迪傑斯特拉算法模板/三種圖的存儲模板 Single Source Shortest Path II Aizu - ALDS1_12_C

題目：

Single Source Shortest Path II

For a given weighted graph G=(V,E)

, find the shortest path from a source to each vertex. For each vertex u, print the total weight of edges on the shortest path from vertex 0 to u

.

Input

In the first line, an integer n

denoting the number of vertices in G is given. In the following n lines, adjacency lists for each vertex u

are respectively given in the following format:

u

k v1 c1 v2 c2 ... vk ck

Vertices in G

are named with IDs 0,1,...,n−1. u is ID of the target vertex and k denotes its degree. vi(i=1,2,...k) denote IDs of vertices adjacent to u and ci denotes the weight of a directed edge connecting u and vi (from u to vi

).

Output

For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.

Constraints

• 1≤n≤10,000

0≤ci≤100,000
|E|<500,000
All vertices are reachable from vertex 0

• 
  

Sample Input 1

5
0 3 2 3 3 1 1 2
1 2 0 2 3 4
2 3 0 3 3 1 4 1
3 4 2 1 0 1 1 4 4 3
4 2 2 1 3 3

Sample Output 1

0 0
1 2
2 2
3 1
4 3

題意：有一個有向帶權圖。

第一行輸入n表示圖的頂點數。

接下來n行輸入圖的鄰接表。

每行第一個數字爲頂點序號u（頂點序號範圍【0，n-1】），第二個數字爲與這個點相鄰接的頂點數k。之後輸入k組數據，每組數據由點to和權值weight組成，表示由u到這個點的邊權值爲weight。

鄰接矩陣存儲圖：

#include<bits/stdc++.h>

typedef long long ll;

using namespace std;

int n;
int G[10010][10010];
int minlen[10010];
bool vis[10010];


void dijkstra(int p){
	memset(minlen,-1,sizeof(minlen));
	memset(vis,0,sizeof(0));
	
	minlen[p] = 0;
	
	while (1){
		int minp = -1;
		int minn = 1<<30;
	
		for(int i = 0 ; i<n ; i++){
			if(!vis[i] && minlen[i]!=-1 && minn>minlen[i]){
				minp = i;
				minn = minlen[i];
			}
		}
		if(minp == -1) break;
		
		vis[minp] = 1;
		for(int j = 0 ; j<n ; j++){
			if(!vis[j] && G[minp][j]!=1<<30){
				if(minlen[j] == -1){
					minlen[j] = minlen[minp]+G[minp][j];
				}
				else if( minlen[j] > minlen[minp]+G[minp][j]){
					minlen[j] = minlen[minp]+G[minp][j];
				}
			}
		}
	}
}

int main(){
	ios::sync_with_stdio(false);
	cin>>n;
	for(int i = 0 ; i<n ; i++)
		for(int j = 0 ; j<n ; j++)
			G[i][j] = 1<<30;
	
	for(int t = 0 ; t<n ; t++){
		int u,k;
		cin>>u>>k;
		for(int i = 0 ; i<k ; i++){
			int to,weight;
			cin>>to>>weight;
			G[u][to] = weight;
		}
	}

	dijkstra(0);	
	for(int i = 0 ; i<n ; i++){
		cout<<i<<" "<<minlen[i]<<endl;
	}
	return 0;
}

鄰接表存儲圖：

#include<bits/stdc++.h>

typedef long long ll;

using namespace std;

int minlen[10010];
bool vis[10010];

struct node{
	int to;
	int weight;
	node(int to,int weight){
		this->to = to;
		this->weight= weight;
	}
};
vector<node> G[10010];

struct point{
	int p;
	int len;
	point(int p,int len){
		this->p = p;
		this->len = len;
	}
	friend bool operator< (point t1 , point t2){
		if(t1.len == t2.len)
			return t1.p > t2.p;
		return t1.len > t2.len; 
	}
};

void dijkstra(int p){
	memset(minlen,-1,sizeof(minlen));
	memset(vis,0,sizeof(0));
	
	priority_queue<point> q;
	q.push(point(p,0));
	minlen[p] = 0;
	
	while (!q.empty()){
		point temp = q.top();	q.pop();
		int now = temp.p;
		vis[now] = 1;
		
		if(minlen[now]!=-1 && minlen[now] < temp.len)
			continue;
		
		for(int i = 0 ; i<G[now].size() ; i++){
			int to = G[now][i].to;
			int len = G[now][i].weight;
			if(!vis[to]){
				if(minlen[to] == -1){
					minlen[to] = minlen[now] + len;
					q.push(point(to,minlen[to]));
				}
				else if(minlen[to] > minlen[now]+len){
					minlen[to] = minlen[now]+len;
					q.push(point(to,minlen[to]));
				}
			}
		}
	}
}

int main(){
	ios::sync_with_stdio(false);
	int n;
	cin>>n;
	
	for(int t = 0 ; t<n ; t++){
		int u,k;
		cin>>u>>k;
		for(int i = 0 ; i<k ; i++){
			int to,weight;
			cin>>to>>weight;
			G[u].push_back(node(to,weight));
		}
	}
	dijkstra(0);	
	for(int i = 0 ; i<n ; i++){
		cout<<i<<" "<<minlen[i]<<endl;
	}
	return 0;
}

鏈式前向星存儲圖

#include<bits/stdc++.h>

typedef long long ll;

using namespace std;

int n;
int head[10010];
struct{
	int to;
	int w;
	int next;
}mapp[500010];

int minlen[10010];
bool vis[10010];

struct node{
	int n;
	int len;
	
	node(const int n,const int len){
		this->n = n;
		this->len = len;
	}
	
	friend bool operator < (node f1, node f2){
		if(f1.len != f2.len)
			return f1.len > f2.len;
        return f1.n > f2.n; 
    }
};


void dijkstra(int p){
	memset(minlen,-1,sizeof(minlen));
	memset(vis,0,sizeof(0));
	
	priority_queue<node> q;
	
	minlen[p] = 0;
	vis[p] = 1;
	q.push(node(p,0));
	
	while (!q.empty()){
		node temp = q.top() ; q.pop();
		vis[temp.n] = 1;
		
		if( minlen[temp.n]!=-1 && minlen[temp.n]<temp.len)
			continue;
		
		int now = temp.n;
		
		for(int i = head[now] ; i!=0 ; i = mapp[i].next){
			int nxt = mapp[i].to;
			if(!vis[nxt]){
				if(minlen[nxt] == -1){
					minlen[nxt] = minlen[now]+mapp[i].w;
					q.push(node(nxt,minlen[nxt]));
				}
				else if(minlen[nxt] > minlen[now]+mapp[i].w){
					minlen[nxt] = minlen[now]+mapp[i].w;
					q.push(node(nxt,minlen[nxt]));
				}
			}
		}
	}
	
}

int main(){
	ios::sync_with_stdio(false);
	cin>>n;
	
	memset(head,0,sizeof(head));
	memset(mapp,0,sizeof(mapp));
	
	int num = 1;
	for(int t = 0 ; t<n ; t++){
		int u,k;
		cin>>u>>k;
		for(int i = 0 ; i<k ; i++){
			int to,weight;
			cin>>to>>weight;
			
			mapp[num].to = to;
			mapp[num].w = weight;
			mapp[num].next = head[u];
			head[u] = num;
			num++;
		}
	}
	
	dijkstra(0);	
	for(int i = 0 ; i<n ; i++){
		cout<<i<<" "<<minlen[i]<<endl;
	}
	return 0;
}