1.問題描述

描述：

　　Given n points in the plane that are all pairwise distinct, a "boomerang" is a tuple of points (i, j, k) such that the distance between i and jequals the distance between i and k (the order of the tuple matters). Find the number of boomerangs. You may assume that n will be at most 500 and coordinates of points are all in the range [-10000, 10000]

示例：

Input:
[[0,0],[1,0],[2,0]]

Output:
2

Explanation:
The two boomerangs are [[1,0],[0,0],[2,0]] and [[1,0],[2,0],[0,0]]

2.問題分析

1. 第一遍：
   • 如果到點a的距離為distance的點共有n個，那麽從這n個點中有序找兩個點就能與A點構成回旋，根據排列公式，總的回旋個數為A_n²個，即n * (n - 1)個。遍歷每一個點，map的key是距離，value是距離該點key個單位的點的個數。

     class Solution {
         
      
     public int numberOfBoomerangs(int[][] points) {
             int res = 0;
             for(int i = 0; i < points.length; i++){
                 Map<Double, Integer> map = new HashMap<>();
                 for(int j = 0; j < points.length; j++){
                     Double distance = Math.pow(points[i][0] - points[j][0], 2) + Math.pow(points[i][1] - points[j][1], 2);
                     
      
     if(map.containsKey(distance)){
                         map.put(distance, map.get(distance) + 1);
                     }else{
                         map.put(distance, 1);
                     }
                 }
                 
                 for(Integer count : map.values()){
                     res += count * (count - 1);
                 }
             }
             return res;
         }
     }

     

   • 改進：將map移到for循壞外，之後每次外部循環結束後，執行map.clear()操作。不再每次都新建map集合。

             Map<Double, Integer> map = new HashMap<>();
             for(int i = 0; i < points.length; i++){
                 for(int j = 0; j < points.length; j++){
                     Double distance = Math.pow(points[i][0] - points[j][0], 2) + Math.pow(points[i][1] - points[j][1], 2);
                     if(map.containsKey(distance)){
                         map.put(distance, map.get(distance) + 1);
                     }else{
                         map.put(distance, 1);
                     }
                 }
                 
                 for(Integer count : map.values()){
                     res += count * (count - 1);
                 }
                 map.clear();
             }

     View Code

     

leetcode447-Number of Boomerangs