Objective-C实现最近点对问题

点的定义

#import @interface Point : NSObject {@property (nonatomic, assign) double x;@property (nonatomic, assign) double y;}

  
      
    
       
预处理步骤
    
       
      
        
将所有点按照横坐标进行排序
      
        
从中选出一部分点作为递归分治的子问题
      
        
递归处理左右子问题，然后合并结果
    
       
  
      
  
      
    
       
递归函数实现
    
       
      

+(NSArray *)closestPairOfPoints:(NSArray *)points {

// 基线情况if (points.count <= 3) {return [self bruteForce(points)];}

// 分割点集Point *midPoint = [points[points.count/2]];NSArray *leftPoints = [self splitPoints:points[0...midPoint];NSArray *rightPoints = [self splitPoints:points[midPoint...-1]];

// 递归求解左右子问题NSArray *leftPair = [self closestPairOfPoints:leftPoints];NSArray *rightPair = [self closestPairOfPoints:rightPoints];

// 合并结果if ([leftPair distanceTo:rightPair] < [self distanceToPoints:leftPoints rightPoints]) {return leftPair;} else {return rightPair;}}

// 分割点集-(NSArray *)splitPoints:(NSArray *)points {return [self sortedPointsByX:points];}

  
      
    
       
优化部分
    
       
      
        
减少分割次数
      
        
使用平面扫描法减少计算量
      
        
提前终止递归