 3 → 54 → 3 → 5We can see that each pair of squares is encountered in some triple, so all colors have to be distinct.Illustration for the second sample.
In the third example there are following triples:
1 → 2 → 32 → 3 → 43 → 4 → 5We can see that one or two colors is not enough, but there is an answer that uses three colors only.
Illustration for the third sample题意：给定N个节点，N-1个关系，并且任意节点所相连的节点的颜色都不相同，问最少多少种颜色可以实现，打印出每个节点的颜色思路：暴力求解，dfs（）来求解，一层一层的来求解AC代码：
#include <iostream>#include <cstdio>#include <vector>using namespace std;const int MAX_N = 200005;vector<int> G[MAX_N];//用来表示图int m,n,a,b;//n个节点int color[MAX_N];//每个节点的颜色int ans;void dfs(int now,int p){//now表示当前节点，p表示和它相连的结点     int cur = 1;//用来记录当前的颜色     for(int i = 0;i < G[now].size();++i){        int v = G[now][i];        if(v == p){//说明当前的这个结点所连接的这个结点已经图过色了            continue;        }        while(cur == color[p] || cur==color[now]){//求得可以涂的最大颜色；            cur++;        }        color[v] = cur++;        ans = max(ans,color[v]);        dfs(v,now);     }}int main() {    cin >> n;    ans = 0;    for (int i = 0; i < n-1; i++) {//        cin >> a >> b;        G[a].push_back(b);        G[b].push_back(a);    }    color[1] =1;    dfs(1,0);    printf("%d/n",ans);    for(int i = 1;i <= n;i++){        printf("%d ",color[i]);    }    return 0;}.真的是，自己对深搜的理解简直差的要死，做起题目来感觉会写，但写的时候很容易错，继续加油吧，人一我十，总能赶上的。