12 posts tagged with "Algorithms"

A conversation about solving the Minimum Coin Combination problem that reveals why greedy algorithms sometimes fail—and how recognizing overlapping subproblems is the foundation of dynamic programming thinking.

A conversation about solving the LRU Cache problem that reveals one of the most elegant hybrid data structure designs—and why sometimes the "crazy" idea of combining two data structures is actually brilliant.

A conversation about solving the Widest Binary Tree Level problem that reveals how mathematical position formulas and DFS traversal create an elegant solution—and why we need to track both min and max positions at each level.

A conversation about solving the Subarray Sum Equals K problem that reveals how cumulative sums and hashmaps create an elegant O(n) solution—and why we need that mysterious map.put(0, 1) initialization.

A conversation between two engineers about the Range Sum Query problem that reveals why some algorithmic techniques exist—and when they actually matter.

Want to truly understand dynamic programming? This isn't just another tutorial with code solutions. We'll explore why these algorithms work, how they connect to other problems, and when to apply them. By the end, you'll think like a DP expert.

A dialogue between Professor Chen and Alex, a senior Computer Science student, as they unravel why some DP problems resist the standard recursive → memoization → tabulation pipeline.

The Student's Confusion​

Alex: [walks into office hours with laptop open] Professor Chen, I'm really confused about this LeetCode problem I'm working on. I thought I understood DP, but something's not clicking.

Professor Chen: Let's see what you've got. Walk me through it.

Alex: It's LC 740: Delete and Earn. Here's the problem:

A dialogue between an engineer learning DP and a professor clarifying the optimal learning path

The Question​

Engineer: Professor, I've been breaking down how to approach dynamic programming problems, and I want to validate my thinking. Here's my approach:

1. First, I solve the problem using recursion in the worst possible way - not worrying about time or space complexity at all
2. Then, I optimize that recursive solution with memoization, which gives me a top-down DP solution
3. Finally, I convert it to bottom-up DP for an even better solution in terms of both time and space complexity

Am I thinking about this correctly? Or am I missing something critical?

The Remove Linked List Elements problem is a fundamental linked list manipulation challenge that teaches essential pointer handling techniques. This problem is excellent for understanding when and why to use dummy nodes in linked list operations.

The Minimum Subarray Sum problem (also known as "Minimum Size Subarray Sum") is an excellent introduction to the sliding window technique. This problem demonstrates how we can optimize from a brute force O(n³) solution to an elegant O(n) solution.