Recurrence equations describing the work done during recursion are only useful for divide and conquer algorithm analysisQuestion 10Select one:TrueFalse

The statement is True. Recurrence equations are often used to describe the work done during recursion, especially in the context of divide and conquer algorithms. This is because divide and conquer approaches typically break a problem into smaller subproblems, solve them independently, and then combine their results. This process, structured recursively, naturally leads to recurrence relations that can capture the time complexity effectively.

For example, the classic merge sort algorithm can be analyzed using the recurrence relation $T(n) = 2T\left(\frac{n}{2}\right) + O(n)$, where $T(n)$ represents the time complexity of sorting $n$ elements, $2T\left(\frac{n}{2}\right)$ accounts for the recursive calls on the two halves of the array, and $O(n)$ represents the linear time needed to merge the sorted halves. Thus, recurrence equations are particularly suitable for analyzing algorithms that utilize recursion in a divide and conquer manner.