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. Hereβs a detailed explanation of the methodology for solving this problem, along with corresponding pseudocode incorporating extensive comments.
Explanation
Understanding the Problem:
- Objective : Combine digits from both input arrays \( nums1 \) and \( nums2 \) to form the largest possible number of length \( k \).
- 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 \( nums2 \).
- Select Subarrays : Determine the best subarrays from both \( nums1 \) and \( nums2 \) of varying lengths that sum to \( k \).
- Merge Subarrays : Combine the optimal subarrays in a manner that preserves their internal order but results in the maximum overall number.
- Maximize Number : Select the maximum possible number through comparisons and by forming candidate solutions.
- 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 \( k \).
- Merge Two Subarrays :
- While merging two subarrays, always select the larger leading digit from the remaining parts of the subarrays.
- Generate and Compare Results :
- Iterate over all possible divisions of \( k \) between \( nums1 \) and \( nums2 \) and determine the best combination through comparisons.
Key Steps:
Detailed Steps:
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.