Invitation Cards HDU - 1535 基础最短路

本文介绍了一种针对特殊公交网络的最短路径算法实现,该网络具备单向线路及中央检查站等特性。通过双向建立边的方式,利用SPFA算法分别计算从中央检查站到各个站点以及从各个站点返回中央检查站的最短路径,以此来帮助Antique Comedians of Malidinesia团体最小化每日员工通勤成本。

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In the age of television, not many people attend theater performances. Antique Comedians of Malidinesia are aware of this fact. They want to propagate theater and, most of all, Antique Comedies. They have printed invitation cards with all the necessary information and with the programme. A lot of students were hired to distribute these invitations among the people. Each student volunteer has assigned exactly one bus stop and he or she stays there the whole day and gives invitation to people travelling by bus. A special course was taken where students learned how to influence people and what is the difference between influencing and robbery. 
The transport system is very special: all lines are unidirectional and connect exactly two stops. Buses leave the originating stop with passangers each half an hour. After reaching the destination stop they return empty to the originating stop, where they wait until the next full half an hour, e.g. X:00 or X:30, where 'X' denotes the hour. The fee for transport between two stops is given by special tables and is payable on the spot. The lines are planned in such a way, that each round trip (i.e. a journey starting and finishing at the same stop) passes through a Central Checkpoint Stop (CCS) where each passenger has to pass a thorough check including body scan. 

All the ACM student members leave the CCS each morning. Each volunteer is to move to one predetermined stop to invite passengers. There are as many volunteers as stops. At the end of the day, all students travel back to CCS. You are to write a computer program that helps ACM to minimize the amount of money to pay every day for the transport of their employees. 

Input
The input consists of N cases. The first line of the input contains only positive integer N. Then follow the cases. Each case begins with a line containing exactly two integers P and Q, 1 <= P,Q <= 1000000. P is the number of stops including CCS and Q the number of bus lines. Then there are Q lines, each describing one bus line. Each of the lines contains exactly three numbers - the originating stop, the destination stop and the price. The CCS is designated by number 1. Prices are positive integers the sum of which is smaller than 1000000000. You can also assume it is always possible to get from any stop to any other stop. 
Output
For each case, print one line containing the minimum amount of money to be paid each day by ACM for the travel costs of its volunteers. 
Sample Input
2
2 2
1 2 13
2 1 33
4 6
1 2 10
2 1 60
1 3 20
3 4 10
2 4 5
4 1 50
Sample Output
46
210


题意: 求1号点到其它点的最短距离 + 其他点到1号点的最短距离

思路: 1号点到其他点就直接跑一遍最短路。 其他点到一号点, 反过来跑一遍就好了。
双向建边



#include <iostream>
#include <cstring>
#include <queue>
using namespace std;
#define ll long long
#define INF 0x3f3f3f3f
const int maxn = 1e6+5;

struct Node {
	int to, next;
	ll w;
}edge[2][maxn<<1];
int head[2][maxn], cnt;
ll dis[2][maxn];
bool vis[maxn];

void init(int n) {
	cnt = 0;
	memset(dis, INF, sizeof(dis));
	memset(head, -1, sizeof(head));
}

void addEdge(int cur, int from, int to, ll w) {
	edge[cur][cnt].to = to;
	edge[cur][cnt].w = w;
	edge[cur][cnt].next = head[cur][from];
	head[cur][from] = cnt;
}


void spfa(int s, int cur) {
	dis[cur][s] = 0;
	queue<int> q;
	q.push(s);
	vis[s] = 1;
	while (!q.empty()) {
		
		int num = q.front(); q.pop();
		vis[num] = 0;
		for (int i = head[cur][num]; i != -1; i = edge[cur][i].next) {
			Node e = edge[cur][i];
			if (dis[cur][e.to] > dis[cur][num] + e.w) {
				dis[cur][e.to] = dis[cur][num] + e.w;
				if (!vis[e.to]) {
					vis[e.to] = 1;
					q.push(e.to);
				}
			}
		}
	}
}


int main(void) {
	ios::sync_with_stdio(false);
	int t;
	cin >> t;
	while (t--) {
		int P, Q;
		init(P);
		cin >> P >> Q;
		int u, v;
		ll w;
		for (int i = 0; i < Q; i++) {
			cin >> u >> v >> w;
			addEdge(0, u, v, w);
			addEdge(1, v, u, w);
			cnt++;
		}
		spfa(1, 0);
		spfa(1, 1);
		ll ans = 0;
		for (int i = 2; i <= P; i++) {
			ans += dis[0][i] + dis[1][i];
		}
		cout << ans << endl;
	}
	return 0;
}


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