Dijkstra's algorithm

最新推荐文章于 2024-10-01 17:00:59 发布

原创最新推荐文章于 2024-10-01 17:00:59 发布 · 1.3k 阅读

1 ·

CC 4.0 BY-SA版权

C++ 同时被 3 个专栏收录

39 篇文章

订阅专栏

Code

21 篇文章

订阅专栏

work

9 篇文章

订阅专栏

本文介绍了一种使用最小堆优化的Dijkstra最短路径算法实现，并通过一个具体的C++程序实例展示了如何构建和维护堆，以提高算法效率。该程序从文件中读取图数据，并计算指定顶点之间的最短路径。

https://sites.google.com/site/indy256/algo_cpp/dijkstra_heap

#include <iostream>
#include <fstream>
#include <math.h>
#include <vector>
#include <sstream>
#include <map>

using namespace std;

int heap[1000];
int prior[1000];
int heapSize = 0;
//int pos2Id[1000];
int id2Pos[1000];
bool boolX[1000];

void InsertHeap(int id)
{
	heap[heapSize++] = id;
	id2Pos[id] = heapSize-1;
	int pos = heapSize-1;
	while (pos > 0)
	{
		int parent = pos-1 >> 1;
		if(prior[id] > prior[heap[parent]])
		{
			break;
		}
		int temp = heap[parent];
		heap[parent] = id;
		heap[pos] = temp;

		id2Pos[id] = parent;
		id2Pos[temp] = pos;

		pos = parent;
	}
}

void DeleteHeap(int id)
{
	int pos = id2Pos[id];
	if (pos < 0)
	{
		return;
	}

	heap[pos] = heap[--heapSize];
	id2Pos[heap[pos]] = pos;
	while (pos < (heapSize>>1))
	{
		int child = 2*pos+1;
		if (child+1< heapSize && prior[heap[child+1]] < prior[heap[child]])
		{
			child++;
		}

		if (prior[heap[pos]] <= prior[heap[child]])
		{
			break;
		}

		int temp = heap[pos];
		heap[pos] = heap[child];
		heap[child] = temp;

		id2Pos[temp] = child;
		id2Pos[heap[pos]] = pos;

		pos = child;
	}
}

int PopMin()
{
	int id = heap[0];
	heap[0] = heap[--heapSize];
	int pos = 0;
	id2Pos[heap[pos]] = pos;
	while (pos < (heapSize>>1))
	{
		int child = 2*pos+1;
		if (child+1< heapSize && prior[heap[child+1]] < prior[heap[child]])
		{
			child++;
		}

		if (prior[heap[pos]] <= prior[heap[child]])
		{
			break;
		}

		int temp = heap[pos];
		heap[pos] = heap[child];
		heap[child] = temp;

		id2Pos[temp] = child;
		id2Pos[heap[pos]] = pos;

		pos = child;
	}

	return id;
}


void Dijkstra(vector<vector<pair<int, int>>> g, int s)
{
	int numV = g.size();
	prior[s] = 0;
	InsertHeap(s);

	while(heapSize >0)
	{
		int u = PopMin();
		boolX[u] = true;
		for (int i=0; i<g[u].size(); i++)
		{
			int v = g[u][i].first;
			int w = g[u][i].second;
			if (boolX[v-1])
			{
				continue;
			}

			DeleteHeap(v-1);
			prior[v-1] = min(prior[v-1], prior[u]+w);
			InsertHeap(v-1);
		}
	}
}

int main()
{
	ifstream infile;
	infile.open("dijkstraData.txt");

	// ------------- Read the Graph --------------
	vector<vector<pair<int, int>>> graph;
	const int numV = 200;
	vector<pair<int, int>> temp;
	for (int i=0; i< numV; i++)
	{
		graph.push_back(temp);
	}

	string line;
	char cline[10000];
	
	/*while (infile.getline(cline, 10000))*/
	while(getline(infile, line))
	{
		std::stringstream ss;
		ss << line;
		int u;
		int v;
		char t;
		int w;
		ss >> u;
		while(ss >> v)
		{
			ss >> t;
			ss >> w;
			graph[u-1].push_back(make_pair(v, w));
		}
		ss.clear();
		line.clear();
	}

	// --------------
	for (int i=0; i<numV; i++)
	{
		id2Pos[i] = -1;
		prior[i] = 1000000;
		boolX[i] = false;
	}
	Dijkstra(graph, 0);
	int r[]= {7,37,59,82,99,115,133,165,188,197};
	for (int i=0; i<10; i++)
	{
		cout<< r[i] << " : " << prior[r[i]-1] << endl; 
		/*cout << prior[i] << endl;*/
	}
	infile.close();
	graph.clear();
	return 0;

}