Create Maximum Number

To solve this coding challenge, we need to create the maximum number of length \( k \) from two given integer arrays \( nums1 \) and \( nums2 \), while ensuring that the relative order of digits from the same array is preserved. Here’s a detailed explanation of the methodology for solving this problem, along with corresponding pseudocode incorporating extensive comments.

Explanation

Understanding the Problem:
  1. Objective : Combine digits from both input arrays \( nums1 \) and \( nums2 \) to form the largest possible number of length \( k \).
  2. Constraints :
    • Digits from each array must maintain their relative order.
    • The length \( k \) can range from 1 to the sum of lengths of \( nums1 \) and \( nums2 \).
    Key Steps:
  3. Select Subarrays : Determine the best subarrays from both \( nums1 \) and \( nums2 \) of varying lengths that sum to \( k \).
  4. Merge Subarrays : Combine the optimal subarrays in a manner that preserves their internal order but results in the maximum overall number.
  5. Maximize Number : Select the maximum possible number through comparisons and by forming candidate solutions.
  6. Detailed Steps:
  7. Function to Create Maximum Subarray :
    • Use a stack to keep track of the largest possible digits while considering the deletions required to form a subarray of exact length \( k \).
  8. Merge Two Subarrays :
    • While merging two subarrays, always select the larger leading digit from the remaining parts of the subarrays.
  9. Generate and Compare Results :
    • Iterate over all possible divisions of \( k \) between \( nums1 \) and \( nums2 \) and determine the best combination through comparisons.
Pseudocode
Function to Form Maximum Subarray:
                                            
# Function to form the largest number of length `length` from `array`
function maxSubarray(array, length):
    initialize stack as empty list
    initialize drop as len(array) - length
    
    for each digit in array:
        # Ensure forming the largest number by comparing and possibly dropping smaller elements
        while drop > 0 and stack is not empty and stack[-1] < digit:
            pop from stack
            decrement drop by 1
        
        # Add the current digit to stack
        push digit to stack
    
    # Return the subarray of required length from stack
    return stack[0:length]

                                        
Function to Merge Two Subarrays:
                                            
# Function to merge two subarrays maintaining order
function merge(subarray1, subarray2):
    initialize merged_list as empty list
    
    while subarray1 is not empty or subarray2 is not empty:
        # Choose the larger leading digit and append it to merged_list
        if subarray1 > subarray2:
            append subarray1[0] to merged_list
            subarray1 = subarray1[1:]
        else:
            append subarray2[0] to merged_list
            subarray2 = subarray2[1:]
    
    return merged_list

                                        
Main Function to Solve the Challenge:
                                            
# Main function to solve the problem
function createMaximumNumber(nums1, nums2, k):
    initialize result as empty list
    
    for i from max(0, k - len(nums2)) to min(k, len(nums1)) + 1:
        subarray1 = maxSubarray(nums1, i)
        subarray2 = maxSubarray(nums2, k - i)
        
        # Merge the two subarrays to form a larger combined number
        merged_list = merge(subarray1, subarray2)
        
        # Compare and update the result
        if merged_list > result:
            result = merged_list
    
    return result

                                        

Detailed Steps in Pseudocode

  • maxSubarray function is designed to form the largest possible subarray by leveraging a strategy that involves using a stack and removing smaller elements when necessary.
  • merge function is responsible for combining two subarrays, continually appending the larger front element to ensure the resulting array is the largest possible.
  • createMaximumNumber iteratively selects subarrays from \( nums1 \) and \( nums2 \), merges them, and keeps track of the maximum array found throughout the iterations.
This structured approach ensures that all potential subarray configurations are explored, and the optimal solution is found, adhering both to the challenge constraints and the problem requirements.