Number of Boomerangs Problem in Java

In the world of programming, problem-solving skills are essential. They help developers tackle complex scenarios and devise efficient solutions. One such intriguing problem is the "Number of Boomerangs" problem, which challenges programmers to find the count of boomerang arrangements in an array. In this article, we will explore the problem in detail and provide a Java solution to solve it.

The problem derives its name from the boomerang, a traditional Australian throwing tool that returns to its original position after being thrown. In the context of this problem, a boomerang is represented as a tuple of three points: (i, j, k). For a boomerang arrangement to exist, the distance between the first two points (i and j) must be equal to the distance between the last two points (j and k).

The objective is to determine how many boomerang arrangements can be formed within a given array of points. Each point in the array is represented by a coordinate pair (x, y), where x and y are the respective Cartesian coordinates.

Understanding the Number of Boomerangs Problem:

The Number of Boomerangs problem involves finding the count of boomerang arrangements in an array. A boomerang is defined as a tuple of three points (i, j, k), where the distance between i and j is equal to the distance between j and k. In simpler terms, for three distinct points, if the distance between the first two points is the same as the distance between the last two points, then it forms a boomerang.

To illustrate the problem, let's consider an example. Given an array of points: [[0,0],[1,0],[2,0]], we can see that the point [1,0] is the pivot point. The distance between [0,0] and [1,0] is 1, and the distance between [2,0] and [1,0] is also 1. Therefore, we have a boomerang arrangement. The solution requires finding all such boomerang arrangements in the array and returning their count.

Solution To the Problem:

To solve the Number of Boomerangs problem in Java, we can utilize nested loops and calculate the distance between each pair of points in the array. We will use a HashMap to store the distances and their frequencies. The steps to solve the problem are as follows:

• Initialize a variable, say "count," to keep track of the total count of boomerangs.
• Iterate through each point in the array and consider it as the pivot point.
• For each pivot point, initialize an empty HashMap to store the distances and their frequencies.
• Iterate through the remaining points in the array and calculate the distance between the pivot point and each point.
• Store the distances and their frequencies in the HashMap.
• For each distance in the HashMap, calculate the count of boomerang arrangements.
• Increment the "count" variable by the product of the frequencies of distances (freq) and (freq - 1) for each distance.
• Return the final count.

Below is the Java implementation of the Number of Boomerangs problem:

NumberofBoomerangs.java

Output:

Number of boomerang arrangements: 2

In the given example, the array of points [[0, 0], [1, 0], [2, 0]] has two boomerang arrangements: ([0, 0], [1, 0], [2, 0]) and ([2, 0], [1, 0], [0, 0]). Thus, the output of the code will be 2, indicating the count of boomerang arrangements.

The Number of Boomerangs problem challenges programmers to find the count of boomerang arrangements in an array. By utilizing nested loops and a HashMap to store distances and their frequencies, we can efficiently solve this problem in Java. The provided Java implementation offers a clear solution to count the number of boomerangs in an array of points. Remember to consider edge cases and validate the input array to ensure robustness in your implementation.