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Longest Increasing Subsequence

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 10

Write a C# program to find the length of the longest strictly increasing subsequence in an array of integers. A subsequence is a sequence that can be derived from an array by deleting some or no elements without changing the order of the remaining elements.

Example 1
    
  
  • Input: nums = [10,9,2,5,3,7,101,18]
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  • Output: 4
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  • Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4.
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Example 2
    
  
  • Input: nums = [0,1,0,3,2,3]
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  • Output: 4
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  • Explanation: The longest increasing subsequence is [0,1,2,3], therefore the length is 4.
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Constraints
    
  
  • 1 ≤ nums.length ≤ 2500
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  • -10^4 ≤ nums[i] ≤ 10^4
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  • Time Complexity: O(n²)
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  • Space Complexity: O(n)
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ArraysDynamic Programming eBayOracle
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Hint
Solution
    
  
  • Consider using dynamic programming to solve this problem
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  • Create a DP array where dp[i] represents the length of the LIS ending at index i
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  • For each element, compare with all previous elements to find the longest chain
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  • The maximum value in the DP array will be your answer
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  • For better time complexity, consider using binary search
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Steps to solve by this approach:

 Step 1: Create a dynamic programming array dp where dp[i] represents the length of LIS ending at index i.
 Step 2: Initialize all values in dp array to 1 (minimum LIS length for any single element).
 Step 3: For each position i, compare with all previous positions j (where j < i).
 Step 4: If nums[i] > nums[j], update dp[i] = max(dp[i], dp[j] + 1).
 Step 5: Keep track of the maximum value in dp array during the process.
 Step 6: Return the maximum value as the longest increasing subsequence length.
 Step 7: For optimization, binary search can be used to achieve O(n log n) time complexity.

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