UVa 1613：K-Graph Oddity（BFS）

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题目链接：https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=845&page=show_problem&problem=4488

题意：输入一个n(3≤n≤9999)个点m条边(2≤m≤100000)的连通图，n保证为奇数。设k为最小的奇数，使得每个点的度数不超过k，你的任务是把图中的结点涂上颜色1~k，使得相邻结点的颜色不同。多解时输出任意解。输入保证有解。（本段摘自《算法竞赛入门经典（第2版）》）

分析：
对于n为奇数的情况，每个结点的度数最多为n−1，为偶数，则k为n为奇数，对于n这个结点和与之相邻的n−1个结点一定存在一种染色方案，因此直接BFS进行染色即可。

代码：

#include <iostream>#include <fstream>#include <cstring>#include <vector>#include <queue>#include <cmath>#include <algorithm>#include <set>#include <string>using namespace std;const int maxn = 10005;struct Edge{    int from, to, dist;    Edge(int f, int t, int d) : from(f), to(t), dist(d) {}};struct Map{    int n, m, k;    vector< Edge > edges;    vector< int > G[maxn];    int color[maxn];    int v[maxn];    int vc[maxn];    int q[maxn];    void init(int n)    {        this->n = n;        for (int i = 0; i < n; ++i)            G[i].clear();        edges.clear();    }    void AddEdge(int from, int to, int dist)    {        edges.push_back(Edge(from, to, dist));        m = edges.size();        G[from].push_back(m - 1);    }    void find_k()    {        k = 0;        for (int i = 0; i < n; ++i)            k = max(k, (int)G[i].size());        if (!(k & 1))            ++k;        printf("%d\n", k);    }    void BFS()    {        memset(color, -1, sizeof(color));        memset(v, 0, sizeof(v));        int head = 0, tail = 0;        q[tail++] = 0;        v[0] = 1;        while (head != tail)        {            memset(vc, 0, sizeof(vc));            for (int i = 0; i < G[q[head]].size(); ++i)            {                Edge& e = edges[G[q[head]][i]];                if (!v[e.to])                {                    q[tail++] = e.to;                    v[e.to] = 1;                }                else if (color[e.to] != -1)                    vc[color[e.to]] = 1;            }            for (int i = 1; i <= k; ++i)                if (!vc[i])                {                    color[q[head]] = i;                    break;                }            ++head;        }        for (int i = 0; i < n; ++i)            printf("%d\n", color[i]);    }};Map M;int n, m, x, y;bool first;int main(){    while (~scanf("%d%d", &n, &m))    {        if (first)            printf("\n");        else            first = true;        M.init(n);        for (int i = 0; i < m; ++i)        {            scanf("%d%d", &x, &y);            M.AddEdge(x - 1, y - 1, 1);            M.AddEdge(y - 1, x - 1, 1);        }        M.find_k();        M.BFS();    }    return 0;}

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