[HIHO1176]欧拉路·一（欧拉图判定）

最新推荐文章于 2019-07-18 14:11:00 发布

转载最新推荐文章于 2019-07-18 14:11:00 发布 · 151 阅读

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原文链接：http://www.cnblogs.com/kirai/p/5580304.html

本文解析了一道图论竞赛题目，介绍了如何判断图的连通性和是否存在0个或2个度为奇数的节点，通过并查集实现节点连接状态的判断。

题目链接：http://hihocoder.com/problemset/problem/1176

思路：先判是否连通，再判是否有0个或2个度为奇数的点。

  1 /*
  2 ━━━━━┒ギリギリ♂ eye！
  3 ┓┏┓┏┓┃キリキリ♂ mind！
  4 ┛┗┛┗┛┃＼○／
  5 ┓┏┓┏┓┃ /
  6 ┛┗┛┗┛┃ノ)
  7 ┓┏┓┏┓┃
  8 ┛┗┛┗┛┃
  9 ┓┏┓┏┓┃
 10 ┛┗┛┗┛┃
 11 ┓┏┓┏┓┃
 12 ┛┗┛┗┛┃
 13 ┓┏┓┏┓┃
 14 ┃┃┃┃┃┃
 15 ┻┻┻┻┻┻
 16 */
 17 #include <algorithm>
 18 #include <iostream>
 19 #include <iomanip>
 20 #include <cstring>
 21 #include <climits>
 22 #include <complex>
 23 #include <fstream>
 24 #include <cassert>
 25 #include <cstdio>
 26 #include <bitset>
 27 #include <vector>
 28 #include <deque>
 29 #include <queue>
 30 #include <stack>
 31 #include <ctime>
 32 #include <set>
 33 #include <map>
 34 #include <cmath>
 35 using namespace std;
 36 #define fr first
 37 #define sc second
 38 #define cl clear
 39 #define BUG puts("here!!!")
 40 #define W(a) while(a--)
 41 #define pb(a) push_back(a)
 42 #define Rint(a) scanf("%d", &a)
 43 #define Rll(a) scanf("%lld", &a)
 44 #define Rs(a) scanf("%s", a)
 45 #define Cin(a) cin >> a
 46 #define FRead() freopen("in", "r", stdin)
 47 #define FWrite() freopen("out", "w", stdout)
 48 #define Rep(i, len) for(int i = 0; i < (len); i++)
 49 #define For(i, a, len) for(int i = (a); i < (len); i++)
 50 #define Cls(a) memset((a), 0, sizeof(a))
 51 #define Clr(a, x) memset((a), (x), sizeof(a))
 52 #define Full(a) memset((a), 0x7f7f7f, sizeof(a))
 53 #define lrt rt << 1
 54 #define rrt rt << 1 | 1
 55 #define pi 3.14159265359
 56 #define RT return
 57 #define lowbit(x) x & (-x)
 58 #define onenum(x) __builtin_popcount(x)
 59 typedef long long LL;
 60 typedef long double LD;
 61 typedef unsigned long long ULL;
 62 typedef pair<int, int> pii;
 63 typedef pair<string, int> psi;
 64 typedef pair<LL, LL> pll;
 65 typedef map<string, int> msi;
 66 typedef vector<int> vi;
 67 typedef vector<LL> vl;
 68 typedef vector<vl> vvl;
 69 typedef vector<bool> vb;
 70 
 71 const int maxn = 10010;
 72 int n, m;
 73 int d[maxn];
 74 int pre[maxn];
 75 
 76 int find(int x) { return x == pre[x] ? x : pre[x] = find(pre[x]); }
 77 void unite(int x, int y) { x = find(x); y = find(y); if(x != y) pre[x] = y; }
 78 
 79 int main() {
 80     // FRead();
 81     int u, v;
 82     while(~Rint(n) && ~Rint(m)) {
 83         Cls(d); For(i, 1, n+5) pre[i] = i;
 84         Rep(i, m) {
 85             Rint(u); Rint(v);
 86             unite(u, v);
 87             d[u]++; d[v]++;
 88         }
 89         bool exflag = 0;
 90         int cnt = 0;
 91         int fa = find(1);
 92         For(i, 1, n+1) {
 93             if(fa != find(i)) exflag = 1;
 94             if(d[i] & 1) cnt++;
 95         }
 96         if(!(cnt == 2 || cnt == 0)) exflag = 1;
 97         exflag ? printf("Part\n") : printf("Full\n");
 98     }
 99     RT 0;
100 }