Type of Triangle

Type of Triangle - Problem

You are given a 0-indexed integer array nums of size 3 which can form the sides of a triangle.

A triangle is called:

Equilateral if it has all sides of equal length
Isosceles if it has exactly two sides of equal length
Scalene if all its sides are of different lengths

Return a string representing the type of triangle that can be formed or "none" if it cannot form a triangle.

Input & Output

Example 1 — Equilateral Triangle

$ Input: nums = [3,3,3]

› Output: "equilateral"

💡 Note: All three sides are equal (3 = 3 = 3), and they satisfy triangle inequality (3+3 > 3), so it forms an equilateral triangle.

Example 2 — Isosceles Triangle

$ Input: nums = [3,4,3]

› Output: "isosceles"

💡 Note: Two sides are equal (3 = 3), and triangle inequality holds (3+3 > 4), so it forms an isosceles triangle.

Example 3 — Invalid Triangle

$ Input: nums = [1,2,3]

› Output: "none"

💡 Note: Triangle inequality fails: 1+2 = 3, which is not greater than 3, so these sides cannot form a triangle.

Constraints

nums.length == 3
1 ≤ nums[i] ≤ 10⁹

Visualization

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Asked in

a Amazon 15 M Microsoft 12

The key insight is to first check the triangle inequality (sum of any two sides > third side) to ensure a valid triangle can be formed. Then classify by comparing sides: all equal = equilateral, two equal = isosceles, all different = scalene. Best approach is direct comparison with Time: O(1), Space: O(1).

Common Approaches

✓ Direct Comparison

⏱️ Time: O(1) Space: O(1)

First verify triangle inequality for all three combinations of sides. Then check if all sides are equal (equilateral), exactly two are equal (isosceles), or all different (scalene).

Sort and Compare

⏱️ Time: O(1) Space: O(1)

Sort the three sides in ascending order, then check triangle inequality only once (a+b>c). After validation, compare sides to determine triangle type.

Direct Comparison — Algorithm Steps

Step 1: Check triangle inequality: a+b>c, a+c>b, b+c>a
Step 2: If valid, count equal sides to determine triangle type
Step 3: Return appropriate triangle type or 'none'

Visualization

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Step-by-Step Walkthrough

Triangle Inequality Check

Verify a+b>c, a+c>b, b+c>a

Side Comparison

Compare sides to determine triangle type

Result

Return triangle type or 'none'

Code -

solution.c — C

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

char* solution(int* nums) {
    int a = nums[0], b = nums[1], c = nums[2];
    
    // Check triangle inequality
    if (a + b <= c || a + c <= b || b + c <= a) {
        return "none";
    }
    
    // Check triangle type
    if (a == b && b == c) {
        return "equilateral";
    } else if (a == b || b == c || a == c) {
        return "isosceles";
    } else {
        return "scalene";
    }
}

int main() {
    char line[100];
    fgets(line, sizeof(line), stdin);
    
    // Parse array manually
    int nums[3];
    char* token = strtok(line, "[,]");
    for (int i = 0; i < 3; i++) {
        nums[i] = atoi(token);
        token = strtok(NULL, "[,]");
    }
    
    char* result = solution(nums);
    printf("%s\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Fixed number of comparisons for 3 elements

✓ Linear Growth

Space Complexity

O(1)

Only using variables, no extra data structures

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Direct Comparison — Algorithm Steps

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Code -

Time & Space Complexity

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