Minimum increment in the sides required to get non-negative area of a triangle
Given three sides of the triangle, find the minimum increase in the length of the side of the triangle to make the area of the triangle non-negative.
Examples:
Input: a = 3, b = 4, c = 10
Output: 3
With the given sides, the area is negative.
If a is increased to 5 and b to 5, then the area becomes 0, which is not negative.Input: a = 6, b = 6, c = 10
Output: 2
Approach: Since the area of any triangle is non-negative if the sum of the smallest two sides is always greater than or equal to the third side, hence the following steps should be followed to solve the above problem:
- Sort the three sides in increasing order.
- Check if the sum of the first two sides is greater than or equal to the third side, if it is, then the answer is 0.
- If it is not, then the answer will be (third side – (first side + second side)).
Below is the implementation of the given approach.
C++
// C++ program to find Minimum // increase in sides to get // non-negative area of a triangle #include <bits/stdc++.h> using namespace std; // Function to return the minimum increase in side // lengths of the triangle int minimumIncrease( int a, int b, int c) { // push the three sides to a array int arr[] = { a, b, c }; // sort the array sort(arr, arr + 3); // check if sum is greater than third side if (arr[0] + arr[1] >= arr[2]) return 0; else return arr[2] - (arr[0] + arr[1]); } // Driver Code int main() { int a = 3, b = 5, c = 10; cout << minimumIncrease(a, b, c); return 0; } |
Java
// Java Program to find Minimum // increment in the sides required // to get non-negative area of // a triangle import java.util.*; class GFG { static int minimumIncrease( int a, int b, int c) { // push the three sides // to a array int arr[] = { a, b, c }; // sort the array Arrays.sort(arr); // check if sum is greater // than third side if (arr[ 0 ] + arr[ 1 ] >= arr[ 2 ]) return 0 ; else return arr[ 2 ] - (arr[ 0 ] + arr[ 1 ]); } // Driver Code public static void main (String[] args) { int a = 3 , b = 5 , c = 10 ; System.out.println(minimumIncrease(a, b, c)); } } // This code is contributed // by Shashank |
Python 3
# Python program to find Minimum # increase in sides to get # non-negative area of a triangle # Function to return the # minimum increase in side # lengths of the triangle def minimumIncrease(a, b, c) : # push the three sides # to a array arr = [ a, b, c ] # sort the array arr.sort() # check if sum is greater # than third side if arr[ 0 ] + arr[ 1 ] > = arr[ 2 ] : return 0 else : return arr[ 2 ] - (arr[ 0 ] + arr[ 1 ]) # Driver code if __name__ = = "__main__" : a, b, c = 3 , 5 , 10 print (minimumIncrease(a, b, c)) # This code is contributed # by ANKITRAI1 |
C#
// C# Program to find Minimum // increment in the sides required // to get non-negative area of // a triangle using System; class GFG { static int minimumIncrease( int a, int b, int c) { // push the three sides // to a array int [] arr = { a, b, c }; // sort the array Array.Sort(arr); // check if sum is greater // than third side if (arr[0] + arr[1] >= arr[2]) return 0; else return arr[2] - (arr[0] + arr[1]); } // Driver Code public static void Main () { int a = 3, b = 5, c = 10; Console.Write(minimumIncrease(a, b, c)); } } // This code is contributed // by ChitraNayal |
PHP
<?php // PHP program to find Minimum // increase in sides to get // non-negative area of a triangle // Function to return the // minimum increase in side // lengths of the triangle function minimumIncrease( $a , $b , $c ) { // push the three sides to a array $arr = array ( $a , $b , $c ); // sort the array sort( $arr ); // check if sum is greater // than third side if ( $arr [0] + $arr [1] >= $arr [2]) return 0; else return $arr [2] - ( $arr [0] + $arr [1]); } // Driver Code $a = 3; $b = 5; $c = 10; echo minimumIncrease( $a , $b , $c ); // This code is contributed // by ChitraNayal ?> |
Javascript
<script> // Javascript Program to find Minimum // increment in the sides required // to get non-negative area of // a triangle function minimumIncrease(a , b , c) { // push the three sides // to a array var arr = [ a, b, c ]; // sort the array arr.sort((a,b)=>a-b); // check if sum is greater // than third side if (arr[0] + arr[1] >= arr[2]) return 0; else return arr[2] - (arr[0] + arr[1]); } // Driver Code var a = 3, b = 5, c = 10; document.write(minimumIncrease(a, b, c)); // This code contributed by aashish1995 </script> |
Output
2
complexity Analysis:
- Time Complexity: O(1)
- Auxiliary Space: O(1)