Lecture 11: Data Structures and Algorithms II

Quick Quiz — Binary Search

Binary search requires which of the following preconditions?

A) Array must be mutable B) Array must be sorted C) Array must contain distinct elements only D) Array length must be even

When inserting a value equal to an existing node, the implementation above places it to which side (as written)?

A) Left B) Right C) It replaces the node D) Insertion fails

In a 0-based array representation of a binary heap, the left child index for node i is:

A) 2*i + 1 B) 2*i C) i + 1 D) floor(i/2)

Which property is true for merge sort?

A) Stable and O(n log n) B) Unstable and O(n^2) C) In-place and O(log n) D) Stable and O(n^2)

Algorithm	Time Complexity	Space Complexity	Stable
Linear Search	O(n)	O(1)	N/A
Binary Search	O(log n)	O(1)	N/A
Heap Sort	O(n log n)	O(1)	No
Merge Sort	O(n log n)	O(n)	Yes

Heapsort is in-place, merge sort needs extra space but is stable.

Which algorithm guarantees O(n log n) worst-case time?

A) Merge Sort B) Quick Sort C) Bubble Sort D) Selection Sort