Count Occurrences of Element in Sorted Array in DSA Go - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main advantage of using a sorted array to count occurrences of an element?

A sorted array allows us to use binary search to find the first and last positions of the element quickly, making the counting efficient.

intermediate

How do you find the first occurrence of an element in a sorted array?

Use binary search to find the element, but when found, continue searching to the left half to find the earliest index where the element appears.

beginner

How do you calculate the count of an element once you have the first and last occurrence indices?

Count = (last occurrence index - first occurrence index) + 1

beginner

Why is linear search not efficient for counting occurrences in a sorted array?

Linear search checks each element one by one, which takes O(n) time, while binary search uses the sorted property to reduce time to O(log n).

intermediate

What is the time complexity of counting occurrences of an element in a sorted array using binary search?

O(log n) because binary search is used twice to find the first and last occurrences.

What is the first step to count occurrences of an element in a sorted array?

A Find the first occurrence of the element using binary search

B Count elements by scanning the whole array

C Sort the array first

D Find the maximum element

We start by finding the first occurrence of the element using binary search to leverage the sorted property.

If the first occurrence of element 5 is at index 2 and last occurrence is at index 4, what is the count?

A 4

B 2

C 3

D 5

Count = (4 - 2) + 1 = 3

Which search method is best for counting occurrences in a sorted array?

A Linear search

B Breadth-first search

C Depth-first search

D Binary search

Binary search efficiently finds positions in O(log n) time in sorted arrays.

What happens if the element is not found in the array?

A Count is zero

B Count is one

C Count is array length

D Count is negative

If the element is not found, its count is zero.

How many times do we perform binary search to count occurrences?

A Once

B Twice

C Three times

D Four times

We perform binary search twice: once for the first occurrence and once for the last occurrence.

Explain how to count occurrences of an element in a sorted array using binary search.

Think about finding boundaries of the element's positions.

Why is binary search preferred over linear search for counting occurrences in a sorted array?

Consider time complexity and array order.