ABC-397-E - Path Decomposition of a Tree · znzryb

## 思路讲解

总的来说就是问你这颗树能不能分解成由K个点组成的路径

哈哈，我的理解有问题，其实这个所谓的“路径”是“链”（根据形式化题意）

## AC代码

[https://atcoder.jp/contests/abc397/submissions/64463352](https://atcoder.jp/contests/abc397/submissions/64463352)

```cpp
// Problem: E - Path Decomposition of a Tree
// Contest: AtCoder - OMRON Corporation Programming Contest 2025 (AtCoder Beginner Contest 397)
// URL: https://atcoder.jp/contests/abc397/tasks/abc397_e
// Memory Limit: 1024 MB
// Time Limit: 2000 ms
// by znzryb
// 
// Powered by CP Editor (https://cpeditor.org)

#include <bits/stdc++.h>
#define FOR(i, a, b) for (int i = (a); i <= (b); ++i)
#define ROF(i, a, b) for (int i = (a); i >= (b); --i)
#define all(x) x.begin(),x.end()
#define CLR(i,a) memset(i,a,sizeof(i))
#define fi first
#define se second
#define pb push_back
#define SZ(a) ((int) a.size())

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef __int128 i128;
typedef pair<ll,ll> pll;
typedef array<ll,3> arr;
typedef double DB;
typedef pair<DB,DB> pdd;
typedef pair<ll,bool> plb;
constexpr ll MAXN=static_cast<ll>(2e5)+10,INF=static_cast<ll>(5e18)+3;

ll N,K,T;
vector<ll> g[MAXN];
bool vis[MAXN];
bool Ans=true;
// bool needed[MAXN];

ll dfs(ll x){	// 如果return 0，就说明子树已经自行满足了，其他数就说明还需要K-x个点
	if(!Ans) return 0;
	vis[x]=true;
	// vector<ll> rec;
	ll sum=0;
	ll cnt=0;
	for(int i=0;i<g[x].size();++i){
		ll node=g[x][i];
		if(vis[node]) continue;
		ll lrec=dfs(node);
		if(lrec!=0) ++cnt;
		// rec.pb(lrec);
		sum+=lrec;
	}
	if(sum+1==K && cnt<=2){
		return 0;
	}
	if(sum+1<K && cnt<=1){
		return sum+1;
	}
	Ans=false;
	return 0;
}

inline void solve(){
	cin>>N>>K;
	if(K==1){
		cout<<"Yes\n";
		return;
	}
	FOR(i,1,N*K-1){
		ll u,v;
		cin>>u>>v;
		g[u].pb(v);
		g[v].pb(u);
	}
	Ans=true;
	dfs(1);
	if(Ans) cout<<"Yes\n";
	else cout<<"No\n";
}

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);cout.tie(0);
	// cin>>T;
	// while(T--){
		// solve();
	// }
	solve();
	return 0;
}
/*
AC
https://atcoder.jp/contests/abc397/submissions/64463352
*/
```

## 心路历程（WA，TLE，MLE……）

一个是没有注意到链

还有这个条件是cnt≤1

```cpp
	if(sum+1<K && cnt<=1){
		return sum+1;
	}
```