图论matlab代码整理
时间: 2023-11-25 17:56:33 浏览: 34
以下是一些常用的图论算法的 MATLAB 代码:
1. 最短路径算法(Dijkstra 算法)
输入:邻接矩阵 adjacencyMatrix,起点 startNode,终点 endNode
输出:最短路径长度 shortestPathLength,最短路径 shortestPath
```
function [shortestPathLength,shortestPath] = dijkstra(adjacencyMatrix,startNode,endNode)
numNodes = size(adjacencyMatrix,1);
pathLengths = Inf(1,numNodes);
visited = false(1,numNodes);
previousNodes = zeros(1,numNodes);
pathLengths(startNode) = 0;
while ~all(visited)
[~,index] = min(pathLengths(~visited));
currentNode = find(~visited,1,'first');
currentNode = index(1);
visited(currentNode) = true;
neighbors = find(adjacencyMatrix(currentNode,:));
for neighbor = neighbors
tentativePathLength = pathLengths(currentNode) + adjacencyMatrix(currentNode,neighbor);
if tentativePathLength < pathLengths(neighbor)
pathLengths(neighbor) = tentativePathLength;
previousNodes(neighbor) = currentNode;
end
end
end
shortestPathLength = pathLengths(endNode);
shortestPath = endNode;
while shortestPath(1) ~= startNode
shortestPath = [previousNodes(shortestPath(1)), shortestPath];
end
```
2. 最小生成树算法(Prim 算法)
输入:邻接矩阵 adjacencyMatrix
输出:最小生成树 minimumSpanningTree
```
function minimumSpanningTree = prim(adjacencyMatrix)
numNodes = size(adjacencyMatrix,1);
minimumSpanningTree = zeros(1,numNodes);
costs = Inf(1,numNodes);
visited = false(1,numNodes);
minimumSpanningTree(1) = 1;
visited(1) = true;
for i=2:numNodes
costs(i) = adjacencyMatrix(1,i);
end
for i=2:numNodes
[~,index] = min(costs(~visited));
currentNode = find(~visited,1,'first');
currentNode = index(1);
visited(currentNode) = true;
minimumSpanningTree(i) = currentNode;
neighbors = find(adjacencyMatrix(currentNode,:));
for neighbor = neighbors
if adjacencyMatrix(currentNode,neighbor) < costs(neighbor) && ~visited(neighbor)
costs(neighbor) = adjacencyMatrix(currentNode,neighbor);
end
end
end
```
3. 拓扑排序算法
输入:邻接矩阵 adjacencyMatrix
输出:拓扑排序结果 topologicalOrder
```
function topologicalOrder = topologicalSort(adjacencyMatrix)
numNodes = size(adjacencyMatrix,1);
inDegree = sum(adjacencyMatrix);
queue = find(inDegree == 0);
topologicalOrder = [];
while ~isempty(queue)
currentNode = queue(1);
queue = queue(2:end);
topologicalOrder = [topologicalOrder, currentNode];
neighbors = find(adjacencyMatrix(currentNode,:));
for neighbor = neighbors
inDegree(neighbor) = inDegree(neighbor) - 1;
if inDegree(neighbor) == 0
queue = [queue, neighbor];
end
end
end
if length(topologicalOrder) ~= numNodes
topologicalOrder = [];
end
```
以上是一些常用的图论算法的 MATLAB 代码,希望能对你有所帮助。