传送门
文章目录
- 题意:
- 思路:
题意:
给定一棵树,再给定若干两点最短路之间边权的最小值,让你给树的边权赋值,使得满足给定的条件,如果不存在输出−1-1−1。
思路:
观察一个性质,加入经过这条边的路径的最小边权为w1,w2,..,wxw_1,w_2,..,w_xw1,w2,..,wx,那么当前这个边的边权wnow≥max(w1,w2,...,wx)w_{now}\ge max(w_1,w_2,...,w_x)wnow≥max(w1,w2,...,wx)。所以我们先按照边权从小到大排序,让后每次都直接将(a,b)(a,b)(a,b)之间的边都赋值为wiw_iwi,最后判断一下是否合法即可。
nnn很小,暴力可过,这里用的lcalcalca来暴力的,个人感觉比较方便。
// Problem: F. Berland Beauty
// Contest: Codeforces - Codeforces Round #617 (Div. 3)
// URL: https://codeforces.com/contest/1296/problem/F
// Memory Limit: 256 MB
// Time Limit: 3000 ms
//
// Powered by CP Editor (https://cpeditor.org)//#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native")
//#pragma GCC optimize(2)
#include<cstdio>
#include<iostream>
#include<string>
#include<cstring>
#include<map>
#include<cmath>
#include<cctype>
#include<vector>
#include<set>
#include<queue>
#include<algorithm>
#include<sstream>
#include<ctime>
#include<cstdlib>
#define X first
#define Y second
#define L (u<<1)
#define R (u<<1|1)
#define pb push_back
#define mk make_pair
#define Mid (tr[u].l+tr[u].r>>1)
#define Len(u) (tr[u].r-tr[u].l+1)
#define random(a,b) ((a)+rand()%((b)-(a)+1))
#define db puts("---")
using namespace std;//void rd_cre() { freopen("d://dp//data.txt","w",stdout); srand(time(NULL)); }
//void rd_ac() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//AC.txt","w",stdout); }
//void rd_wa() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//WA.txt","w",stdout); }typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;const int N=5010,M=N*2,mod=1e9+7,INF=0x3f3f3f3f;
const double eps=1e-6;int n,m;
PII p[N];
int e[M],ne[M],w[M],h[N],idx;
int depth[N],fa[N][20];
int g[N][N],flag;
struct Node
{int a,b,w;bool operator < (const Node &W) const {return w<W.w;}
}q[N];void add(int a,int b)
{e[idx]=b,ne[idx]=h[a],h[a]=idx++;
}void dfs_dep(int u,int f)
{depth[u]=depth[f]+1;fa[u][0]=f;for(int i=1;i<=16;i++) fa[u][i]=fa[fa[u][i-1]][i-1];for(int i=h[u];~i;i=ne[i]){int j=e[i];if(j==f) continue;dfs_dep(j,u);}
}int lca(int a,int b)
{if(depth[a]<depth[b]) swap(a,b);for(int i=16;i>=0;i--)if(depth[fa[a][i]]>=depth[b])a=fa[a][i];if(a==b) return a;for(int i=16;i>=0;i--)if(fa[a][i]!=fa[b][i])a=fa[a][i],b=fa[b][i];return fa[a][0];
}bool check()
{for(int i=1;i<=m;i++){int a=q[i].a,b=q[i].b,c=q[i].w;int f=lca(a,b);int mi=INF;while(a!=f){if(g[a][fa[a][0]]) mi=min(mi,g[a][fa[a][0]]);a=fa[a][0];}while(b!=f){if(g[b][fa[b][0]]) mi=min(mi,g[b][fa[b][0]]);b=fa[b][0];}if(mi!=c) return false;}return true;
}int main()
{
// ios::sync_with_stdio(false);
// cin.tie(0);memset(h,-1,sizeof(h));scanf("%d",&n);for(int i=1;i<=n-1;i++) {int a,b; scanf("%d%d",&a,&b);add(a,b); add(b,a);p[i]={a,b};}dfs_dep(1,0);scanf("%d",&m);for(int i=1;i<=m;i++){int a,b,c; scanf("%d%d%d",&a,&b,&c);q[i]={a,b,c};}sort(q+1,q+1+m);for(int i=1;i<=m;i++){int a=q[i].a,b=q[i].b,c=q[i].w;int f=lca(a,b);while(a!=f){g[a][fa[a][0]]=c;g[fa[a][0]][a]=c;a=fa[a][0];}while(b!=f){g[b][fa[b][0]]=c;g[fa[b][0]][b]=c;b=fa[b][0];}}if(check()) for(int i=1;i<=n-1;i++) printf("%d ",g[p[i].X][p[i].Y]==0? 1:g[p[i].X][p[i].Y]);else puts("-1");return 0;
}
/**/