Largest Triangle Area - Practice Coding Problems

Largest Triangle Area - Problem

Find the Maximum Triangle Area from Points

You're given an array of points on a 2D coordinate plane, where each point is represented as [x, y]. Your task is to find the largest possible area of a triangle that can be formed by selecting any three different points from the array.

Goal: Return the area of the largest triangle
Input: Array of points points[i] = [xi, yi]
Output: Maximum triangle area as a floating-point number

The area calculation uses the mathematical formula for triangle area given three vertices. Answers within 10^-5 of the actual answer will be accepted, so you don't need to worry about extreme precision.

Input & Output

example_1.py — Basic Triangle

$ Input: points = [[0,0],[0,1],[1,0],[0,2],[2,0]]

› Output: 2.0

💡 Note: The largest triangle is formed by points [0,0], [0,2], and [2,0] with area = 0.5 * |0*(2-0) + 0*(0-0) + 2*(0-2)| = 0.5 * 4 = 2.0

example_2.py — Collinear Points

$ Input: points = [[1,0],[0,0],[2,0]]

› Output: 0.0

💡 Note: All three points are collinear (on the same line), so they cannot form a triangle. The area is 0.

example_3.py — Square Formation

$ Input: points = [[0,0],[1,0],[0,1],[1,1]]

› Output: 0.5

💡 Note: Multiple triangles can be formed, but the maximum area is 0.5 from triangles like [0,0], [1,0], [0,1]

Visualization

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Understanding the Visualization

Examine All Combinations

Check every possible set of three points

Calculate Areas

Use the coordinate formula to find each triangle's area

Track Maximum

Keep the largest area found so far

Key Takeaway

🎯 Key Insight: For geometric problems like finding maximum triangle area, brute force checking all combinations is often the optimal approach since geometric constraints don't allow for typical optimization shortcuts.

Time & Space Complexity

Time Complexity

⏱️

O(n³)

Three nested loops to check all combinations of three points

⚠ Quadratic Growth

Space Complexity

O(1)

Only using a few variables to store coordinates and maximum area

✓ Linear Space

Constraints

3 ≤ points.length ≤ 50
-50 ≤ x_i, y_i ≤ 50
All points are unique
Answers within 10^-5 of the actual answer will be accepted

Asked in

a Amazon 15 G Google 12 ⊞ Microsoft 8 f Meta 6

The optimal solution uses a brute force approach to check all possible combinations of three points. Since we need to find the maximum triangle area, there's no way to avoid examining every triplet. The key is using the coordinate geometry formula: Area = 0.5 * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| to calculate each triangle's area efficiently.

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force (Check All Triangles)	O(n³)	O(1)	Check every possible combination of three points and calculate triangle areas

Brute Force (Check All Triangles) — Algorithm Steps

Iterate through all possible combinations of three points using three nested loops
For each triplet of points, calculate the triangle area using the coordinate formula
Keep track of the maximum area found so far
Return the maximum area after checking all combinations

Visualization

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Step-by-Step Walkthrough

Select Three Points

Choose three different points from the array

Apply Area Formula

Use coordinate geometry formula to calculate area

Track Maximum

Keep track of the largest area found so far

Code -

solution.c — C

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

double largestTriangleArea(int** points, int pointsSize) {
    double maxArea = 0;
    
    // Check all combinations of three points
    for (int i = 0; i < pointsSize; i++) {
        for (int j = i + 1; j < pointsSize; j++) {
            for (int k = j + 1; k < pointsSize; k++) {
                int x1 = points[i][0], y1 = points[i][1];
                int x2 = points[j][0], y2 = points[j][1];
                int x3 = points[k][0], y3 = points[k][1];
                
                // Calculate triangle area using coordinate formula
                double area = fabs(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)) / 2.0;
                if (area > maxArea) {
                    maxArea = area;
                }
            }
        }
    }
    
    return maxArea;
}

int main() {
    // Example usage
    int points_data[5][2] = {{0,0},{0,1},{1,0},{0,2},{2,0}};
    int* points[5];
    for (int i = 0; i < 5; i++) {
        points[i] = points_data[i];
    }
    printf("%f\n", largestTriangleArea(points, 5));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n³)

Three nested loops to check all combinations of three points

⚠ Quadratic Growth

Space Complexity

O(1)

Only using a few variables to store coordinates and maximum area

✓ Linear Space

Constraints

3 ≤ points.length ≤ 50
-50 ≤ x_i, y_i ≤ 50
All points are unique
Answers within 10^-5 of the actual answer will be accepted

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Related Problems

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Common Approaches

Brute Force (Check All Triangles) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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