Max Dot Product of Two Subsequences LeetCode Challenge

🚀 LeetCode Daily Challenge – Day 8 Problem #1458: Max Dot Product of Two Subsequences (Hard) This was by far one of the hardest problems I’ve worked on so far in my daily streak. 🧭 How I Approached the Question: At first, the problem looks similar to classic subsequence DP questions, but the non-empty subsequence constraint makes it tricky — especially when all values can be negative. A greedy approach doesn’t work here, so I knew this had to be solved using Dynamic Programming. 🧠 Key Idea: Let dp[i][j] represent the maximum dot product using subsequences from: first i elements of nums1 first j elements of nums2 For each pair of indices, I had three choices: Take both elements and extend a previous subsequence Skip current element of nums1 Skip current element of nums2 The most important insight: 👉 When starting a new subsequence, we should not carry forward negative values, so we use max(0, dp[i-1][j-1]). This ensures: The subsequence is non-empty We always keep the best possible dot product 🛠️ Transition: Multiply the current elements Either start fresh or extend a previous valid subsequence Compare with skipping options ⏱ Time Complexity: O(n × m) 📦 Space Complexity: O(n × m) This problem really tested my: DP fundamentals Edge case handling Patience 😄 👉 A great reminder that “Hard” problems are hard for a reason — but breaking them down step by step makes them manageable. 📌 Consistent practice, even when the problem feels overwhelming. #LeetCode #DailyCoding #DynamicProgramming #HardProblem #DSA #ProblemSolving #Python #CodingJourney #LearningInPublic

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