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Objective-C实现卡恩算法（Kahn’s Algorithm）

卡恩算法是一种用于图的拓扑排序算法，由哈尔维·卡恩（Harold Kahn）在1962年提出。该算法通过计算每个节点的入度，并逐步移除入度为零的节点，最终生成一个拓扑序列。以下将详细介绍Objective-C中如何实现卡恩算法。

首先，我们需要定义一个图的节点类。节点类将包含节点的值以及指向其他节点的邻接点列表。

#import 
   
    @interface GraphNode : NSObject@property (nonatomic, assign) NSInteger value;@property (nonatomic, retain) NSArray *adjacentNodes;@end
   

接下来，我们实现图的邻接表表示。通过创建一个字典来存储每个节点及其对应的入度和邻接点。

@implementation Graph- (GraphNode *)createNodeWithValue:(NSInteger)value {    GraphNode *node = [[GraphNode alloc] init];    node.value = value;    return node;}- (GraphNode *)addEdgeFromNode:(GraphNode *)fromNode toNode:(GraphNode *)toNode {    [toNode.adjacentNodes addObject:fromNode];    return toNode;}- (GraphNode *)buildGraph {    // 1. 创建节点    GraphNode *node1 = [self createNodeWithValue:1];    GraphNode *node2 = [self createNodeWithValue:2];    GraphNode *node3 = [self createNodeWithValue:3];    GraphNode *node4 = [self createNodeWithValue:4];        // 2. 添加边    [self addEdgeFromNode:node1 toNode:node2];    [self addEdgeFromNode:node1 toNode:node3];    [self addEdgeFromNode:node2 toNode:node4];        return node1;}

然后，我们实现卡恩算法的主要逻辑。我们使用一个队列来存储入度为零的节点，并一个数组来跟踪节点的状态。

- (void)kahnAlgorithm {    // 初始化每个节点的入度    [self initializeInDegree];        // 初始化队列    DispatchQueue queue = [DispatchQueue queueWithLabel:DispatchQueueGlobal];    [queue setLabel:DispatchQueueSerial];        // 开始处理    while (!queue.isEmpty) {        GraphNode *node = [queue.pop];                // 遍历节点的邻接点        for (GraphNode *neighbor in node.adjacentNodes) {            // 减少邻接点的入度            [self decreaseInDegree:neighbor];                        // 如果邻接点的入度变为零，加入队列            if (neighbor.inDegree == 0) {                [queue enqueue:neighbor];            }        }                // 处理当前节点        [self processNode:node];    }}

卡恩算法的关键在于正确维护每个节点的入度。我们需要一个方法来初始化入度，并在处理每个节点时递减邻接点的入度。

- (void)initializeInDegree {    // 创建入度字典    NSMutableDictionary *inDegreeDict = [NSMutableDictionary dictionary];        // 初始化所有节点的入度为零    for (GraphNode *node in [self getNodes]) {        inDegreeDict[node] = 0;    }        // 设置初始入度    [self setInDegree:inDegreeDict];}- (void)setInDegree:(NSMutableDictionary *)inDegreeDict {    for (GraphNode *node in [self getNodes]) {        node.inDegree = [inDegreeDict[node] intValue];    }}- (void)decreaseInDegree:(GraphNode *)node {    node.inDegree -= 1;        // 如果入度变为零，加入队列    if (node.inDegree == 0) {        [DispatchQueue globalQueue enqueue:^{            [node markAsProcessed];        }];    }}

最后，我们需要处理每个节点。具体处理逻辑可以根据实际需求进行扩展。

- (void)processNode:(GraphNode *)node {    // 处理节点的逻辑    // 例如，输出节点的值或进行其他操作}

完整实现代码如下：

#import 
   
    @interface GraphNode : NSObject@property (nonatomic, assign) NSInteger value;@property (nonatomic, retain) NSArray *adjacentNodes;@property (nonatomic, assign) NSInteger inDegree;@property (nonatomic, assign) bool processed;@end@interface Graph : NSObject- (GraphNode *)createNodeWithValue:(NSInteger)value;- (GraphNode *)addEdgeFromNode:(GraphNode *)fromNode toNode:(GraphNode *)toNode;- (GraphNode *)buildGraph;- (void)initializeInDegree;- (void)kahnAlgorithm;- (void)processNode:(GraphNode *)node;- (void)decreaseInDegree:(GraphNode *)node;- (void)setInDegree:(NSMutableDictionary *)inDegreeDict;- (NSArray *)getNodes;- (void)markAsProcessed:(GraphNode *)node;@end@implementation GraphNode@end@implementation Graph- (GraphNode *)createNodeWithValue:(NSInteger)value {    GraphNode *node = [[GraphNode alloc] init];    node.value = value;    node.adjacentNodes = [NSArray array];    node.inDegree = 0;    node.processed = false;    return node;}- (GraphNode *)addEdgeFromNode:(GraphNode *)fromNode toNode:(GraphNode *)toNode {    if (!toNode.adjacentNodes) {        toNode.adjacentNodes = [NSArray array];    }    [toNode.adjacentNodes addObject:fromNode];    return toNode;}- (GraphNode *)buildGraph {    GraphNode *node1 = [self createNodeWithValue:1];    GraphNode *node2 = [self createNodeWithValue:2];    GraphNode *node3 = [self createNodeWithValue:3];    GraphNode *node4 = [self createNodeWithValue:4];        [self addEdgeFromNode:node1 toNode:node2];    [self addEdgeFromNode:node1 toNode:node3];    [self addEdgeFromNode:node2 toNode:node4];        return node1;}- (void)initializeInDegree {    NSMutableDictionary *inDegreeDict = [NSMutableDictionary dictionary];        for (GraphNode *node in [self getNodes]) {        inDegreeDict[node] = 0;    }        [self setInDegree:inDegreeDict];}- (void)setInDegree:(NSMutableDictionary *)inDegreeDict {    for (GraphNode *node in [self getNodes]) {        node.inDegree = [inDegreeDict[node] intValue];    }}- (void)decreaseInDegree:(GraphNode *)node {    node.inDegree -= 1;        if (node.inDegree == 0 && !node.processed) {        node.processed = true;        [DispatchQueue globalQueue enqueue:^{            [self processNode:node];        }];    }}- (void)kahnAlgorithm {    DispatchQueue *queue = [DispatchQueue queueWithLabel:DispatchQueueGlobal];    [queue setLabel:DispatchQueueSerial];        while (!queue.isEmpty) {        GraphNode *node = [queue pop];                for (GraphNode *neighbor in node.adjacentNodes) {            [self decreaseInDegree:neighbor];        }    }}- (void)processNode:(GraphNode *)node {    // 在这里可以实现节点的处理逻辑}- (NSArray *)getNodes {    return [self createNodeWithValue:1] ? [NSArray arrayContainingAllObjects] : [NSArray array];}- (void)markAsProcessed:(GraphNode *)node {    node.processed = true;}
   

这个实现展示了如何在Objective-C中使用卡恩算法进行拓扑排序。您可以根据具体需求扩展节点处理逻辑。

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