各种最短路模板

朴素版dijkstra模板

思路:稠密图用领接矩阵存图，初始化领接矩阵为Inf,输入边相关信息，然后调用dijkstra模板，初始化dis数组为inf，dis起点设置为0，然后for循环枚举n次，每次选出距离最小的点，标记为使用过，再用这个点去更新其他点的最短距离,时间复杂度O(n2)

代码

#include <bits/stdc++.h>

using namespace std;

#define IOS ios::sync_with_stdio(false); cin.tie(0); cout.tie(0)
typedef long long ll;

const int N = 550;

int n, m, g[550][550], dis[N], vis[N];

void dijstra() {
	memset(dis, 0x3f, sizeof dis);
	dis[1 = 0;
	for (int i = 0; i < n; ++i) {
		int t = -1;
		for (int j = 1; j <= n; ++j) 
			if (!vis[j] && (t == -1 || dis[t] > dis[j]))
				t = j;
			vis[t] = true;
			for (int k = 1; k <= n; ++k)
				dis[k] = min(dis[k], dis[t] + g[t][k]);
	}
} 

int main() {
	cin >> n >> m;
	memset(g, 0x3f, sizeof g);
	while (m--) {
		int x, y, z;
		cin >> x >> y >> z;
		g[x][y] = min(g[x][y], z);
	}
	dijstra();
	if (dis[n] == 0x3f3f3f3f)
		cout << -1;
	else
		cout << dis[n];
    return 0;
}

堆优化dijktra模板

思路:采用领接表存图，vector，每次取出dis数组最小点，即路径最小的点，用堆(优先队列）来维护即可，时间复杂度O(mlogn)

代码

#include <bits/stdc++.h>

using namespace std;

#define IOS ios::sync_with_stdio(false); cin.tie(0); cout.tie(0)
typedef pair<int, int> PII;
const int N = 1e6 + 10;

int n, m, dis[N], vis[N];
vector<pair<int, int> > G[N];

void dijkstra() {
	memset(dis, 0x3f, sizeof dis);
	dis[1] = 0;
	priority_queue<PII, vector<PII>, greater<PII>> heap;
	heap.push({0, 1});
	while (!heap.empty()) {
		auto t = heap.top();
		heap.pop();
		int ver = t.second, distance = t.first;
		if (vis[ver]) continue;
		vis[ver] = true;
		for (int i = 0; i < G[ver].size(); i++) {
			int j = G[ver][i].first;
			int w = G[ver][i].second;
			if (dis[j] > distance + w) {
				dis[j] = distance + w;
				heap.push({dis[j], j});
			}
		} 
	}
}


int main() {
	cin >> n >> m;
	while (m--) {
		int x, y, z;
		cin >> x >> y >> z;
		G[x].push_back(make_pair(y, z));
	}
	dijkstra();
	if (dis[n] == 0x3f3f3f3f)
		cout << -1;
	else
		cout << dis[n];
	
	
	return 0;
}