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Right Angle Triangle

Check if three given side lengths form a right-angled triangle using the Pythagorean theorem

Understand the Problem

Problem Statement

Given the lengths of three sides of a triangle (A, B, C), determine if the triangle is a right-angled triangle. A triangle is right-angled if the square of the longest side equals the sum of squares of the other two sides (Pythagorean theorem: a² + b² = c²).

Constraints

  • 1 ≤ A, B, C ≤ 9999
  • All inputs are positive integers representing side lengths
  • The triangle inequality must be satisfied for a valid triangle

Examples

Example 1
Input
5
3
4
Output
YES
Explanation

The sides are 3, 4, and 5. Sorting them gives 3, 4, 5. Checking: 3² + 4² = 9 + 16 = 25 = 5². Since 3² + 4² = 5², this forms a right-angled triangle.

Example 2
Input
11
6
9
Output
NO
Explanation

The sides are 6, 9, and 11. Sorting them gives 6, 9, 11. Checking: 6² + 9² = 36 + 81 = 117, but 11² = 121. Since 6² + 9² ≠ 11², this does not form a right-angled triangle.

Solution

#include <stdio.h>
#include <math.h>

int main() {
    int a, b, c;
    scanf("%d %d %d", &a, &b, &c);
    
    // Sort the sides to identify the largest
    if (a > b) {
        int temp = a;
        a = b;
        b = temp;
    }
    if (b > c) {
        int temp = b;
        b = c;
        c = temp;
    }
    if (a > b) {
        int temp = a;
        a = b;
        b = temp;
    }
    
    // Check Pythagorean theorem: a² + b² = c²
    if (a*a + b*b == c*c) {
        printf("YES\n");
    } else {
        printf("NO\n");
    }
    
    return 0;
}
Time:O(1) - Constant time operations regardless of input size
Space:O(1) - Uses only a fixed number of integer variables
Approach:

The C solution follows these steps:

  1. Read three integers representing the side lengths
  2. Sort the three values using simple swap operations to identify the longest side (c)
    3. <3>Check if a² + b² equals c² using integer arithmetic
  3. Print "YES" if the Pythagorean theorem holds, otherwise "NO"

The sorting ensures we always compare the two shorter sides against the longest side.

Visual Explanation

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