LeetCode 64: Minimum Path Sum | Java Solution | Dynamic Programming
🔍 In this video, I tackle the #minimum #path #sum problem where we need to find the path with the minimum sum from top-left to bottom-right of a grid. This is a classic #dynamicprogramming problem often asked in #codinginterviews.
⏱️ Time Complexity: O(m×n) where m and n are the dimensions of the grid
🗃️ Space Complexity: O(m×n) for standard DP, can be optimized to O(n)
Timestamps
00:00 - Understanding problem statement
00:39 - Brute force approach
01:39 - Big O Notation calculated
02:00 - Using Dynamic Programming
03:31 - Dry run
05:16 - Big O Notation calculated
06:00 - Java code walk-through
06:53 - Solution analysis - runtime + memory
07:00 - Conclusion
Key Concepts
• 2D Dynamic Programming
• Bottom-up tabulation
• Grid traversal
• Path optimization
Learning Points
💡 Understanding how to build a DP matrix for path-based problems
💡 Recognizing optimal substructure in grid problems
💡 Space optimization techniques for 2D DP problems
💡 Handling edge cases in grid traversal
Related Problems
• #62 Unique Paths
• #63 Unique Paths II
• #120 Triangle
• #931 Minimum Falling Path Sum
Target Audience
This video is ideal for software engineers preparing for coding interviews, computer science students studying algorithms, and anyone interested in dynamic programming problems.
Prerequisites
• Basic understanding of Java
• Familiarity with arrays and matrices
• Understanding of dynamic programming concepts
Links
📝 Problem: https://leetcode.com/problems/minimum...
💻 Solution Code: https://leetcode.com/problems/minimum...
Additional Tips
• Pay special attention to the state transition formula: dp[i][j] = grid[i][j] + min(dp[i-1][j], dp[i][j-1])
• Consider edge cases when there's only one row or column
• Notice how this problem builds upon the concepts from Unique Paths
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