Introduction

In this blog post, we will explore how to solve the LeetCode problem "1537" 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 two sorted arrays of distinct integers nums1 and nums2. A valid path is defined as follows: Choose array nums1 or nums2 to traverse (from index-0). Traverse the current array from left to right. If you are reading any value that is present in nums1 and nums2 you are allowed to change your path to the other array. (Only one repeated value is considered in the valid path). The score is defined as the sum of unique values in a valid path. Return the maximum score you can obtain of all possible valid paths. Since the answer may be too large, return it modulo 109 + 7. Example 1: Input: nums1 = [2,4,5,8,10], nums2 = [4,6,8,9] Output: 30 Explanation: Valid paths: [2,4,5,8,10], [2,4,5,8,9], [2,4,6,8,9], [2,4,6,8,10], (starting from nums1) [4,6,8,9], [4,5,8,10], [4,5,8,9], [4,6,8,10] (starting from nums2) The maximum is obtained with the path in green [2,4,6,8,10]. Example 2: Input: nums1 = [1,3,5,7,9], nums2 = [3,5,100] Output: 109 Explanation: Maximum sum is obtained with the path [1,3,5,100]. Example 3: Input: nums1 = [1,2,3,4,5], nums2 = [6,7,8,9,10] Output: 40 Explanation: There are no common elements between nums1 and nums2. Maximum sum is obtained with the path [6,7,8,9,10]. Constraints: 1 <= nums1.length, nums2.length <= 105 1 <= nums1[i], nums2[i] <= 107 nums1 and nums2 are strictly increasing.

Explanation

Here's the breakdown of the solution:

• Identify Common Elements: Iterate through both arrays simultaneously to find common elements.
• Calculate Path Sums: At each common element, calculate the sum of the path up to that point in both arrays. Choose the larger sum to maximize the score.

• Accumulate and Modulo: Accumulate the maximum sum along the way and apply the modulo operator to prevent overflow.

• Runtime Complexity: O(m + n), where m and n are the lengths of nums1 and nums2, respectively.

• Storage Complexity: O(1).

Code

    def max_sum(nums1, nums2):
    """
    Calculates the maximum score of a valid path through two sorted arrays.

    Args:
        nums1: The first sorted array of distinct integers.
        nums2: The second sorted array of distinct integers.

    Returns:
        The maximum score modulo 10^9 + 7.
    """
    n1 = len(nums1)
    n2 = len(nums2)
    i = 0
    j = 0
    sum1 = 0
    sum2 = 0
    result = 0
    MOD = 10**9 + 7

    while i < n1 or j < n2:
        if i < n1 and (j == n2 or nums1[i] < nums2[j]):
            sum1 += nums1[i]
            i += 1
        elif j < n2 and (i == n1 or nums2[j] < nums1[i]):
            sum2 += nums2[j]
            j += 1
        else:
            # nums1[i] == nums2[j]
            result += max(sum1, sum2) + nums1[i]
            result %= MOD
            sum1 = 0
            sum2 = 0
            i += 1
            j += 1

    result += max(sum1, sum2)
    result %= MOD
    return result