Triangle Validator - Problem

Given three positive integers representing the lengths of three sides, determine if they can form a valid triangle. If they can form a valid triangle, classify it as:

Equilateral - All three sides are equal
Isosceles - Exactly two sides are equal
Scalene - All three sides are different

For three sides to form a valid triangle, they must satisfy the triangle inequality theorem: the sum of any two sides must be greater than the third side.

Input: Three positive integers a, b, and c representing side lengths.

Output: Return "Invalid" if they cannot form a triangle, otherwise return the triangle type as a string.

Input & Output

Example 1 — Valid Scalene Triangle

$ Input: a = 5, b = 12, c = 13

› Output: Scalene

💡 Note: Triangle inequality: 5+12=17>13 ✓, 5+13=18>12 ✓, 12+13=25>5 ✓. All sides different, so it's Scalene.

Example 2 — Valid Isosceles Triangle

$ Input: a = 5, b = 5, c = 8

› Output: Isosceles

💡 Note: Triangle inequality: 5+5=10>8 ✓, 5+8=13>5 ✓, 5+8=13>5 ✓. Two sides equal (a=b=5), so it's Isosceles.

Example 3 — Invalid Triangle

$ Input: a = 1, b = 2, c = 5

› Output: Invalid

💡 Note: Triangle inequality fails: 1+2=3 is not greater than 5. Cannot form a valid triangle.

Constraints

1 ≤ a, b, c ≤ 1000
All inputs are positive integers

Visualization

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Asked in

a Amazon 15 M Microsoft 12 G Google 8

The key insight is applying the triangle inequality theorem: for sides a, b, c to form a valid triangle, a+b>c, a+c>b, and b+c>a must all be true. The optimized approach sorts the sides first, then only checks if the sum of the two smallest exceeds the largest. Time: O(1), Space: O(1).

Common Approaches

✓ Combined Validation and Classification

⏱️ Time: O(1) Space: O(1)

Optimize by combining triangle validity check with type classification in one logical flow, avoiding redundant comparisons.

Step-by-Step Validation

⏱️ Time: O(1) Space: O(1)

First validate if the three sides can form a triangle by checking all three triangle inequality conditions separately. If valid, then determine the triangle type by comparing side lengths.

Combined Validation and Classification — Algorithm Steps

Sort or compare sides to check triangle inequality efficiently
While validating, track equality relationships
Return result based on validation and equality pattern

Visualization

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Step-by-Step Walkthrough

Sort Sides

Arrange sides in ascending order

Single Check

Check if smallest two sum > largest

Classify

Determine triangle type if valid

Code -

solution.c — C

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

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

char* solution(int a, int b, int c) {
    // Sort the sides to make validation easier
    int sides[3] = {a, b, c};
    qsort(sides, 3, sizeof(int), compare);
    int x = sides[0], y = sides[1], z = sides[2];
    
    // Check triangle inequality (only need to check if smallest two sum > largest)
    if (x + y <= z) {
        return "Invalid";
    }
    
    // Valid triangle - classify based on original sides
    if (a == b && b == c) {
        return "Equilateral";
    } else if (a == b || b == c || a == c) {
        return "Isosceles";
    } else {
        return "Scalene";
    }
}

int main() {
    int a, b, c;
    scanf("%d", &a);
    scanf("%d", &b);
    scanf("%d", &c);
    
    char* result = solution(a, b, c);
    printf("%s\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Still constant time but fewer total comparisons than brute force

✓ Linear Growth

Space Complexity

O(1)

Uses same amount of variables as brute force approach

✓ Linear Space

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Triangle Validator - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Combined Validation and Classification — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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