```html Easy Problem

Python: Easy Problem

Thought Process

The Easy Problem requires finding the number of ways to represent a given number 'n' as a sum of two positive integers. Here are two approaches:

Approach 1: Brute Force - Use nested loops to iterate through all possible pairs of positive integers (i, j) such that i + j = n. Count the number of valid pairs and print the result.

Approach 2: Mathematical Optimization - Since the problem involves finding the number of ways to represent 'n' as a sum of two positive integers, we can directly calculate the result as n - 1. This is because for any number 'n', there are exactly n - 1 pairs of positive integers that sum up to 'n'.

Approach 1: Brute Force 

def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        cnt = 0
        for i in range(1, 101):
            for j in range(1, 101):
                if i + j == n:
                    cnt += 1
        print(cnt)

if __name__ == "__main__":
    main()

Approach 2: Mathematical Optimization 

def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        print(n - 1)

if __name__ == "__main__":
    main()

Code Complexity

Time Complexity: O(n2) & O(1)

Approach 1 uses nested loops, resulting in quadratic time complexity, while Approach 2 calculates the result in constant time.

Space Complexity: O(1)

Both approaches use constant extra space, making them highly efficient.

Code copied!
```