hdu 5379 Mahjong tree 树形DP入门

Posted 2020-07-03 ZhangMengzhi

Description Little sun is an artist. Today he is playing mahjong alone. He suddenly feels that the tree in the yard doesn‘t look good. So he wants to decorate the tree.（The tree has n vertexs, indexed from 1 to n.） Thought for a long time, finally he decides to use the mahjong to decorate the tree. His mahjong is strange because all of the mahjong tiles had a distinct index.（Little sun has only n mahjong tiles, and the mahjong tiles indexed from 1 to n.） He put the mahjong tiles on the vertexs of the tree. As is known to all, little sun is an artist. So he want to decorate the tree as beautiful as possible. His decoration rules are as follows: (1)Place exact one mahjong tile on each vertex. (2)The mahjong tiles‘ index must be continues which are placed on the son vertexs of a vertex. (3)The mahjong tiles‘ index must be continues which are placed on the vertexs of any subtrees. Now he want to know that he can obtain how many different beautiful mahjong tree using these rules, because of the answer can be very large, you need output the answer modulo 1e9 + 7. Input The first line of the input is a single integer T, indicates the number of test cases. For each test case, the first line contains an integers n. (1 <= n <= 100000) And the next n - 1 lines, each line contains two integers ui and vi, which describes an edge of the tree, and vertex 1 is the root of the tree. Output For each test case, output one line. The output format is "Case #x: ans"(without quotes), x is the case number, starting from 1. Sample Input 2 9 2 1 3 1 4 3 5 3 6 2 7 4 8 7 9 3 8 2 1 3 1 4 3 5 1 6 4 7 5 8 4 Sample Output Case #1: 32 Case #2: 16

 

题目大意：有一颗n个点的树，在这n个点中填上1~n的数，求满足下列条件的最多填法数量

1、任意节点的所有儿子节点都应填上连续的数。

2、任意子树里面的所有结点都应填上连续的数。

 

思路：定义dp[u]表示以u为根的子树填上连续的数的填法数量。

对于当前节点u，对于它的儿子节点进行分类讨论：

1、u的儿子节点中如果有超过两个节点不是叶子节点，那么dp[u]=0

2、u只有一个儿子节点v，dp[u] = dp[v]*2;

3、u有两个儿子节点v1,v2，且这两个儿子节点都不是叶子节点，dp[u] = dp[v1]*dp[v2]

……大致思路就是这样，剩下的分类情况略去。

#include <vector>
#include<cstdio>
#include<cstring>
using namespace std;
const int maxn = 100005;
const int mod = 1e9 + 7;
int n;
long long dp[maxn];
bool vis[maxn];
vector<int> adj[maxn];
long long solve(int u)
{
    if(dp[u]!=-1) return dp[u];
    vis[u] = true;
    int x=0,v1=-1,v2=-1;
    dp[u] = 1;
    int len=adj[u].size();
    int son=0;
    for(int i=0; i<len; i++)
    {
        int v = adj[u][i];
        if(vis[v]) continue;
        solve(v);
        dp[u]*=dp[v];
        dp[u]%=mod;
        if(dp[v]==1) x++;
        son++;
    }
    if(son-x>2||dp[u]==0) return dp[u]=0;
    else if(son==1)
    {
        dp[u]*=2;
        return dp[u]%=mod;
    }
    if(x)
    {
        if(son==x||son-x==1) dp[u]*=2;
        dp[u]%=mod;
        while(x)
        {
            dp[u]*=x;
            dp[u]%=mod;
            x--;
        }
    }
    return dp[u]%=mod;
}

int main()
{
    int T;
    scanf("%d",&T);
    int kase=1;
    while(T--)
    {
        scanf("%d",&n);
        for (int i=1; i<n; i++)
        {
            int x,y;
            scanf("%d%d",&x,&y);
            adj[x].push_back(y);
            adj[y].push_back(x);
        }

        int root = 1;
        memset(dp,-1,sizeof(dp));
        memset(vis,0,sizeof(vis));
        printf("Case #%d: %I64d\n",kase++,solve(root));
        for(int i=1; i<=n; i++) adj[i].clear();
        //for(int i=1;i<=n;i++) printf("%d %d\n",i,dp[i]);
    }
    return 0;
}