[最短路dijkstra]，启动！！！

总时间复杂度为 O ( ( n + m ) log ⁡ m ）

P4779 【模板】单源最短路径（标准版）

#include<bits/stdc++.h>
#define ll long long
#define fi first
#define se second
#define pb push_back
#define PII pair<int,int >
#define IOS ios::sync_with_stdio(false),cin.tie(0),cout.tie(0)
using namespace std;
const int N = 1e5+5;
int n,m,s;
vector<PII> v[N];
int dis[N];
bool vis[N];
void dijkstra(int s)
{
	priority_queue<PII,vector<PII>,greater<PII> > q;//
	for(int i=1;i<=n;i++) dis[i] = 1e9;
	q.push({0,s});//
	dis[s] = 0;
	while(q.size())
	{
		auto t = q.top();//
		q.pop();
		int now = t.se;//
		if(vis[now]==1) continue;//
		vis[now] = 1;//
		for(auto tt:v[now])
		{
			int spot = tt.fi,w = tt.se;
			if(dis[spot]>dis[now]+w)
			{
				dis[spot] = dis[now]+w;
				q.push({dis[spot],spot});//
			}
		}
	}
}
int main()
{
	IOS;
	cin>>n>>m>>s;
	while(m--)
	{
		int a,b,w;
		cin>>a>>b>>w;
		v[a].pb({b,w});
	} 
	dijkstra(s);
	for(int i=1;i<=n;i++) cout<<dis[i]<<' ';
	return 0;
}

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P3905 道路重建

#include<bits/stdc++.h>
#define ll long long
#define fi first
#define se second
#define pb push_back
#define PII pair<int,int >
#define IOS ios::sync_with_stdio(false),cin.tie(0),cout.tie(0)
using namespace std;
const int N = 1e6+5;
int n,m,A,B;
int va[10005][10005];
vector<PII> v[N];
int dis[N];
bool vis[N];
void dijkstra(int s)
{
	priority_queue<PII,vector<PII>,greater<PII> > q;
	for(int i=1;i<=n;i++) dis[i] = 1e9;
	dis[s] = 0;
	q.push({0,s});
	while(q.size())
	{
		auto t = q.top();
		q.pop();
		int now = t.se;
		if(vis[now]==1) continue;
		vis[now] = 1;
		for(auto tt:v[now])
		{
			int spot = tt.fi,w = 0;
			if(va[now][spot]==1) w = tt.se;
			if(dis[spot]>dis[now]+w)
			{
				dis[spot] = dis[now]+w;
				q.push({dis[spot],spot});
			}	
		}
	}
}
int main()
{
	IOS;
	cin>>n>>m;
	while(m--)
	{
		int a,b,w;
		cin>>a>>b>>w;
		v[a].pb({b,w});
		v[b].pb({a,w});
	}	
	int d;
	cin>>d;
	while(d--)
	{
		int a,b;
		cin>>a>>b;
		va[a][b] = 1;
		va[b][a] = 1;	
	}
	cin>>A>>B;
	dijkstra(A);
	cout<<dis[B];
}

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P4554 小明的游戏

#include<bits/stdc++.h>
#define ll long long
#define fi first
#define se second
#define pb push_back
#define PII pair< int,pair<int,int> >
#define IOS ios::sync_with_stdio(false),cin.tie(0),cout.tie(0)
using namespace std;
const int N = 1e4+5;
int n,m,s,stx,sty,edx,edy;
int dis[N][N];
bool vis[N][N];
char va[N][N];
int dx[4] ={0,0,1,-1};
int dy[4] ={1,-1,0,0};
void distra()
{
	priority_queue<PII,vector<PII>,greater<PII> > q;//
	for(int i=1;i<=n;i++)
	{
		for(int j=1;j<=m;j++)
		{
			dis[i][j] = 1e9;
			vis[i][j] = 0;
		}
	}
	q.push({0,{stx,sty}});//
	dis[stx][sty] = 0;
	while(q.size())
	{
		auto t = q.top();//
		q.pop();
		auto now = t.se;//
		int x = now.fi,y = now.se;
		if(vis[x][y]==1) continue;//
		vis[x][y] = 1;//
		for(int i=0;i<=3;i++)
		{
			int xx = x+dx[i],yy = y+dy[i];
			if(xx>=1&&xx<=n&&yy>=1&&yy<=m)
			{
				int w = 0;
				if(va[x][y]!=va[xx][yy]) w = 1;
				if(dis[xx][yy]>dis[x][y]+w)
				{
					dis[xx][yy] = dis[x][y]+w;
					q.push({dis[xx][yy],{xx,yy}});//
				}
			}
		}
	}
}
int main()
{
	IOS;
	while(1)    
	{
		cin>>n>>m;
		if(n==0&&m==0) break;
		for(int i=1;i<=n;i++)
		{
			for(int j=1;j<=m;j++)
			{
				cin>>va[i][j];
			}
		}
		cin>>stx>>sty>>edx>>edy;
		stx += 1;sty += 1;edx += 1;edy += 1;
		distra();
		cout<<dis[edx][edy]<<"\n";
	}
}

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