zyBooks_17_1
Suppose a recursive function's runtime is
T(n−1)+Θ(n){"version":"1.1","math":"T(n-1) + \Theta(n)"}
How many levels will the recursion tree have?

Question

zyBooks_17_1
Suppose a recursive function's runtime is 
T(n−1)+Θ(n){"version":"1.1","math":"T(n-1) + \Theta(n)"}
How many levels will the recursion tree have?

BlackTom AI · Accepted Answer

To determine how many levels the recursion tree has, we look at how the function calls itself: T(n) = T(n-1) + Θ(n). Each recursive step reduces the problem size by 1, so the depth of the recursion corresponds to how many times we can subtract 1 from n until we reach the base case. This means the recursion runs for n, n-1, n-2, ..., down to the base case, giving a total of n levels.

Option 1: n. This matches the intuitive depth of the tree since each level decreases the input by 1, resulting in a linear number of levels.

Option 2: nlogn. This would suggest a depth that grows faster than linear, which is not supported by a constant decrement of 1 per level. The log factor does not arise from the step n -> n-1.

Option 3: n^2. A quadratic depth would imply many more levels than the problem provides; the recurrence reduces n by 1 each time, so depth cannot be quadratic in n.

Option 4: logn. A logarithmic depth would occur if the size halved (or divided by a constant factor) at each step, not when it decreases by 1. Therefore, depth is not logarithmic here.

zyBooks_17_1 Suppose a recursive function's runtime is T(n−1)+Θ(n){"version":"1.1","math":"T(n-1) + \Theta(n)"} How many levels will the recursion tree have?

查看解析

登录即可查看完整答案

类似问题

Recr_4 Identify the recurrence relation for the binary_search function described below, which recursively searches for a value in a sorted list.

Recr_Q_6 What is the recurrence relation for the quick_sort function given below in the average case scenario as described below?

Recr_12 Identify the recurrence relation for the function shown below.

Ms_1 Consider the recurrence relation for an algorithm \(T(n)\) given by: \[ T(n) = \begin{cases} \Theta(1) & \text{if } n = 0 \\T\left(\frac{n}{2}\right) + \Theta(1) & \text{otherwise}\end{cases}\] The Master Theorem is provided below. Use it as you see fit:

Recr_1 What is the correct recurrence relation for the power function provided below, which calculates xn using a recursive divide-and-conquer approach?

zyB_17_1 Suppose a recursive function's runtime is T(n−1)+Θ(n){"version":"1.1","math":"T(n-1) + \Theta(n)"} How many levels will the recursion tree have?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单