UVA 10004 Bicoloring

Source:

https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=12&page=show_problem&problem=945

Description

原题：
In 1976 the “Four Color Map Theorem” was proven with the assistance of a computer. This theorem states that every map can be colored using only four colors, in such a way that no region is colored using the same color as a neighbor region.
Here you are asked to solve a simpler similar problem. You have to decide whether a given arbitrary connected graph can be bicolored. That is, if one can assign colors (from a palette of two) to the nodes in such a way that no two adjacent nodes have the same color. To simplify the problem you can assume:
no node will have an edge to itself.
the graph is nondirected. That is, if a node a is said to be connected to a node b, then you must assume that b is connected to a.
the graph will be strongly connected. That is, there will be at least one path from any node to any other node.

翻译：
1976年“四色定理”在计算机的帮助下被证明。 这个定理宣告任何一个地图都可以只用四种颜色来填充， 并且没有相邻区域的颜色是相同的。
现在让你解决一个更加简单的问题。 你必须决定给定的任意相连的图能不能够用两种颜色填充。 就是说，如果给其中一个分配一种颜色， 要让所有直接相连的两个节点不能是相同的颜色。 为了让问题更简单，你可以假设：
1. 没有自环。
2. 是无向图。
3. 图是强连通的。就是说至少有一条路径可走向所有节点。

Sample Input

The input consists of several test cases. Each test case starts with a line containing the number n (1

3
3
0 1
1 2
2 0
3
2
0 1
1 2
9
8
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0

Sample Output

You have to decide whether the input graph can be bicolored or not, and print it as shown below.

NOT BICOLORABLE.
BICOLORABLE.
BICOLORABLE.

Caution:

题目大意其实就是说能不能只用两种颜色染遍图中的所有顶点。

我们从任意一个顶点出发，用dfs染过，分别用1和-1代表不同的颜色，不出现冲突即可。

一直WA，错在忘记每次循环应该把全局数组memset，导致同一问题两次输入的结果是不一样的……

然而我发现在下面这个random case上，debug里的结果应该是可染的，然而所有ac的代码包括我的都在这个案例上不可染，我很怀疑是不是他case output的答案给错了

15
58
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 9
0 10
0 14
1 2
1 4
1 6
1 8
1 9
1 10
1 11
1 12
1 14
2 3
2 4
2 5
2 8
2 9
2 10
2 12
3 5
3 7
3 8
3 11
3 12
4 8
4 9
4 10
4 13
5 6
5 7
5 11
5 13
6 7
6 9
6 10
6 11
6 12
6 13
6 14
7 8
7 11
7 13
7 14
8 10
8 13
8 14
9 13
10 11
12 13
12 14
13 14

示例代码：

#include
#include
#include
#include
#include 

using namespace std;

int m, n, u, v;
vector<int> g[10001];
int color[10001];

void init()
{
    memset(g, 0, sizeof(g));
    memset(color, 0, sizeof(color));
    for (int i = 0; i < n; ++i)
    {
        cin >> u >> v;
        g[u].push_back(v);
    }
}

bool dfs(int s,int c)
{
    color[s] = c;
    for (int i = 0; i < g[s].size(); ++i)
    {
        if (color[g[s][i]] == c)
            return false;
        if (color[g[s][i]] == 0 && !dfs(g[s][i], -c))
            return false;
    }
    return true;
}

void work()
{
    for (int i = 0; i < m; ++i)
    {
        if (color[i] == 0)
            if (!dfs(i, 1))
            {
                cout << "NOT BICOLORABLE." << endl;
                return;
            }
    }
    cout << "BICOLORABLE." << endl;
}

int main()
{
    while (cin >> m && m)
    {
        cin >> n;
        init();
        work();
    }
    return 0;
}