Next Permutation of Array in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the goal of the Next Permutation algorithm?

To rearrange numbers into the lexicographically next greater permutation of numbers. If such arrangement is not possible, it rearranges it as the lowest possible order (sorted in ascending order).

intermediate

In the Next Permutation algorithm, what is the significance of finding the first decreasing element from the right?

It identifies the pivot point where we can make a change to get the next bigger permutation. This element is the first one that can be swapped to increase the sequence.

intermediate

Why do we reverse the suffix after swapping in the Next Permutation algorithm?

Because the suffix after the pivot is in descending order, reversing it makes it the smallest ascending order, ensuring the next permutation is just one step bigger.

beginner

What happens if the entire array is in descending order in the Next Permutation algorithm?

It means the current permutation is the highest possible. The algorithm then reverses the entire array to get the lowest possible order (ascending order).

intermediate

Show the step-by-step transformation of the array [1, 3, 2] using the Next Permutation algorithm.

1. Find pivot: from right, 1 < 3 (pivot at index 0) 2. Find element just larger than pivot: 2 at index 2 3. Swap pivot and this element: [2, 3, 1] 4. Reverse suffix after pivot: suffix is [3, 1], reversed to [1, 3] 5. Result: [2, 1, 3]

What is the first step in finding the next permutation of an array?

A Find the first element from the right that is smaller than the element next to it

B Reverse the entire array

C Sort the array in ascending order

D Swap the first and last elements

The first step is to find the pivot, which is the first element from the right that is smaller than its next element.

If no pivot is found (array is in descending order), what should the next permutation be?

A The array sorted in descending order

B The array reversed (ascending order)

C The same array

D Swap first two elements

If the array is in descending order, it is the highest permutation, so the next permutation is the lowest, which is the reversed array (ascending order).

After swapping the pivot with the next larger element, what is the next step?

A Swap the first and last elements

B Sort the entire array

C Reverse the suffix after the pivot

D Do nothing

Reversing the suffix after the pivot ensures the suffix is in ascending order, giving the next smallest permutation.

What is the time complexity of the Next Permutation algorithm?

A O(n)

B O(n^2)

C O(log n)

D O(1)

The algorithm scans the array a few times linearly, so the time complexity is O(n).

Given the array [1, 2, 3], what is the next permutation?

A [1, 2, 3]

B [3, 2, 1]

C [2, 1, 3]

D [1, 3, 2]

The next permutation after [1, 2, 3] is [1, 3, 2].

Explain the steps of the Next Permutation algorithm in your own words.

Think about how to get the next bigger number by changing the array minimally.

Why do we reverse the suffix after swapping in the Next Permutation algorithm?

Consider the order of numbers after the pivot.