The running time of an algorithm for inputs is given as follows: Here and are constants. Determine the Big-O complexity.

Explanation: To find the running time complexity, we solve the recurrence relation by expanding it: Given Substitute , so Continuing this pattern for steps: We continue the expansion until we reach the base case, where . This implies . Substituting this value into our equation: Since the base case is given as , we get: In Big-O notation, we focus on the dominant term as grows. Since and are constants, the term grows linearly with . Therefore, the time complexity is .

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WBJECA 2025 — Computer PYQ

WBJECA | Computer | 2025

The running time $T (n)$ of an algorithm for $n$ inputs is given as follows:

$T(n) = c + T(n-1), \text{ if } n > 1$

$T (n) = d, if n \leq 1$

Here $c$ and $d$ are constants. Determine the Big-O complexity.

Choose the correct answer: