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Create Maximum Number

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C program to create the maximum number by picking k digits from two given arrays nums1 and nums2. The relative order of the digits from the same array must be preserved. Return an array of length k representing the largest number you can create.

Example 1
    
            
  • Input: nums1 = [3,4,6,5], nums2 = [9,1,2,5,8,3], k = 5
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  • Output: [9,8,6,5,3]
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  • Explanation: 
    • Need to pick 5 digits total from both arrays. 
    • Try different combinations: 0 from nums1 + 5 from nums2, 1 from nums1 + 4 from nums2, etc. 
    • Best combination is 2 from nums1 ([6,5]) and 3 from nums2 ([9,8,3]). 
    • Merge to get [9,8,6,5,3] which is the maximum possible.
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Example 2
    
            
  • Input: nums1 = [6,7], nums2 = [6,0,4], k = 5
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  • Output: [6,7,6,0,4]
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  • Explanation: 
    • Need all 5 digits from both arrays (2 + 3 = 5). 
    • Take all from nums1 ([6,7]) and all from nums2 ([6,0,4]). 
    • Merge arrays to maximize result: [6,7,6,0,4]. 
    • This gives the maximum number possible with k=5 digits.
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Constraints
    
            
  • 1 ≤ nums1.length, nums2.length ≤ 500
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  • 1 ≤ nums1.length + nums2.length ≤ 1000
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  • 0 ≤ nums1[i], nums2[i] ≤ 9
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  • 1 ≤ k ≤ nums1.length + nums2.length
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  • Time Complexity: O(k*(m+n)^2) where m, n are array lengths
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  • Space Complexity: O(k) for result array
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NumberHCL TechnologiesD. E. Shaw
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Hint
Solution

Solution Hints

    
            
  • You hve to try all possible ways to distribute k digits between the two arrays
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  • For each distribution, find maximum subsequence of required length from each array
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  • Use a stack-based approach to find maximum subsequence maintaining relative order
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  • Merge the two maximum subsequences to create the final maximum number
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  • Compare different combinations and return the lexicographically largest result
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  • When merging, always pick the digit that makes the result larger
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  • Handle edge cases where one array contributes 0 digits
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Steps to solve by this approach:

 Step 1: Iterate through all possible ways to distribute k digits between nums1 and nums2 arrays

 Step 2: For each distribution (i digits from nums1, k-i digits from nums2), find maximum subsequence from each array

 Step 3: Use stack-based greedy approach to extract maximum subsequence while maintaining relative order

 Step 4: Merge the two maximum subsequences by always choosing the digit that creates larger result

 Step 5: When merging equal digits, look ahead in both arrays to determine which contributes to larger number

 Step 6: Compare all possible merged results and keep track of the lexicographically largest one

 Step 7: Return the maximum number found across all possible distributions of k digits

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