HardCompleted

Longest Increasing Subsequence

Dynamic programming optimization problem

Overall Grade

Performance Overview

Time Taken

45 minutes

Complexity Accuracy

Poor

Edge Cases Discussed

Alternative Solutions

Your Solution

function lengthOfLIS(nums) {
    let maxLength = 1;
    
    for (let i = 0; i < nums.length; i++) {
        let currentLength = 1;
        let lastNum = nums[i];
        
        for (let j = i + 1; j < nums.length; j++) {
            if (nums[j] > lastNum) {
                currentLength++;
                lastNum = nums[j];
            }
        }
        
        maxLength = Math.max(maxLength, currentLength);
    }
    
    return maxLength;
}

Incorrect algorithm - greedy approach

O(n²) time complexity, not optimal

Misses optimal substructure

AI Feedback

Critical Issues

• Used greedy approach instead of dynamic programming
• Algorithm produces incorrect results for many inputs
• Missed the optimal substructure property
• No consideration of overlapping subproblems

What You Missed

This is a classic DP problem. The key insight is that for each position, you need to consider all previous elements that are smaller and build upon their LIS lengths.

Study Recommendations

• Review dynamic programming fundamentals
• Practice identifying optimal substructure
• Study the O(n log n) binary search solution
• Work through more DP problems step by step

Correct DP Solution

function lengthOfLIS(nums) {
    if (nums.length === 0) return 0;
    
    const dp = new Array(nums.length).fill(1);
    
    for (let i = 1; i < nums.length; i++) {
        for (let j = 0; j < i; j++) {
            if (nums[j] < nums[i]) {
                dp[i] = Math.max(dp[i], dp[j] + 1);
            }
        }
    }
    
    return Math.max(...dp);
}

Key insight: dp[i] represents the length of the longest increasing subsequence ending at index i. For each position, we check all previous positions and extend their LIS if the current element is larger.

Detailed Performance Metrics

Problem Understanding45%

Code Quality35%

Communication55%

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