Maximum Sum Path in Two Arrays

In this article, we will solve the problem of finding the sum of the maximum sum path in two sorted arrays having some elements in common.

Problem Statement: Given two sorted arrays, where some elements are common between them, find the sum of the maximum sum path from the beginning of either array to the end of either array. You can switch from one array to the other at any of the common elements.

Example:

Input: array1 = [2, 3, 7, 10, 12], array2 = [1, 5, 7, 8]

Output: 35

Explanation: The maximum sum path is 1 + 5 + 7 + 8 + 10 + 12 = 35.

Solution:

To solve this problem, we will use the following approach:

1.    Initialize Pointers and Sums:

• Initialize two pointers, one for each array.

• Initialize two sums to keep track of the sums of elements traversed in each array.

2.    Traverse Both Arrays:

• Traverse both arrays using the pointers.

• If the current element of array1 is smaller than the current element of array2, add the element of array1 to the sum of array1 and move the pointer of array1 forward.

• If the current element of array2 is smaller than the current element of array1, add the element of array2 to the sum of array2 and move the pointer of array2 forward.

• If the current elements of both arrays are equal, add the maximum of the two sums (plus the common element) to the result, reset the sums, and move both pointers forward.

3.    Add Remaining Elements:

• After the traversal, add the remaining elements of both arrays to their respective sums and add the maximum of the two sums to the result.

Time Complexity: O(n1 + n2)

Space Complexity: O(1)