Question

Solve the following recurrence relations:
x(n) = x(n/2) + n, for n > 1 and x(1) = 0.

Answer 1

To solve the recurrence relation x(n) = x(n/2) + n, start by finding the base case value x(1) = 0. Then, use the equation to find the value of x(n) step by step.

Step-by-step explanation:

To solve the recurrence relation x(n) = x(n/2) + n, we can use a divide and conquer approach. We will first find the value of x(2) using the base case x(1) = 0. Then, we can find x(4) by substituting n = 2 into the equation. We can continue this process until we find the value of x(n).

To illustrate this with an example, let's find the value of x(4):

1. x(4) = x(2) + 4
2. Substituting x(2) = x(1) + 2 = 0 + 2 into the equation, we get x(4) = 2 + 4 = 6

Therefore, x(4) = 6. Similarly, you can find the value of x(n) for any given value of n.