C++ program to count number of minutes needed to increase stick length to form a triangle

Suppose we have three numbers a, b and c. There are three sticks whose lengths are a, b and c. In one minute, we can pick one arbitrary stick and increase its length by 1 cm, but we cannot break sticks. We have to count the minimum number of minutes needed to increase their lengths and we can form a triangle with them.

So, if the input is like a = 2; b = 3; c = 5, then the output will be 1, because by increasing any one of a or b by 1, we can make a triangle (a + b) > c. So one minute is sufficient.

Steps

To solve this, we will follow these steps −

Define an array A = { a, b, c }
sort the array A
return maximum of (A[2] - A[1] - A[0] + 1) and 0

Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;

int solve(int a, int b, int c) {
   vector<int> A = { a, b, c };
   sort(A.begin(), A.end());
   return max(A[2] - A[1] - A[0] + 1, 0);
}
int main() {
   int a = 2;
   int b = 3;
   int c = 5;
   cout << solve(a, b, c) << endl;
}

Input

2, 3, 5

Output

1