Codeforces-1144F-Graph Without Long Directed Paths（深度搜索）

原题链接：http://codeforces.com/contest/1144/problem/F

题目原文：

F. Graph Without Long Directed Paths

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given a connected undirected graph consisting of nn vertices and mm edges. There are no self-loops or multiple edges in the given graph.

You have to direct its edges in such a way that the obtained directed graph does not contain any paths of length two or greater (where the length of path is denoted as the number of traversed edges).

Input

The first line contains two integer numbers nn and mm (2≤n≤2⋅1052≤n≤2⋅105, n−1≤m≤2⋅105n−1≤m≤2⋅105) — the number of vertices and edges, respectively.

The following mm lines contain edges: edge ii is given as a pair of vertices uiui, vivi (1≤ui,vi≤n1≤ui,vi≤n, ui≠viui≠vi). There are no multiple edges in the given graph, i. e. for each pair (ui,viui,vi) there are no other pairs (ui,viui,vi) and (vi,uivi,ui) in the list of edges. It is also guaranteed that the given graph is connected (there is a path between any pair of vertex in the given graph).

Output

If it is impossible to direct edges of the given graph in such a way that the obtained directed graph does not contain paths of length at least two, print "NO" in the first line.

Otherwise print "YES" in the first line, and then print any suitable orientation of edges: a binary string (the string consisting only of '0' and '1') of length mm. The ii-th element of this string should be '0' if the ii-th edge of the graph should be directed from uiui to vivi, and '1' otherwise. Edges are numbered in the order they are given in the input.

Example

input

Copy
6 5
1 5
2 1
1 4
3 1
6 1
output

Copy
YES
10100
Note

The picture corresponding to the first example:

And one of possible answers:

题目大意：

给一个无向图，保证没有自环和多边，现在给每条边标记方向，要求不存在路径长度大于1.

解题思路：

观察发现，要满足条件则要求图中不存在奇数边的环。使用深度搜索。

AC代码：

#include <cstdio>
#include <cstring>
#include <vector>
using namespace std;

const int N = int(2e5 + 5);

int g_n, g_m;
vector<int> g_vec[N];
int g_u[N], g_v[N], g_flag[N];

void init()
{
    memset(g_flag, -1, sizeof(g_flag));
    int i;
    for (i = 1; i <= g_n; i++)
    {
        g_vec[i].clear();
    }
}

bool dfs(int p, int flag)
{
    if (g_flag[p] == -1) g_flag[p] = flag;
    if (g_flag[p] != flag) return false;
    int i;
    for (i = 0; i < g_vec[p].size(); i++)
    {
        if (g_flag[g_vec[p][i]] == -1)
        {
            if (!dfs(g_vec[p][i], flag ^ 1)) return false;
        } else if (g_flag[g_vec[p][i]] == flag) return false;
    }
    return true;
}

int main()
{
    int i;
    while (scanf("%d%d", &g_n, &g_m) != EOF)
    {
        init();
        for (i = 0; i < g_m; i++)
        {
            scanf("%d%d", &g_u[i], &g_v[i]);
            g_vec[g_u[i]].push_back(g_v[i]);
            g_vec[g_v[i]].push_back(g_u[i]);
        }
        if (dfs(1, 0))
        {
            printf("YES\n");
            for (i = 0; i < g_m; i++)
            {
                printf("%d", g_flag[g_v[i]]);
            }
            printf("\n");
        }
        else printf("NO\n");
    }
    return 0;
}

Codeforces-1144F-Graph Without Long Directed Paths（深度搜索）

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