codefores 786B. Legacy(最短路，线段树优化拆点，好题)
題目鏈接
B. Legacy
time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
Rick and his co-workers have made a new radioactive formula and a lot of bad guys are after them. So Rick wants to give his legacy to Morty before bad guys catch them.
There are n planets in their universe numbered from 1 to n. Rick is in planet number s (the earth) and he doesn't know where Morty is. As we all know, Rick owns a portal gun. With this gun he can open one-way portal from a planet he is in to any other planet (including that planet). But there are limits on this gun because he's still using its free trial.
By default he can not open any portal by this gun. There are q plans in the website that sells these guns. Every time you purchase a plan you can only use it once but you can purchase it again if you want to use it more.
Plans on the website have three types:
With a plan of this type you can open a portal from planet v to planet u.
With a plan of this type you can open a portal from planet v to any planet with index in range [l,?r].
With a plan of this type you can open a portal from any planet with index in range [l,?r] to planet v.
Rick doesn't known where Morty is, but Unity is going to inform him and he wants to be prepared for when he finds and start his journey immediately. So for each planet (including earth itself) he wants to know the minimum amount of money he needs to get from earth to that planet.
Input
The first line of input contains three integers n, q and s (1?≤?n,?q?≤?105, 1?≤?s?≤?n) — number of planets, number of plans and index of earth respectively.
The next q lines contain the plans. Each line starts with a number t, type of that plan (1?≤?t?≤?3). If t?=?1 then it is followed by three integers v, u and w where w is the cost of that plan (1?≤?v,?u?≤?n, 1?≤?w?≤?109). Otherwise it is followed by four integers v, l, r and w where w is the cost of that plan (1?≤?v?≤?n, 1?≤?l?≤?r?≤?n, 1?≤?w?≤?109).
Output
In the first and only line of output print n integers separated by spaces. i-th of them should be minimum money to get from earth to i-th planet, or ?-?1 if it's impossible to get to that planet.
Examples
input
3 5 1
2 3 2 3 17
2 3 2 2 16
2 2 2 3 3
3 3 1 1 12
1 3 3 17
output
0 28 12
input
4 3 1
3 4 1 3 12
2 2 3 4 10
1 2 4 16
output
0 -1 -1 12
Note
In the first sample testcase, Rick can purchase 4th plan once and then 2nd plan in order to get to get to planet number 2.
題意：給出 \(n\) 個點，存在 \(q\) 條路徑，起點為 \(s\)，路徑有一下三種：
1.給出 \(u,v,w\) ，表示點 \(u\) 到點 \(v\) 有一條費用為 \(w\) 的邊.
2.給出 \(v,l,r,w\) 表示點 \(v\) 到區間 \([l,r]\) 的點，費用為 \(w\).
3.給出 \(v,l,r,w\) 表示區間 \([l,r]\) 的點到點 \(v\) ，費用為 \(w\).
求起點 \(s\) 到每個點的最小花費。
題解：其實和這一題思路大體一樣，不過，直接對 \([l,r]\) 縮成點連接 \([l,r]\) 的所有點，那么 \(10^5\) 的 \(q\) 可能得連 \(10^{10}\) 的邊，肯定不行，這里用到了一個輔助工具—線段樹，建立兩顆線段樹，一棵是每個結點連出去的出度“大點”，一棵是連向每個點的入度“大點”，對于第一棵，建樹時就
\(add(seg[i*2][ty],seg[i][ty],0);\)
\(add(seg[i*2+1][ty],seg[i][ty],0);\)
然后對于每個類型2,3，找到對應區間 \([l,r]\) 的點進行連接即可。
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<vector>
#include<queue>
#include<stack>
#include<set>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define fi first
#define se second
#define dbg(...) cerr<<"["<<#__VA_ARGS__":"<<(__VA_ARGS__)<<"]"<<endl;
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> PII;
const ll inf=1e17;
const ll mod=1000000007;
const int maxn=1e5+100;
int seg[maxn*4][2];
int tot=0;
vector<PII> g[maxn*9];
void add(int u,int v,int w)
{g[u].pb(make_pair(v,w));
}
void build(int i,int l,int r,int ty)
{seg[i][ty]=++tot;if(l==r){if(!ty) add(seg[i][ty],l,0);else add(l,seg[i][ty],0);return;}int m=(l+r)/2;build(i*2,l,m,ty);build(i*2+1,m+1,r,ty);if(!ty){add(seg[i][ty],seg[i*2][ty],0);add(seg[i][ty],seg[i*2+1][ty],0);}else{add(seg[i*2][ty],seg[i][ty],0);add(seg[i*2+1][ty],seg[i][ty],0);}
}VI V;
void update(int i,int l,int r,int L,int R,int ty)
{if(l==L&&r==R){V.pb(seg[i][ty]);return;}int m=(L+R)/2;if(r<=m) update(i*2,l,r,L,m,ty);else if(l>m) update(i*2+1,l,r,m+1,R,ty);else{update(i*2,l,m,L,m,ty);update(i*2+1,m+1,r,m+1,R,ty);}
}
set<pair<ll,int> > st;
ll d[maxn*10];
void dij(int s)
{rep(i,1,tot+1) d[i]=inf;d[s]=0;st.insert(make_pair(0,s));while(!st.empty()){int u=st.begin()->se;st.erase(st.begin());for(int i=0;i<g[u].size();i++){int v=g[u][i].fi;if(d[v]>d[u]+1ll*g[u][i].se){st.erase(make_pair(d[v],v));d[v]=d[u]+1ll*g[u][i].se;st.insert(make_pair(d[v],v));}}}
}
int main()
{int n,q,s;scanf("%d%d%d",&n,&q,&s);tot=n;build(1,1,n,0);build(1,1,n,1);while(q--){int ty,v,u,w;scanf("%d%d",&ty,&v);int l,r;if(ty==1){scanf("%d%d",&u,&w);add(v,u,w);}else{scanf("%d%d%d",&l,&r,&w);V.clear();update(1,l,r,1,n,ty-2);for(int i=0;i<V.size();i++){if(ty-2)add(V[i],v,w);elseadd(v,V[i],w);}}}dij(s);rep(i,1,n+1){if(d[i]==inf) d[i]=-1;printf("%lld ",d[i]);}puts("");return 0;
}轉載于:https://www.cnblogs.com/tarjan/p/7473525.html
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