CodeForces 589H Tourist Guide（树形DP）

题目链接：http://codeforces.com/problemset/problem/589/H

题意：给出一张无向图，图上有些点是被标记的，现在要找出尽量多的路径满足：

1.路径的起点和终点都是被标记过的点

2.每个被标记的点最多只能作为某一路径的端点

3.任意两条路径不能有公共边

思路：考虑可以把环切开当成树来做，那么对于子树，如果该子树内有偶数个标记点，那么就可以两两匹配成路径，如果是奇数个点，那就将多出的那个点与其他子树多出来的点相匹配

#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>
#include <string>

#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 = 100010;

struct UF
{
int fa[maxn];

void init(int n)
{
for (int i = 0; i <= n; i++)
fa[i] = i;
}

int Find(int x)
{
if (fa[x] == x) return x;
return fa[x] = Find(fa[x]);
}
} uf;

int deep[maxn], fa[maxn], road[maxn];
int head[maxn], tot;
bool flag[maxn], vis[maxn];
int ans;

struct Edge
{
int to, next;
} e[maxn << 1];

void init()
{
tot = 0;
memset(head, -1, sizeof(head));
}

void addedge(int u, int v)
{
e[tot].to = v;
e[tot].next = head[u];
head[u] = tot++;
}

int dfs(int u, int pre)
{
vis[u] = true;
deep[u] = deep[pre] + 1;
fa[u] = pre;

int now = -1, nxt = -1;
int sz = 0;
for (int i = head[u]; ~i; i = e[i].next)
{
int v = e[i].to;
if (v == pre || vis[v]) continue;

// printf("***********%d %d %d\n", u, v, pre);
sz++;
nxt = dfs(v, u);
if (nxt == -1) continue;
if (now == -1) now = nxt;
else
{
road[now] = nxt;
road[nxt] = now;

//printf("%d %d\n", now, nxt);
now = -1;
ans++;
}
}

if (flag[u])
{
if (now == -1) now = u;
else
{
road[now] = u;
road[u] = now;

//printf("%d %d\n", now, nxt);
now = -1;
ans++;
}
}

return now;
}

void Init(int n)
{
ans = 0;
init();
uf.init(n);
memset(flag, false, sizeof(flag));
memset(vis, false, sizeof(vis));
memset(road, -1, sizeof(road));
}

int main()
{
int n, m, k;
while (~scanf("%d%d%d", &n, &m, &k))
{
Init(n);
for (int i = 0; i < m; i++)
{
int u, v;
scanf("%d%d", &u, &v);

int fu = uf.Find(u);
int fv = uf.Find(v);
if (fu != fv)
{
uf.fa[fu] = fv;
addedge(u, v);
addedge(v, u);
}
}

for (int i = 1; i <= k; i++)
{
int x;
scanf("%d", &x);
flag[x] = true;
}

for (int i = 1; i <= n; i++) if (!vis[i]) dfs(i, -1);

cout << ans << endl;
for (int i = 1; i <= n; i++)
{
if (road[i] > i)
{
int x = i, y = road[i];

//printf("********** %d %d\n", x, y);
if (deep[x] > deep[y]) swap(x, y);

vector <int> vx, vy;
while (deep[y] > deep[x])
{
vy.push_back(y);
y = fa[y];
}

while (x != y)
{
vx.push_back(x), vy.push_back(y);
x = fa[x], y = fa[y];
}

int sx = vx.size(), sy = vy.size();
printf("%d", sx + sy);
for (int j = 0; j < sx; j++)
printf(" %d", vx[j]);
printf(" %d", y);
for (int j = sy - 1; j >= 0; j--)
printf(" %d", vy[j]);
printf("\n");
}
}
}
return 0;
}