Largest Perimeter Triangle

Largest Perimeter Triangle - Problem

Given an integer array nums, return the largest perimeter of a triangle with a non-zero area, formed from three of these lengths.

If it is impossible to form any triangle of a non-zero area, return 0.

Note: For three sides to form a valid triangle, the sum of any two sides must be greater than the third side (triangle inequality).

Input & Output

Example 1 — Basic Valid Triangle

$ Input: nums = [2,1,1,1]

› Output: 3

💡 Note: The largest perimeter triangle can be formed with sides [1,1,1] giving perimeter 1+1+1=3. We can verify the triangle inequality: 1+1>1 ✓ for all combinations. The triangle [2,1,1] is invalid because 1+1=2 which is not > 2.

Example 2 — Multiple Options

$ Input: nums = [4,2,2,1]

› Output: 5

💡 Note: We can form triangles with [2,2,1] since 2+2>1, 2+1>2, 2+1>2. The perimeter is 2+2+1=5. Triangle [4,2,2] fails since 2+2=4 which is not > 4.

Example 3 — No Valid Triangle

$ Input: nums = [1,2,1,10]

› Output: 0

💡 Note: No combination of 3 sides can form a valid triangle. For example: [1,2,1] fails since 1+1=2 which is not > 2. [1,2,10] fails since 1+2=3 < 10.

Constraints

3 ≤ nums.length ≤ 10⁴
1 ≤ nums[i] ≤ 10⁶

Visualization

Tap to expand

Asked in

G Google 12 A Amazon 8 M Microsoft 6

The key insight is that after sorting in descending order, the first valid triangle we find will automatically have the maximum perimeter. Best approach is sort-first greedy: Time: O(n log n), Space: O(1)

Common Approaches

✓ Brute Force - Try All Combinations

⏱️ Time: O(n³) Space: O(1)

Generate all possible combinations of 3 elements from the array, check if they can form a valid triangle using triangle inequality, and track the maximum perimeter found.

Sort and Greedy Search

⏱️ Time: O(n log n) Space: O(1)

Sort the array in descending order, then check consecutive triplets starting from the largest values. The first valid triangle found will have the maximum perimeter.

Brute Force - Try All Combinations — Algorithm Steps

Step 1: Generate all combinations of 3 sides from the array
Step 2: For each combination, check triangle inequality: a + b > c for all permutations
Step 3: If valid, calculate perimeter and update maximum
Step 4: Return maximum perimeter found, or 0 if none

Visualization

Tap to expand

Step-by-Step Walkthrough

Generate Combinations

Create all possible groups of 3 sides

Check Triangle Inequality

Verify each combination can form a valid triangle

Track Maximum

Keep the largest valid perimeter found

Code -

solution.c — C

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

int solution(int* nums, int numsSize) {
    int maxPerimeter = 0;
    
    // Try all combinations of 3 sides
    for (int i = 0; i < numsSize; i++) {
        for (int j = i + 1; j < numsSize; j++) {
            for (int k = j + 1; k < numsSize; k++) {
                int a = nums[i], b = nums[j], c = nums[k];
                // Check triangle inequality
                if (a + b > c && a + c > b && b + c > a) {
                    int perimeter = a + b + c;
                    if (perimeter > maxPerimeter) {
                        maxPerimeter = perimeter;
                    }
                }
            }
        }
    }
    
    return maxPerimeter;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    
    // Simple JSON array parsing
    int nums[1000];
    int count = 0;
    char* token = strtok(line, "[,]\n");
    while (token != NULL) {
        nums[count++] = atoi(token);
        token = strtok(NULL, "[,]\n");
    }
    
    int result = solution(nums, count);
    printf("%d\n", result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n³)

Three nested loops to generate all combinations of 3 elements

⚡ Linearithmic

Space Complexity

O(1)

Only using a few variables to track maximum perimeter

✓ Linear Space

32.0K Views

Medium Frequency

~15 min Avg. Time

890 Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force - Try All Combinations — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Select Compiler