Codeforces Round #403 (Div. 2) C. Andryusha and Colored Balloons DFS
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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 3
31 3 2
52 35 34 31 3
51 3 2 5 4
52 13 24 35 4
31 2 3 1 2
In the first sample the park consists of three squares: 1 → 3 → 2. Thus, the balloon colors have to be distinct.
![](http://codeforces.com/predownloaded/15/d5/15d5e3019b81029bc9f906b57d39a5b644042072.png)
In the second example there are following triples of consequently connected squares:
- 1 → 3 → 2
- 1 → 3 → 4
- 1 → 3 → 5
- 2 → 3 → 4
- 2 → 3 → 5
- 4 → 3 → 5
![](http://codeforces.com/predownloaded/07/fa/07fa42e9aaad0fe29656db148493605d0dfcb30a.png)
In the third example there are following triples:
- 1 → 2 → 3
- 2 → 3 → 4
- 3 → 4 → 5
![](http://codeforces.com/predownloaded/b7/0d/b70df28032774ef36bae4df1b307f5ef44e14e32.png)
Source
Codeforces Round #403 (Div. 2, based on Technocup 2017 Finals)
My Solution
题意:给出一颗无根树,要求如果a-b相连 b-c相连,则要求abc涂上不同的颜色,要求用最少的颜色给这颗树上色且求具体涂色。
DFS
首先这个最少的颜色数必定是 最大度+1,
然后具体涂色的时候可以dfs来涂色,因为dfs的时候孙子节点的颜色只跟相应子节点和父节点有关,跟该父节点的其它子节点没有关系,
所以用dfs来涂色。
复杂度 O(n)
#include <iostream>#include <cstdio>#include <cstring>#include <vector>using namespace std;typedef long long LL;const int maxn = 2e5 + 8;vector<int> sons[maxn];int p[maxn];void dfs(const int &g, const int &u){ int j, sz, ptr = 1; sz = sons[u].size(); if(sz == 1) return; for(j = 0; j < sz; j++){ while(ptr == p[g] || ptr == p[u]) ptr++; if(sons[u][j] == g) continue; p[sons[u][j]] = ptr; ptr++; dfs(u, sons[u][j]); }}int main(){ #ifdef LOCAL freopen("c.txt", "r", stdin); //freopen("c.out", "w", stdout); int T = 4; while(T--){ #endif // LOCAL ios::sync_with_stdio(false); cin.tie(0); int n, v, u, t, ans = 0, i, j, sz, maxi; cin >> n; t = n - 1; while(t--){ cin >> u >> v; sons[u].push_back(v); sons[v].push_back(u); } for(i = 1; i <= n; i++){ sz = sons[i].size(); if(ans < sz + 1){ ans = sz + 1; maxi = i; } } p[maxi] = ans; p[0] = 0; dfs(0, maxi); cout << ans << "\n" << p[1]; for(i = 2; i <= n; i++) cout << " " << p[i]; #ifdef LOCAL for(int i = 1; i <= n; i++){ sons[i].clear(); } memset(p, 0, sizeof p); cout << endl; } #endif // LOCAL return 0;}
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