Number Of Boomerangs

                                            
class Solution {
public:
    int numberOfBoomerangs(vector<vector<int>>& points) {
        int res = 0;
        for(int i = 0; i < points.size(); i++){
            unordered_map<int, int> counter;
            for(int j = 0; j < points.size(); j++){
                int dist = pow(points[i][0] - points[j][0], 2) + pow(points[i][1] - points[j][1], 2);
                counter[dist]++;
            }
            for(auto it = counter.begin(); it != counter.end(); it++){
                res += it->second * (it->second - 1);
            }
        }
        return res;
    }
};

                                            
class Solution {
    public int numberOfBoomerangs(int[][] points) {
        int result = 0;
        Map<Integer, Integer> map = new HashMap<>();
        
        for (int i = 0; i < points.length; i++) {
            for (int j = 0; j < points.length; j++) {
                if (i == j) continue;
                
                int dist = (int)Math.pow(points[i][0] - points[j][0], 2) + (int)Math.pow(points[i][1] - points[j][1], 2);
                map.put(dist, map.getOrDefault(dist, 0) + 1);
            }
            
            for (int val : map.values()) {
                result += val * (val - 1);
            }
            map.clear();
        }
        
        return result;
    }
}

                                            
class Solution(object):
    def numberOfBoomerangs(self, points):
        """
        :type points: List[List[int]]
        :rtype: int
        """
        def get_distance(p1, p2):
            return (p1[0] - p2[0]) ** 2 + (p1[1] - p2[1]) ** 2
        
        total = 0
        for p1 in points:
            dist_map = {}
            for p2 in points:
                if p1 == p2:
                    continue
                dist = get_distance(p1, p2)
                dist_map[dist] = dist_map.get(dist, 0) + 1
                
            for k in dist_map:
                total += dist_map[k] * (dist_map[k] - 1)
                
        return total

                                            
public class Solution {
    public int NumberOfBoomerangs(int[][] points) {
        int result = 0;
        
        for (int i = 0; i < points.Length; i++) {
            Dictionary<int, int> map = new Dictionary<int, int>();
            
            for (int j = 0; j < points.Length; j++) {
                if (i == j) continue;
                
                int distance = (points[i][0] - points[j][0]) * (points[i][0] - points[j][0]) + (points[i][1] - points[j][1]) * (points[i][1] - points[j][1]);
                
                if (!map.ContainsKey(distance)) {
                    map.Add(distance, 1);
                } else {
                    result += 2 * map[distance];
                    map[distance]++;
                }
            }
        }
        
        return result;
    }
}

                                            
/**
 * @param {number[][]} points
 * @return {number}
 */
var numberOfBoomerangs = function(points) {
    let count = 0;
    
    for (let i = 0; i < points.length; i++) {
        const map = {};
        
        for (let j = 0; j < points.length; j++) {
            if (i === j) continue;
            
            const dist = Math.pow(points[i][0] - points[j][0], 2) + Math.pow(points[i][1] - points[j][1], 2);
            
            if (map[dist]) {
                count += map[dist] * 2;
                map[dist]++;
            } else {
                map[dist] = 1;
            }
        }
    }
    
    return count;
};

                                            
function numberOfBoomerangs(points: number[][]): number {
    let count = 0;

    for (let i = 0; i < points.length; i++) {
        const map = new Map<number, number>();

        for (let j = 0; j < points.length; j++) {
            if (i !== j) {
                const dist = Math.pow(points[i][0] - points[j][0], 2) + Math.pow(points[i][1] - points[j][1], 2);
                map.set(dist, (map.get(dist) || 0) + 1);
            }
        }

        for (const val of map.values()) {
            count += val * (val - 1);
        }
    }

    return count;
};

                                            
class Solution {
    /**
     * @param Integer[][] $points
     * @return Integer
     */
    function numberOfBoomerangs($points) {
        $result = 0;
        for ($i = 0; $i < count($points); $i++) {
            $map = [];
            for ($j = 0; $j < count($points); $j++) {
                if ($i != $j) {
                    $distance = pow($points[$i][0] - $points[$j][0], 2) + pow($points[$i][1] - $points[$j][1], 2);
                    if (isset($map[$distance])) {
                        $result += 2 * $map[$distance];
                        $map[$distance]++;
                    } else {
                        $map[$distance] = 1;
                    }
                }
            }
        }
        return $result;
    }
}

                                            
class Solution {
    func numberOfBoomerangs(_ points: [[Int]]) -> Int {
        var count = 0
        for i in 0..<points.count {
            var map = [Int: Int]()
            for j in 0..<points.count {
                if i != j {
                    let xDist = points[i][0] - points[j][0]
                    let yDist = points[i][1] - points[j][1]
                    let distance = xDist*xDist + yDist*yDist
                    map[distance, default: 0] += 1
                }
            }
            for (_, value) in map {
                count += value * (value - 1)
            }
        }
        return count
    }
}

                                            
class Solution {
    fun numberOfBoomerangs(points: Array<IntArray>): Int {
        var count = 0
        for (i in points.indices) {
            val map = HashMap<Int, Int>()
            for (j in points.indices) {
                if (i == j) continue
                val distance = (points[i][0] - points[j][0]) * (points[i][0] - points[j][0]) + (points[i][1] - points[j][1]) * (points[i][1] - points[j][1])
                map[distance] = map.getOrDefault(distance, 0) + 1
            }
            for (value in map.values) {
                count += value * (value - 1)
            }
        }
        return count
    }
}

                                            
class Solution {
  int numberOfBoomerangs(List<List<int>> points) {
      int count = 0;
  
      for (int i = 0; i < points.length; i++) {
          Map<int, int> map = {};
  
          for (int j = 0; j < points.length; j++) {
              if (i != j) {
                  int dist = (points[i][0] - points[j][0]) * (points[i][0] - points[j][0]) + 
                             (points[i][1] - points[j][1]) * (points[i][1] - points[j][1]);
  
                  map[dist] = (map[dist] ?? 0) + 1;
              }
          }
  
          for (var value in map.values) {
              count += value * (value - 1);
          }
      }
  
      return count;
  }
}

                                            
func numberOfBoomerangs(points [][]int) int {
    count := 0
    for i := 0; i < len(points); i++ {
        distanceMap := make(map[int]int)
        for j := 0; j < len(points); j++ {
            if i != j {
                distance := (points[i][0]-points[j][0])*(points[i][0]-points[j][0]) + (points[i][1]-points[j][1])*(points[i][1]-points[j][1])
                distanceMap[distance]++
            }
        }
        for _, v := range distanceMap {
            count += v * (v - 1)
        }
    }
    return count
}

                                            
# @param {Integer[][]} points
# @return {Integer}
def number_of_boomerangs(points)
    count = 0
    points.each do |p1|
        distance_map = {}
        points.each do |p2|
            next if p1 == p2
            distance = (p2[0] - p1[0])**2 + (p2[1] - p1[1])**2
            count += 2 * distance_map[distance].to_i
            distance_map[distance] = distance_map[distance].to_i + 1
        end
    end
    count
end

                                            
object Solution {
    import scala.collection.mutable

    def numberOfBoomerangs(points: Array[Array[Int]]): Int = {
        def distance(p1: Array[Int], p2: Array[Int]): Int = {
            val dx = p1(0) - p2(0)
            val dy = p1(1) - p2(1)
            dx * dx + dy * dy
        }

        var count = 0
        for (i <- points.indices) {
            val map = mutable.Map[Int, Int]()
            for (j <- points.indices) {
                if (j != i) {
                    val d = distance(points(i), points(j))
                    map.update(d, map.getOrElse(d, 0) + 1)
                }
            }
            for ((_, v) <- map) {
                count += v * (v - 1)
            }
        }
        count
    }
}

                                            
impl Solution {
    pub fn number_of_boomerangs(points: Vec<Vec<i32>>) -> i32 {
        
        let mut count = 0;
        
        for i in 0..points.len() {
            let mut map = std::collections::HashMap::new();
            
            for j in 0..points.len() {
                if i != j {
                    let dist = (points[i][0] - points[j][0]).pow(2) + (points[i][1] - points[j][1]).pow(2);
                    *map.entry(dist).or_insert(0) += 1;
                }
            }
            
            for &val in map.values() {
                count += val * (val - 1);
            }
        }
        
        count
    }
}

To solve this coding challenge, we need to count the number of boomerang tuples (i, j, k) from the given list of points. A boomerang is defined as three points (i, j, k) such that the distance between i and j is equal to the distance between i and k, and the order of the points matters. Here's a detailed explanation and pseudocode solution:

Explanation

Understanding the Problem:

We need to count the number of tuples (i, j, k) where points i, j, and k are such that the distance between i and j is the same as the distance between i and k.
The order matters, meaning (i, j, k) is different from (i, k, j).

Distance Calculation:

Since we are only interested in comparing distances, we can use the squared Euclidean distance to avoid dealing with floating-point operations.
The Euclidean distance between two points (x1, y1) and (x2, y2) is sqrt((x1 - x2)² + (y1 - y2)²). We can use the squared distance (x1 - x2)² + (y1 - y2)² for comparison.

Optimal Approach:

For each point p1, compute the distance to every other point p2.
Use a hashmap (or dictionary) to count the number of points p2 that have the same distance to p1.
For each unique distance, if there are k points at that distance from p1, then the number of boomerang tuples can be calculated as k * (k - 1) since each of the k points can pair with (k-1) other points.

Complexity:

Since we need to compute distances between every pair of points, the time complexity is O(n^2), where n is the number of points.

Detailed Steps in Pseudocode

Initialize a variable
totalBoomerangs

to store the count of boomerangs.
Define a helper function
calculateSquaredDistance

to compute the squared distance between two points.
For each point
p1

in the list of points:

Initialize an empty hashmap
distanceCountMap

.
For each other point
p2

, compute the squared distance from
p1

to
p2

.
Update the count of this distance in
distanceCountMap

.

For each unique distance in
distanceCountMap

, update
totalBoomerangs

using the formula k * (k - 1).
Return
totalBoomerangs

.

Pseudocode

                                            
# Function to calculate squared distance between two points
function calculateSquaredDistance(pointA, pointB):
    deltaX = pointA[0] - pointB[0]
    deltaY = pointA[1] - pointB[1]
    return deltaX * deltaX + deltaY * deltaY

# Main function to count number of boomerangs
function numberOfBoomerangs(points):
    totalBoomerangs = 0  # Initialize the boomerang count
    
    # Iterate through each point as the central point p1
    for each point p1 in points:
        distanceCountMap = {}  # Initialize a hashmap to count distances
        
        # Calculate distances from p1 to all other points p2
        for each point p2 in points:
            if p1 == p2:
                continue  # Skip the same point
            distance = calculateSquaredDistance(p1, p2)  # Calculate squared distance
            
            # Update the count of this distance in distanceCountMap
            if distance in distanceCountMap:
                distanceCountMap[distance] += 1
            else:
                distanceCountMap[distance] = 1
        
        # Calculate boomerangs from the distance count map
        for each distance in distanceCountMap:
            count = distanceCountMap[distance]
            totalBoomerangs += count * (count - 1)  # count different boomerang permutations
    
    return totalBoomerangs  # Return the total number of boomerangs

# Call the function with the input points
points = [[0,0],[1,0],[2,0]]
result = numberOfBoomerangs(points)
# Output: result would be 2 in this case

In the above pseudocode, we initialize the total boomerang count at the beginning, then for each point in the list, we calculate distances to all other points and use a hashmap to keep track of these distances. We then use this hashmap to count the number of boomerangs and return the total count. The pseudocode contains extensive comments to explain each step, ensuring a comprehensive understanding of the process involved in solving the challenge.