MEDIUM NC#111 Blind #25 Dynamic Programming 2D (can be 1D optimized)
62. Unique Paths
📖 Problem
A robot is located at the top-left corner of a m x n grid. The robot can only move either down or right. How many possible unique paths to reach bottom-right corner?
🧠 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
- •Apply Recursion reasoning pattern
💡 Approach
- → dp[i][j] = paths to reach cell (i, j)
- → dp[i][j] = dp[i-1][j] + dp[i][j-1]
- → First row and first column initialized to 1
- → Time: O(m * n), Space: O(m * n) or O(n) optimized
- → 2, m-1), Recursion
🛠️ Hints & Pitfalls
Hints
- •dp[i][j] = paths to reach cell (i, j)
- •dp[i][j] = dp[i-1][j] + dp[i][j-1]
- •First row and first column initialized to 1
Common Pitfalls
- •Time: O(m * n), Space: O(m * n) or O(n) optimized
- •2, m-1), Recursion
🧪 Test Cases
Hidden tests on submit: 1
Test Case 1
Not run Input:
uniquePaths(3, 7); Expected:
28 Test Case 2
Not run Input:
uniquePaths(3, 2); Expected:
3 Test Case 3
Not run Input:
uniquePaths(1, 1); Expected:
1 📝 Code Editor
📤 Output