UVALive 6652 Game of Throne（一般图最大加权匹配）

题目链接：https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=4663

题意：给出一张N个点M条边的无向连通图，需要求出一个总权值最小的边集，使得子图的1~K点度数为奇数，K+1~N度数为偶数，求该权值

思路：比赛时一直没想清楚，对任意一条路径，都有两个奇度点，其余为偶度点，我们只需要关注前K个点，先用Floyd预处理出任意两点最短距离，再让这K个点两两匹配，故而K为奇数时肯定无法完成匹配

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <utility>
#include <cmath>
#include <queue>
#include <set>
#include <map>
#include <climits>
#include <functional>
#include <deque>
#include <ctime>

#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1
#pragma comment(linker, "/STACK:102400000,102400000")

using namespace std;

typedef long long ll;

const int MAXN = 110;
const int INF = 0x3f3f3f3f;

int G[MAXN][MAXN];
int cnt_node;//点的个数
int dis[MAXN];
int match[MAXN];
bool vis[MAXN];
int sta[MAXN], top;

bool dfs(int u)
{
sta[top++] = u;
if (vis[u])return true;
vis[u] = true;
for (int i = 0; i < cnt_node; i++)
if (i != u && i != match[u] && !vis[i])
{
int t = match[i];
if (dis[t] < dis[u] + G[u][i] - G[i][t])
{
dis[t] = dis[u] + G[u][i] - G[i][t];
if (dfs(t))return true;
}
}
top--;
vis[u] = false;
return false;
}

int P[MAXN];

int get_Match(int N)//返回最大匹配权值
{
cnt_node = N;
for (int i = 0; i < cnt_node; i++)P[i] = i;
for (int i = 0; i < cnt_node; i += 2)
{
match[i] = i + 1;
match[i + 1] = i;
}
int cnt = 0;
while (1)
{
memset(dis, 0, sizeof(dis));
memset(vis, false, sizeof(vis));
top = 0;
bool update = false;
for (int i = 0; i < cnt_node; i++)
if (dfs(P[i]))
{
update = true;
int tmp = match[sta[top - 1]];
int j = top - 2;
while (sta[j] != sta[top - 1])
{
match[tmp] = sta[j];
swap(tmp, match[sta[j]]);
j--;
}
match[tmp] = sta[j];
match[sta[j]] = tmp;
break;
}
if (!update)
{
cnt++;
if (cnt >= 3)break;
random_shuffle(P, P + cnt_node);
}
}
int ans = 0;
for (int i = 0; i < cnt_node; i++)
{
int v = match[i];
if (i < v)ans += G[i][v];
}
return ans;
}

int g[MAXN][MAXN];

int main()
{
int t;
scanf("%d", &t);
for (int ca = 1; ca <= t; ca++)
{
printf("Case %d: ", ca);
int n, m, k;
scanf("%d%d%d", &n, &m, &k);

memset(g, INF, sizeof(g));
for (int i = 0; i < n; i++)
g[i][i] = 0;

for (int i = 0; i < m; i++)
{
int u, v, w;
scanf("%d%d%d", &u, &v, &w);
u--, v--;
g[u][v] = g[v][u] = w;
}

if (k % 2 == 1)
{
puts("Impossible");
continue;
}

for (int k = 0; k < n; k++)
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
g[i][j] = min(g[i][j], g[i][k] + g[k][j]);

for (int i = 0; i < k; i++)
for (int j = 0; j < k; j++)
G[i][j] = -g[i][j];

cout << -get_Match(k) << endl;
}
return 0;
}