题目大意:
给定一个(n)的点的图。求(s)到所有点的最短路
边的给定方式有三种:
- (u o v)
- (u o [l,r])
- ([l,r] o v)
设(q)为给定边的次数，有(n,q leq 10^5)
题解
类比于线段树优化网络流建图
写一个线段树优化最短路建图即可。
#include <queue>
#include <vector>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long ll;
inline void read(int &x){
x=0;char ch;bool flag = false;
while(ch=getchar(),ch<'!');if(ch == '-') ch=getchar(),flag = true;
while(x=10*x+ch-'0',ch=getchar(),ch>'!');if(flag) x=-x;
}
#define rg register int
#define rep(i,a,b) for(rg i=(a);i<=(b);++i)
#define per(i,a,b) for(rg i=(a);i>=(b);--i)
const int maxn = 100010;
struct Edge{
int to,dis;
Edge(){}
Edge(const int &a,const int &b){
to = a;dis = b;
}
};
vector<Edge>ve[maxn*10];
inline void add(int u,int v,int d){
ve[u].push_back(Edge(v,d));
}
int T1[maxn<<2],T2[maxn<<2],nodecnt;
void build1(int rt,int l,int r){
T1[rt] = ++ nodecnt;
if(l == r){
add(l,T1[rt],0);
return ;
}
int mid = l+r >> 1;
build1(rt<<1,l,mid);
build1(rt<<1|1,mid+1,r);
add(T1[rt<<1],T1[rt],0);
add(T1[rt<<1|1],T1[rt],0);
}
void build2(int rt,int l,int r){
T2[rt] = ++ nodecnt;
if(l == r){
add(T2[rt],l,0);
return ;
}
int mid = l+r >> 1;
build2(rt<<1,l,mid);
build2(rt<<1|1,mid+1,r);
add(T2[rt],T2[rt<<1],0);
add(T2[rt],T2[rt<<1|1],0);
}
int p,val;
void query1(int rt,int l,int r,int L,int R){
if(L <= l && r <= R){
add(T1[rt],p,val);
return ;
}
int mid = l+r >> 1;
if(L <= mid) query1(rt<<1,l,mid,L,R);
if(R > mid) query1(rt<<1|1,mid+1,r,L,R);
}
void query2(int rt,int l,int r,int L,int R){
if(L <= l && r <= R){
add(p,T2[rt],val);
return ;
}
int mid = l+r >> 1;
if(L <= mid) query2(rt<<1,l,mid,L,R);
if(R > mid) query2(rt<<1|1,mid+1,r,L,R);
}
ll dis[maxn*10];bool inq[maxn*10];
void spfa(int s){
memset(dis,0x3f,sizeof dis);
dis[s] = 0;inq[s] = true;
queue<int>q;q.push(s);
while(!q.empty()){
int u = q.front();q.pop();
for(vector<Edge>::iterator it = ve[u].begin();it != ve[u].end();++ it){
if(dis[it->to] > dis[u] + it->dis){
dis[it->to] = dis[u] + it->dis;
if(!inq[it->to]){
inq[it->to] = true;
q.push(it->to);
}
}
}inq[u] = false;
}
}
int main(){
int n,q,s;read(n);read(q);read(s);
int t,u,v,l,r;
nodecnt = n;
build1(1,1,n);build2(1,1,n);
while(q--){
read(t);
if(t == 1){
read(u);read(v);read(val);
add(u,v,val);
}else if(t == 2){
read(p);read(l);read(r);read(val);
query2(1,1,n,l,r);
}else if(t == 3){
read(p);read(l);read(r);read(val);
query1(1,1,n,l,r);
}
}
spfa(s);
rep(i,1,n){
if(dis[i] != dis[0]) printf("%lld",dis[i]);
else printf("%d",-1);
if(i != n) putchar(' ');
else putchar('
');
}
return 0;
}