MEDIUM 2-D Dynamic Programming
64. Minimum Path Sum
📖 Problem
Given a m x n grid filled with non-negative numbers, find a path from top left corner to bottom right corner which minimizes the sum of all numbers along its path.
🧠 Visual Learning Aid
1 Model the input into the right structure
2 Choose the core technique and invariant
3 Execute step-by-step with a sample
4 Validate complexity and edge cases
JS/TS Refreshers
- •Array methods (`push`, `pop`, `shift`, `slice`)
- •Object/Map/Set usage patterns
- •Function parameter and return typing
- •Array DP table updates
- •State transition thinking
- •Base case initialization
Logical Thinking Concepts
- •Define invariants before coding
- •Check edge cases first (`[]`, single element, duplicates)
- •Estimate time/space before implementation
- •Apply Dynamic Programming reasoning pattern
💡 Approach
- → Use dp[i][j] = min path sum to reach cell (i, j)
- → Base case: dp[0][0] = grid[0][0]
- → For each cell: dp[i][j] = min(from above + left, from left + grid[i][j])
- → Return dp[m-1][n-1]
- → Time: O(m * n), Space: O(m * n) or O(n) optimized
🛠️ Hints & Pitfalls
Hints
- •Use dp[i][j] = min path sum to reach cell (i, j)
- •Base case: dp[0][0] = grid[0][0]
- •For each cell: dp[i][j] = min(from above + left, from left + grid[i][j])
Common Pitfalls
- •Return dp[m-1][n-1]
- •Time: O(m * n), Space: O(m * n) or O(n) optimized
🧪 Test Cases
Test Case 1
Not run Input:
minPathSum([[1,3,1],[1,5,1],[4,2,1],[5,3,1],[2,3,1],[4,2,1]]); Expected:
20 Test Case 2
Not run Input:
minPathSum([[1,2,3],[4,5,6]]); Expected:
16 Test Case 3
Not run Input:
minPathSum(grid: number[][]); Expected:
Computed from hidden reference 📝 Code Editor
📤 Output