Create 0812-largest-triangle-area.java

Author: sanajitjana

Easy/0812-largest-triangle-area.java

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+/*
+    Question: Largest Triangle Area
+    Link: https://leetcode.com/problems/largest-triangle-area/
+
+    Question Info:
+    You are given an array of points on a 2D plane. Each point is represented as an integer coordinate [x, y].
+    Your task is to return the largest area of a triangle formed by any three points in the given array.
+
+    Approach:
+    1. Use the shoelace formula (determinant method) to compute the area of a triangle formed by three points (x1,y1), (x2,y2), (x3,y3).
+       Formula:
+         Area = 0.5 * |x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)|
+    2. Iterate over all possible triplets of points using three nested loops.
+    3. For each triplet, calculate the area using the formula and update the maximum area found.
+    4. Return the maximum area.
+
+    Dry Run:
+    Example: points = [[0,0],[0,1],[1,0],[0,2],[2,0]]
+
+    - Pick (0,0), (0,1), (1,0) → Area = 0.5
+    - Pick (0,0), (0,2), (2,0) → Area = 2
+    - Pick (0,1), (0,2), (2,0) → Area = 1
+    - After checking all triplets, maximum = 2
+
+    Time Complexity: O(n^3), since we check all triplets of points.
+    Space Complexity: O(1), only a few variables used.
+*/
+
+class Solution {
+    public double largestTriangleArea(int[][] points) {
+        int length = points.length;
+        double maxArea = Double.MIN_VALUE;
+
+        for (int i = 0; i < length - 2; i++) {
+            for (int j = i + 1; j < length - 1; j++) {
+                for (int k = j + 1; k < length; 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];
+
+                    double area = 0.5 * Math.abs(
+                            x1 * (y2 - y3) +
+                            x2 * (y3 - y1) +
+                            x3 * (y1 - y2));
+
+                    maxArea = Math.max(maxArea, area);
+                }
+            }
+        }
+        return maxArea;
+    }
+}