iOS深度优先算法

#import <Foundation/Foundation.h>/**************************************** 无向图  对称矩阵  V0--------V1 |         /| |        / | |     V2   | |   /   \  | | /      \ | V3        V4  0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 ******************************************//****************************************** 有向图  0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0   V0->V1 V0->V2 V2->V3 V3->V0 ******************************************//********************************************* 深度优先遍历:从初始点出发，不断向前走，如果碰到死路了，就往回走一步，尝试另一条路，直到发现了目标位置。这种不撞南墙不回头的方法，即使成功也不一定找到一条好路，但好处是需要记住的位置比较少。  广度优先:从初始点出发，把所有可能的路径都走一遍，如果里面没有目标位置，则尝试把所有两步能够到的位置都走一遍，看有没有目标位置；如果还不行，则尝试所有三步可以到的位置。这种方法，一定可以找到一条最短路径，但需要记忆的内容实在很多，要量力而行。 **********************************************/@interface AMWGraph : NSObject@property (nonatomic, strong) NSMutableArray *edges;//邻接矩阵，用来存储边//初始化矩阵，一维数组，和边的数目- (instancetype)initWithN:(NSInteger)n;//得到结点的个数- (NSInteger)getNumOfVertex;//得到边的数目- (NSInteger)getNumOfEdges;// 返回结点i的数据- (id)getValueByIndex:(NSInteger)i;//返回v1,v2的权值- (NSInteger)getWeight:(NSInteger)v1 withV2:(NSInteger)v2;//插入结点- (void)insertVertex:(id)vertex;- (void)insertEdge:(NSInteger)v1 withV2:(NSInteger)v2 withWeight:(NSInteger)weight;//删除结点- (void)deleteEdge:(NSInteger)v1 withV2:(NSInteger)v2;//得到第一个邻接结点的下标- (NSInteger)getFirstNeighbor:(NSInteger)index;//根据前一个邻接结点的下标来取得下一个邻接结点- (NSInteger)getNextNeighbor:(NSInteger)v1 withV2:(NSInteger)v2;//对外公开函数，深度优先遍历，与其同名私有函数属于方法重载- (void)depthFirstSearch:(NSMutableArray *)isVisited;//对外公开函数，广度优先遍历- (void)broadFirstSearch:(NSMutableArray *)isVisited;@end

#import "AMWGraph.h"@interface AMWGraph()@property (nonatomic, strong) NSMutableArray *vertexList;//存储点的链表@property (nonatomic, assign) NSInteger numOfEdges;//边的数目@end@implementation AMWGraph- (instancetype)initWithN:(NSInteger)n{    if (self == [super init]) {        _edges = [NSMutableArray array];        _vertexList = [NSMutableArray arrayWithCapacity:n];        _numOfEdges = 0;    }    return self;}- (NSInteger)getNumOfVertex{    return  self.vertexList.count;}- (NSInteger)getNumOfEdges{    return self.numOfEdges;}- (id)getValueByIndex:(NSInteger)i{    return self.vertexList[i];}- (NSInteger)getWeight:(NSInteger)v1 withV2:(NSInteger)v2{    return [self.edges[v1][v2] integerValue];;}- (void)insertVertex:(id)vertex{    [self.vertexList addObject:vertex];}- (void)insertEdge:(NSInteger)v1 withV2:(NSInteger)v2 withWeight:(NSInteger)weight{    NSMutableArray *arr = [self.edges objectAtIndex:v1];    arr[v2] = [NSNumber numberWithInteger:weight];    self.numOfEdges ++;}- (void)deleteEdge:(NSInteger)v1 withV2:(NSInteger)v2{    self.edges[v1][v2] = [NSNumber numberWithInt:0];    self.numOfEdges --;}- (NSInteger)getFirstNeighbor:(NSInteger)index{    for (NSInteger j = 0; j<[_vertexList count]; j++) {        if ([_edges[index][j] intValue] >0 ) {            return j;        }            }    return  -1;}- (NSInteger)getNextNeighbor:(NSInteger)v1 withV2:(NSInteger)v2{    for (NSInteger j = v2+1; j<[_vertexList count]; j++) {        if ([_edges[v1][j] intValue]>0) {            return j;        }    }    return -1;}- (void)depthFirstSearch:(NSMutableArray *)isVisited withI:(NSInteger)i{    isVisited[i] = [NSNumber numberWithBool:YES];        NSInteger w = [self getFirstNeighbor:i];    while (w!=-1) {        if ([isVisited[w] compare:@(0)] == NSOrderedSame) {            [self depthFirstSearch:isVisited withI:w];        }        w = [self getNextNeighbor:i withV2:w];    }}- (void)depthFirstSearch:(NSMutableArray *)isVisited{    for (NSInteger i =0; i<[self getNumOfVertex]; i++) {        if ([isVisited[i] compare:@(0)] == NSOrderedSame) {            [self depthFirstSearch:isVisited withI:i];        }    }}- (void)broadFirstSearch:(NSMutableArray *)isVisited withI:(NSInteger)i{    NSInteger u,w;    NSMutableArray *queue = [NSMutableArray array];    isVisited[i] = [NSNumber numberWithBool:YES];    //结点入队列    [queue addObject:[NSNumber numberWithInteger:i]];    while ([queue count]>0) {        u = [queue[0]integerValue];        [queue removeObjectAtIndex:0];        w = [self getFirstNeighbor:u];        while (w!=-1) {            if ([isVisited[w] compare:@(0)] == NSOrderedSame) {                isVisited[w] = [NSNumber numberWithBool:YES];                [queue addObject:[NSNumber numberWithInteger:w]];            }            w = [self getNextNeighbor:u withV2:w];        }    }}- (void)broadFirstSearch:(NSMutableArray *)isVisited{    for (NSInteger i =0; i<[self getNumOfVertex]; i++) {        if ([isVisited[i] compare:@(0)] == NSOrderedSame) {            [self broadFirstSearch:isVisited withI:i];        }    }}@end