Add Two Polynomials Represented as Linked Lists

Add Two Polynomials Represented as Linked Lists - Problem

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 with nodes [[5,3],[4,1],[-7,0]].

The polynomial linked list must be in its standard form:

The polynomial must be in strictly descending order by its power value.
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]].

Input & Output

Example 1 — Basic Addition

$ Input: poly1 = [[1,2],[2,1]], poly2 = [[6,2],[4,1]]

› Output: [[7,2],[6,1]]

💡 Note: Both polynomials have terms with powers 2 and 1. For power 2: 1 + 6 = 7. For power 1: 2 + 4 = 6. Result is 7x² + 6x.

Example 2 — Different Powers

$ Input: poly1 = [[1,3]], poly2 = [[1,2],[1,1]]

› Output: [[1,3],[1,2],[1,1]]

💡 Note: No common powers, so all terms appear in the result: x³ + x² + x.

Example 3 — Coefficients Cancel Out

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

› Output: [[3,1],[1,0]]

💡 Note: Power 2 terms cancel: 2 + (-2) = 0, so only 3x + 1 remains.

Constraints

0 ≤ m, n ≤ 10⁴
-10⁹ ≤ poly1[i].coefficient, poly2[i].coefficient ≤ 10⁹
poly1[i].power > poly1[i+1].power
poly2[i].power > poly2[i+1].power

Visualization

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Asked in

G Google 15 a Amazon 12 M Microsoft 8

The key insight is to use two pointers to merge the polynomials like merging two sorted lists, comparing powers and adding coefficients for equal powers. The optimal two-pointer approach achieves O(m+n) time and O(m+n) space complexity.

Common Approaches

✓ Optimized

⏱️ Time: N/A Space: N/A

Convert to Arrays and Reconstruct

⏱️ Time: O((m+n) log(m+n)) Space: O(m+n)

Extract all terms from both polynomials into arrays, combine them, sort by power in descending order, then merge terms with the same power and reconstruct the linked list.

Two Pointers Merge

⏱️ Time: O(m+n) Space: O(m+n)

Since both polynomial linked lists are already sorted by power in descending order, we can use two pointers to traverse them simultaneously, comparing powers and merging terms as we go.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

⚡ Linearithmic Space

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Medium Frequency

~25 min Avg. Time

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Smart Actions

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