1. Question

You are given n points in the plane that are all distinct, where points[i] = [xi, yi]. A boomerang is a tuple of points (i, j, k) such that the distance between i and j equals the distance between i and k (the order of the tuple matters).

Return the number of boomerangs.

2. Analysis

Input: points = [[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]].

2.0 Whole Idea

Set a finding Map to store the distance of every other points.

   const distanceRecord = { 
        [distance]: count  
        1: 2,
        4: 3,
        2: 1
    }

2.1 Get the distance from other points to the points[i].

    type Point = [number, number]

    function getDistance(x: Point, y: Point): number {
        return Math.pow(x[0] - y[0], 2) + Math.pow(x[1] - y[1], 2)
    }

Notice: Don't need to square up here.

2.2 Update the distanceRecord, key is distance, value is the count.

       distanceRecord = { 
           1: 2, // Means There are two points of the 1 distance from points[i]
           4: 3,
           2: 1
       }

2.3 For loop the distanceRecord, answer += value * (value - 1)

        Object.keys(distanceRecord).forEach(distance => {
            answer += distanceRecord[distance] * (distanceRecord[distance] - 1)
        })

Why is it value * (value - 1)?
It's the content of Combinations and permutations.
The number of permutations of value objects taken r at a time is determined by the following formula:
P(n, r) = n! / (n - r)!

5! = 5 * 4 * 3 * 2 * 1

(5 - 2)! = 3 * 2 * 1

So P(5, 2) = 5 * 4

2.4 Repeat the above 3 steps, to get the points[j], points[k]

        Object.keys(distanceRecord).forEach(distance => {
            answer += distanceRecord[distance] * (distanceRecord[distance] - 1)
        })

3. Source code

function numberOfBoomerangs(points: number[][]): number {
    type Point = [number, number]

    function getDistance(x: Point, y: Point): number {
        return Math.pow(x[0] - y[0], 2) + Math.pow(x[1] - y[1], 2)
    }

    type DistanceRecord = {
        [prop: number]: number
    }

    let answer = 0;

    for(let i  = 0; i < points.length; i++) {
        const distanceRecord: DistanceRecord = {}
        for(let j = 0; j < points.length; j++) {
            if(i === j) continue;
            // 1.Get the distance from other points to the points[i].
            const distance = getDistance(points[i] as Point, points[j] as Point);
            // 2.Update the distanceRecord, `key` is distance, `value` is the count.
            if(!distanceRecord[distance]) distanceRecord[distance] = 0;
            distanceRecord[distance]++;
        }

        // 3.For loop the distanceRecord, answer += value * (value - 1)
        Object.keys(distanceRecord).forEach(distance => {
            answer += distanceRecord[distance] * (distanceRecord[distance] - 1)
        })
    }


    return answer;
};