Valid Boomerang

Valid Boomerang - Problem

Given an array points where points[i] = [x_i, y_i] represents a point on the X-Y plane, return true if these points form a boomerang.

A boomerang is a set of three points that are all distinct and not in a straight line.

Input & Output

Example 1 — Valid Boomerang

$ Input: points = [[1,1],[2,3],[3,2]]

› Output: true

💡 Note: The three points are distinct and not collinear, so they form a valid boomerang. Cross product calculation: (2-1)×(2-1) - (3-1)×(3-1) = 1×1 - 2×2 = -3 ≠ 0

Example 2 — Collinear Points

$ Input: points = [[1,1],[2,2],[3,3]]

› Output: false

💡 Note: All three points lie on the same straight line (y = x), so they cannot form a boomerang. Cross product: (2-1)×(3-1) - (2-1)×(3-1) = 1×2 - 1×2 = 0

Example 3 — Duplicate Points

$ Input: points = [[1,1],[2,3],[1,1]]

› Output: false

💡 Note: Two points are identical ([1,1] appears twice), so they cannot form a valid boomerang. Cross product: (2-1)×(1-1) - (3-1)×(1-1) = 1×0 - 2×0 = 0

Constraints

points.length == 3
points[i].length == 2
0 ≤ points[i][j] ≤ 50

Visualization

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Asked in

G Google 15 a Amazon 12 M Microsoft 8

The key insight is to use the cross product of vectors to check if three points are collinear. Three points form a valid boomerang if they are distinct and not collinear. Best approach is the cross product method which avoids division and handles all edge cases naturally. Time: O(1), Space: O(1)

Common Approaches

✓ Cross Product Method

⏱️ Time: O(1) Space: O(1)

Calculate cross product of vectors formed by the three points. If cross product is zero, points are collinear. This avoids division and handles all edge cases naturally.

Slope Comparison

⏱️ Time: O(1) Space: O(1)

Calculate the slope between points 0-1 and points 0-2. If the slopes are different, the points form a valid boomerang. Handle vertical lines separately to avoid division by zero.

Cross Product Method — Algorithm Steps

Form vectors from point A to B and A to C
Calculate cross product of these vectors
Return true if cross product is non-zero

Visualization

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Step-by-Step Walkthrough

Form Vectors

Create vectors from first point to other two points

Cross Product

Calculate cross product of the two vectors

Result

Non-zero cross product means valid boomerang

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int solution(int points[3][2]) {
    // Extract coordinates
    int x1 = points[0][0], y1 = points[0][1];
    int x2 = points[1][0], y2 = points[1][1];
    int x3 = points[2][0], y3 = points[2][1];
    
    // Calculate cross product of vectors (p1->p2) and (p1->p3)
    int crossProduct = (x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1);
    
    // Points form a boomerang if cross product is non-zero
    return crossProduct != 0;
}

int main() {
    char line[1000];
    fgets(line, sizeof(line), stdin);
    
    int points[3][2];
    
    // Simple parsing for [[x1,y1],[x2,y2],[x3,y3]] format
    char *ptr = line;
    int idx = 0;
    
    while (*ptr && idx < 3) {
        if (*ptr == '[') {
            ptr++;
            if (idx > 0) { // Skip outer bracket for first point
                sscanf(ptr, "%d,%d", &points[idx][0], &points[idx][1]);
                idx++;
            } else {
                ptr++; // Skip second bracket
                sscanf(ptr, "%d,%d", &points[idx][0], &points[idx][1]);
                idx++;
            }
        }
        ptr++;
    }
    
    int result = solution(points);
    printf(result ? "true\n" : "false\n");
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Performs constant number of arithmetic operations

✓ Linear Growth

Space Complexity

O(1)

Uses only a few variables for coordinate differences

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Cross Product Method — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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