PTA L1-001 紧急救援-优快云博客

本文链接：https://blog.youkuaiyun.com/weixin_43737829/article/details/89473670

本文深入探讨了Dijkstra算法的实现细节，通过一个具体的代码示例，展示了如何使用该算法来解决最短路径问题。文章涵盖了算法的基本原理、关键步骤以及在实际问题中的应用，适合对图论和算法感兴趣的读者。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

就是考查dijkstra算法的应用

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

#define INF 0x7FFFFFFF
const int maxn = 510;
int dis[maxn], w[maxn], num[maxn];
int n, road_num, start, des;
int weight[maxn], arc[maxn][maxn];
int pre_visit[maxn];
int visit[maxn];
int path[maxn];

void dijkstra(int s)
{
	for (int i = 0; i < n; i++)
	{
		dis[i] = INF;
		visit[i] = w[i] = num[i] = 0;
	}
	w[s] = weight[s];
	dis[s] = 0;
	num[s] = 1;

	for (int i = 0; i < n; i++)
	{
		int minn = INF;
		int mark = -1;
		for (int j = 0; j < n; j++)
		{
			if (!visit[j] && dis[j] < minn)
			{
				minn = dis[j];
				mark = j;
			}
		}

		if (mark == -1)
			break;

		visit[mark] = 1;

		for (int k = 0; k < n; k++)
		{
			if (!visit[k] && arc[mark][k] != INF)
			{
				if (dis[k] > dis[mark] + arc[mark][k])
				{
					dis[k] = dis[mark] + arc[mark][k];
					num[k] = num[mark];
					w[k] = w[mark] + weight[k];
					pre_visit[k] = mark;
				}
				else if (dis[k] == dis[mark] + arc[mark][k])
				{
					num[k] = num[mark] + num[k];
					if (w[k] < w[mark] + weight[k])
					{
						w[k] = w[mark] + weight[k];
						pre_visit[k] = mark;
					}
				}
			}
		}
	}
}

int main()
{
	cin >> n >> road_num >> start >> des;
	int s, e, w1;
	for (int i = 0; i < n; i++)
	{
		cin >> weight[i];
		for (int j = 0; j < n; j++)
		{
			arc[i][j] = INF;
		}
	}

	for (int i = 0; i < road_num; i++)
	{
		cin >> s >> e >> w1;
		arc[s][e] = arc[e][s] = min(w1, arc[s][e]);
	}

	dijkstra(start);
	int cur = des;
	int i = 0;
	while (cur != start)
	{
		path[i++] = cur;
		cur = pre_visit[cur];
	}
	path[i] = start;
	cout << num[des] << " " << w[des] << endl;
	for (int j = i; j > 0; j--)
	{
		cout << path[j] << " ";
	}
	cout << des << endl;
	return 0;
}