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Solve Matrix Traversal and Pair Sum

IllumioSoftware Engineer · Onsite
MediumSoftware EngineerOnsiteCoding & Algorithms

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This problem tests your ability to manipulate 2D matrix indices for spiral traversal and apply efficient hash-based lookups to solve the two-sum problem within a specific sequence.

Problem Statement

Given an n x n matrix, perform a spiral traversal of the elements starting from the top-left corner and moving clockwise. As you traverse the elements, store the visited values in a list. Once you have the flattened list of all matrix elements, find if there exists a pair of numbers in this list that sums up to a target value k.

Function Signature

def solve_spiral_and_pair_sum(matrix, k):
    # Returns True if a pair exists that sums to k, otherwise False

Constraints

  • n is between 1 and 100.
  • Matrix elements are integers between -10^4 and 10^4.
  • k is an integer between -210^4 and 210^4.

Examples

Example 1: Input:

matrix = [[1, 2], [3, 4]]
k = 7

Spiral order: [1, 2, 4, 3]. Pair (3, 4) sums to 7. Output: True

Example 2: Input:

matrix = [[1, 1], [1, 1]]
k = 3

Spiral order: [1, 1, 1, 1]. No two 1s sum to 3. Output: False

Edge Cases

  • Empty matrix or single-element matrix.
  • Matrices with duplicate values.
  • k values that are unreachable by any two elements.

Hints

Hint 1

To perform spiral traversal, maintain four boundaries: top, bottom, left, and right, and update them after processing each row or column.

Hint 2

Once you have the flattened list, you can use a hash set to store seen numbers and check for the existence of `k - current_number` in one pass.

Hint 3

Consider the constraints to ensure your time complexity is O(n^2) and your space complexity is O(n^2) for storing the matrix elements.

Follow-up questions

  • How would you optimize the space complexity if you were required to find the pair sum without explicitly creating the full flattened list?
  • If the matrix were significantly larger than memory, how would you approach the traversal to minimize I/O operations?
  • What changes would be required if the goal was to find a triplet that sums to k instead of a pair?