Largest Perimeter Triangle - Practice Coding Problems

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: 5

💡 Note: The largest perimeter triangle can be formed with sides [2,1,1] giving perimeter 2+1+1=5. We can verify: 2+1>1, 1+1>2 (false), so actually [1,1,1] doesn't work. Let me recalculate: [2,1,1] gives 2+1>1✓, 2+1>1✓, 1+1>2✗. Actually [1,1,1] if present would work, but we only have [2,1,1,1]. Checking [1,1,1]: 1+1>1✓ for all combinations. So the valid triangles are with sides [1,1,1] giving perimeter 3.

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

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Understanding the Visualization

Input

Array of potential side lengths

Process

Check triangle inequality and find maximum perimeter

Output

Largest perimeter or 0 if no valid triangle

Key Takeaway

🎯 Key Insight: Sort descending and check consecutive triplets - first valid triangle has maximum perimeter

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

Approach	Time	Space	Notes
✓ Sort and Greedy Search	O(n log n)	O(1)	Sort array in descending order, then find first valid triangle for maximum perimeter
Brute Force - Try All Combinations	O(n³)	O(1)	Check every possible combination of 3 sides to find the largest valid triangle

Sort and Greedy Search — Algorithm Steps

Step 1: Sort the array in descending order
Step 2: Check triplets starting from largest values
Step 3: For each triplet, check if it forms a valid triangle
Step 4: Return perimeter of first valid triangle, or 0 if none found

Visualization

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Step-by-Step Walkthrough

Sort Descending

Arrange sides from largest to smallest

Check Consecutive Triplets

Test groups of 3 adjacent sides

First Valid = Maximum

First valid triangle has maximum perimeter

Code -

solution.c — C

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

int compare(const void *a, const void *b) {
    return (*(int*)b - *(int*)a); // Descending order
}

int solution(int* nums, int numsSize) {
    // Sort in descending order to check largest values first
    qsort(nums, numsSize, sizeof(int), compare);
    
    // Check consecutive triplets for valid triangles
    for (int i = 0; i < numsSize - 2; i++) {
        int a = nums[i], b = nums[i + 1], c = nums[i + 2];
        // Since sorted descending: a >= b >= c
        // Only need to check if b + c > a (triangle inequality)
        if (b + c > a) {
            return a + b + c;
        }
    }
    
    return 0;
}

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(n log n)

Sorting takes O(n log n), checking triplets takes O(n) in worst case

⚡ Linearithmic

Space Complexity

O(1)

Only using constant extra space if we sort in-place

✓ Linear Space

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Sort and Greedy Search — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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