Introduction

In this blog post, we will explore how to solve the LeetCode problem "1439" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given an m x n matrix mat that has its rows sorted in non-decreasing order and an integer k. You are allowed to choose exactly one element from each row to form an array. Return the kth smallest array sum among all possible arrays. Example 1: Input: mat = [[1,3,11],[2,4,6]], k = 5 Output: 7 Explanation: Choosing one element from each row, the first k smallest sum are: [1,2], [1,4], [3,2], [3,4], [1,6]. Where the 5th sum is 7. Example 2: Input: mat = [[1,3,11],[2,4,6]], k = 9 Output: 17 Example 3: Input: mat = [[1,10,10],[1,4,5],[2,3,6]], k = 7 Output: 9 Explanation: Choosing one element from each row, the first k smallest sum are: [1,1,2], [1,1,3], [1,4,2], [1,4,3], [1,1,6], [1,5,2], [1,5,3]. Where the 7th sum is 9. Constraints: m == mat.length n == mat.length[i] 1 <= m, n <= 40 1 <= mat[i][j] <= 5000 1 <= k <= min(200, nm) mat[i] is a non-decreasing array.

Explanation

Here's a breakdown of the solution:

• Iterative Approach: Start with the first row of the matrix. In each subsequent row, merge the current set of smallest sums with the elements of the next row, keeping only the k smallest sums resulting from the merge.

• Heap-based Merging: Use a min-heap to efficiently find the k smallest sums when merging two arrays of sums. This avoids generating all possible sums and then sorting.

• Limit Sums: We don't need to compute all possible array sums. Since we only need the k-th smallest, we only need to keep track of at most k smallest sums at each step.

• Runtime and Space Complexity: O(m * k * log(k)), O(k). m is the number of rows, and k is the target number of smallest sums.

Code

    import heapq

def kth_smallest_matrix_sum(mat, k):
    """
    Finds the kth smallest array sum among all possible arrays formed by choosing
    one element from each row of the given matrix.

    Args:
        mat (list[list[int]]): A matrix of sorted rows.
        k (int): The desired rank of the smallest sum.

    Returns:
        int: The kth smallest array sum.
    """

    m = len(mat)
    n = len(mat[0])

    # Initialize the smallest sums with the first row.
    smallest_sums = mat[0]

    # Iterate through the remaining rows.
    for i in range(1, m):
        next_smallest_sums = []
        for j in range(len(smallest_sums)):
            for l in range(len(mat[i])):
                next_smallest_sums.append(smallest_sums[j] + mat[i][l])

        next_smallest_sums.sort()  # Sort the sums to get the smallest k sums
        smallest_sums = next_smallest_sums[:min(k, len(next_smallest_sums))]


    return smallest_sums[k - 1]