Dijkstra的堆优化

在寻找未访问过的最小的 d[u] 时， 未优化的dijkstra算法的寻找方法是遍历d数组， 而采用堆优化的dijkstra算法是创建一个优先队列， 每次取队首元素，即所要寻找的d[u]， 时间复杂度上比起未优化的要强太多。

#include <iostream>
#include <cstring>
#include <queue>
#include <algorithm>
#include <cstdio>
using namespace std;

const int maxn = 1e6 + 10;
const int inf = 1e9 + 7;
const int mod = 1e5 + 3;
int head[maxn], d[maxn];
bool vis[maxn];
int num[maxn];
int n, m, cnt;
struct node{
	int v, nex, len;
}edge[maxn * 2];

struct Node{
	int id, dis;
	friend bool operator < (Node x, Node y) {
		return x.dis > y.dis;
	}
	Node(int _id = 0, int _dis = 0) {
		id = _id, dis = _dis;
	}
};

void addedge(int u, int v, int len)
{
	edge[cnt].v = v;
	edge[cnt].nex = head[u];
	edge[cnt].len = len;
	head[u] = cnt++;
}

void init()
{
	memset(head, -1, sizeof(head));
}

int main()
{
	ios::sync_with_stdio(false);
	init();
	int s, t;
	cin >> n >> m;
	s = 1;
	int x, y, z;
	for(int i = 1; i <= m; i++) {
		cin >> x >> y;
		addedge(x, y, 1);
		addedge(y, x, 1);
	}
	fill(d, d + maxn, inf);
	d[s] = 0;
	priority_queue<Node>que;
	que.push(Node(s, 0));
	num[s] = 1;
	while(!que.empty()) {
		Node cur = que.top();
		que.pop();
		int u = cur.id;
		if(vis[u])
			continue;
		vis[u] = true;
		for(int i = head[u]; i != -1; i = edge[i].nex) {
			int v = edge[i].v;
			if(vis[v] == false && d[u] + edge[i].len < d[v]) {
				d[v] = d[u] + edge[i].len;
				que.push(Node(v, d[v]));
				num[v] = num[u];
				num[v] %= mod;
			}
			else if(vis[v] == false && d[u] + edge[i].len == d[v])
				num[v] += num[u], num[v] %= mod;
		}
	}
	for(int i = 1; i <= n; i++)
		cout << num[i] << endl;
	return 0;
}