Is Add Two Polynomials Represented as Linked Lists easy or hard?

This problem is generally classified as Medium difficulty. The challenge comes from correctly merging nodes while handling equal powers and maintaining sorted order. Candidates comfortable with linked list traversal and two-pointer techniques usually solve it quickly.

Add Two Polynomials Represented as Linked Lists Python/Java solution

The typical implementation uses two pointers iterating through both linked lists while constructing a result list. The logic is identical across Python, Java, C++, and JavaScript: compare powers, merge matching terms, and append remaining nodes once one list ends.

How to solve Add Two Polynomials Represented as Linked Lists in O(n)?

Use two pointers to traverse both polynomial lists simultaneously. Compare the powers of the current nodes: if equal, sum the coefficients; otherwise append the node with the larger power. Continue until both lists are fully processed, resulting in a single pass through the data.

What is the best approach for Add Two Polynomials Represented as Linked Lists?

The two-pointer merge approach is the most efficient solution. Since both polynomial linked lists are sorted by decreasing power, you can traverse them simultaneously and merge terms with equal powers. This runs in O(n + m) time and uses O(1) extra space besides the result list.

Is Add Two Polynomials Represented as Linked Lists asked at Google/Amazon/Meta?

Polynomial and linked list merge problems frequently appear in interviews at companies like Amazon, Google, and Meta because they test pointer manipulation and algorithmic thinking. Variations of polynomial addition or merging sorted linked lists are common interview patterns.

What data structure is used in Add Two Polynomials Represented as Linked Lists?

The core data structure is a singly linked list where each node stores a coefficient and power of a polynomial term. The optimal solution uses pointer traversal similar to the merge step in merge sort and relies on the sorted order of the lists.

What is the time complexity of Add Two Polynomials Represented as Linked Lists?

The optimal solution runs in O(n + m) time, where n and m are the number of nodes in the two polynomial linked lists. Each node is visited once during the merge process. The space complexity is O(1) excluding the output list.

Description Hints 3 Solution Video 11:12

1634. Add Two Polynomials Represented as Linked Lists

Medium61.1% acceptance1 companyPremium elsewhere, free here

A polynomial linked list is a special type of linked list where every node represents a term in a polynomial expression.

Each node has three attributes:

coefficient: an integer representing the number multiplier of the term. The coefficient of the term 9x⁴ is 9.
power: an integer representing the exponent. The power of the term 9x⁴ is 4.
next: a pointer to the next node in the list, or null if it is the last node of the list.

For example, the polynomial 5x³ + 4x - 7 is represented by the polynomial linked list illustrated below:

The polynomial linked list must be in its standard form: the polynomial must be in strictly descending order by its power value. Also, terms with a coefficient of 0 are omitted.

Given two polynomial linked list heads, poly1 and poly2, add the polynomials together and return the head of the sum of the polynomials.

PolyNode format:

The input/output format is as a list of n nodes, where each node is represented as its [coefficient, power]. For example, the polynomial 5x³ + 4x - 7 would be represented as: [[5,3],[4,1],[-7,0]].

Example 1:


Input: poly1 = [[1,1]], poly2 = [[1,0]]

Output: [[1,1],[1,0]]

Explanation: poly1 = x. poly2 = 1. The sum is x + 1.

Example 2:


Input: poly1 = [[2,2],[4,1],[3,0]], poly2 = [[3,2],[-4,1],[-1,0]]

Output: [[5,2],[2,0]]

Explanation: poly1 = 2x² + 4x + 3. poly2 = 3x² - 4x - 1. The sum is 5x² + 2. Notice that we omit the "0x" term.

Example 3:


Input: poly1 = [[1,2]], poly2 = [[-1,2]]

Output: []

Explanation: The sum is 0. We return an empty list.

Constraints:

0 <= n <= 10⁴
-10⁹ <= PolyNode.coefficient <= 10⁹
PolyNode.coefficient != 0
0 <= PolyNode.power <= 10⁹
PolyNode.power > PolyNode.next.power

Asked at 1 company

Amazon

Topics

Hints open one at a time

Hint 1

Process both linked lists at the same time

Hint 2

If the current power of the two heads is equal, add this power with the sum of the coefficients to the answer list.

Hint 3

If one head has a larger power, add this power to the answer list and move only this head.

11:12

Still stuck?Read the written solution, or watch a walkthrough.

Open solution