Count Inversions in Array in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is an inversion in an array?

An inversion is a pair of elements where the first element is greater than the second element, but the first element appears before the second in the array.

beginner

Why do we count inversions in an array?

Counting inversions helps measure how far the array is from being sorted. It is useful in sorting algorithms and understanding array disorder.

beginner

What is the naive way to count inversions in an array?

Check every pair of elements and count if the first is greater than the second. This takes O(n²) time for an array of size n.

intermediate

How does the merge sort method help count inversions efficiently?

During merge sort, while merging two sorted halves, we count how many elements from the right half are placed before elements from the left half. This counts inversions in O(n log n) time.

intermediate

What is the time complexity of counting inversions using merge sort?

The time complexity is O(n log n), where n is the size of the array.

What does an inversion in an array represent?

A A pair where the first element is smaller and appears before the second

B Any two elements in the array

C Two equal elements in the array

D A pair where the first element is greater and appears before the second

An inversion is specifically when a larger element appears before a smaller one.

What is the time complexity of the naive method to count inversions?

A O(n)

B O(n log n)

C O(n²)

D O(log n)

The naive method checks all pairs, leading to O(n²) time.

Which sorting algorithm is commonly used to count inversions efficiently?

A Merge Sort

B Insertion Sort

C Bubble Sort

D Selection Sort

Merge Sort can count inversions during the merge step efficiently.

During merge sort, when do we count inversions?

A When merging two sorted halves

B After sorting completes

C Before sorting starts

D When splitting the array

Inversions are counted while merging two sorted halves.

What does a high number of inversions in an array indicate?

A The array is nearly sorted

B The array is highly unsorted

C The array is completely sorted

D The array has duplicates

More inversions mean the array is more unsorted.

Explain how merge sort can be used to count inversions in an array.

Think about how merging two sorted lists can reveal inversions.

Describe the difference between the naive and efficient methods to count inversions.

Focus on time complexity and approach.