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Author: furic

0812-largest-triangle-area/Solution.md

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+# Brute Force Triangle | 25 Lines | O(n³) | 6ms
+
+# Intuition
+To find the largest triangle area, we need to check all possible combinations of 3 points from the given set and calculate their areas. The triangle with the maximum area is our answer.
+
+# Approach
+Use a brute force approach to generate all possible triangles by selecting 3 points from the input array. For each combination, calculate the triangle area using the cross product formula: `|x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| / 2`. Keep track of the maximum area found and return it.
+
+# Complexity
+- Time complexity: $$O(n^3)$$
+- Space complexity: $$O(1)$$
+
+# Code
+```typescript
+const largestTriangleArea = (points: number[][]): number => {
+ const totalPoints = points.length;
+ let maxTriangleArea = 0;
+
+ const calculateTriangleArea = (point1: number[], point2: number[], point3: number[]): number => {
+ return Math.abs(
+ point1[0] * (point2[1] - point3[1]) +
+ point2[0] * (point3[1] - point1[1]) +
+ point3[0] * (point1[1] - point2[1])
+ ) / 2;
+ };
+
+ for (let firstIndex = 0; firstIndex < totalPoints; firstIndex++) {
+ for (let secondIndex = firstIndex + 1; secondIndex < totalPoints; secondIndex++) {
+ for (let thirdIndex = secondIndex + 1; thirdIndex < totalPoints; thirdIndex++) {
+ const currentTriangleArea = calculateTriangleArea(
+ points[firstIndex], 
+ points[secondIndex], 
+ points[thirdIndex]
+ );
+ maxTriangleArea = Math.max(maxTriangleArea, currentTriangleArea);
+ }
+ }
+ }
+
+ return maxTriangleArea;
+};
+```