Largest Triangle Area

Largest Triangle Area - Problem

Given an array of points on the X-Y plane points where points[i] = [x_i, y_i], return the area of the largest triangle that can be formed by any three different points.

Answers within 10^-5 of the actual answer will be accepted.

Input & Output

Example 1 — Basic Triangle

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

› Output: 1.5

💡 Note: The largest triangle is formed by points [0,1], [1,0], [2,2] with area = |0(0-2) + 1(2-1) + 2(1-0)| / 2 = |0 + 1 + 2| / 2 = 1.5

Example 2 — Minimum Case

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

› Output: 0.5

💡 Note: Only one triangle possible with points forming a right triangle, area = 0.5 * 1 * 1 = 0.5

Example 3 — Collinear Points

$ Input: points = [[0,0],[1,1],[2,2],[3,4]]

› Output: 1.0

💡 Note: Points [0,0], [1,1], [2,2] are collinear (area = 0), largest triangle uses [0,0], [2,2], [3,4] with area = |0(2-4) + 2(4-0) + 3(0-2)| / 2 = |0 + 8 - 6| / 2 = 1.0

Constraints

3 ≤ points.length ≤ 50
-50 ≤ x_i, y_i ≤ 50
All the given points are unique.

Visualization

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Asked in

a Amazon 15 G Google 12

The key insight is to use the cross product formula to calculate triangle area efficiently. The best approach is the brute force method checking all C(n,3) combinations since n ≤ 50. Time: O(n³), Space: O(1).

Common Approaches

✓ Binary Search Answer

⏱️ Time: N/A Space: N/A

Brute Force - Check All Combinations

⏱️ Time: O(n³) Space: O(1)

For each combination of three points, calculate the triangle area using the cross product formula and keep track of the maximum area found.

Optimized Brute Force

⏱️ Time: O(n³) Space: O(1)

Use the same brute force approach but optimize the area calculation by avoiding floating point operations until the final division, which can improve precision and performance slightly.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

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Smart Actions

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