dijkstra

dijkstra的大概思路：
基于贪心的思想，且要保证起点一定是最短的
不断地取出未访问过且dis最小的点，用这些点对所有边进行松弛操作。
朴素版 + 邻接矩阵 dijkstra：

#include <bits/stdc++.h>
using namespace std;
int a[3010][3010], d[3010], n, m;
bool v[3010];
void dijkstra (int s) {
	memset(d, 0x3f, sizeof d);
	memset(v, 0, sizeof v);
	d[s] = 0;
	for (int i = 1; i <= n; i++) {
		int x = 0;
	    for (int  j = 1;j <= n; j++) 
			if (!v[j] && (x == 0 || d[j] < d[x])) x = j;
	v[x] = 1;
	for (int y = 1; y <= n; y++)
		d[y] = min(d[y], d[x] + a[x][y]);
	}
}
int main () {
	cin >> n >> m;
	memset(a, 0x3f, sizeof a);
	for (int i = 1; i <= n; i++) a[i][i] = 0;
	for (int i = 1; i <= n; i++) {
		int x, y, z;
		cin >> x >> y >> z;
		a[x][y] = min(a[x][y], z);
	}
	dijkstra(s);
	for (int i = 1, i <= n; i++) cout << d[i] << endl;
	return 0;
}

二根堆优化+链式前向星dijkstra

#include <bits/stdc++.h>
using namespace std;
const int N = 100010, M = 1000010;
int head[N], ver[M], edge[M], ne[M], d[N];
bool v[N];
int n, m, tot;
priority_queue<pair<int, int> >q;
void add (int x, int y, int z) {
	ver[++tot] = y; edge[tot] = z; ne[tot] = head[x]; head[x] = tot;
}
void dijkstra () {
	memset(d, 0x3f, sizeof d);
	memset(v, 0, sizeof v);
	d[1] = 0;
	q.push(make_pair(0, 1));
	while (q.size()) {
		int x = q.top().second; q.pop();
		if (v[x]) continue;
		v[x] = 1;
		for (int i = head[x]; i; i = ne[i]) {
			int y = ver[i], z = edge[i];
			if (d[y] > d[x] + z) {
				d[y] = d[x] + z;
				q.push(make_pair(-d[y], y));
			}
		}
	}
}
int main () {
	cin >> n >> m;
	for (int i = 1; i <= m; i++) {
		int x, y, z;
		cin >> x >> y >> z;
		add(x, y, z);
	}
	dijkstra();
	for (int i = 1; i <= n; i++) cout << d[i];
	cout << endl;
	return 0;
}