MEDIUM Blind #21 1-D Dynamic Programming
377. Combination Sum IV
📖 Problem
Given an array of distinct integers nums and a target integer target, return the number of possible combinations that add up to target. The test cases are generated so that the answer can fit in a 32-bit integer. Different sequences are counted as different combinations.
🧠 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 where dp[i] = number of combinations to sum to i
- → For each target sum, consider adding each number from nums
- → dp[i] = sum(dp[i - num] for all num in nums where num <= i)
- → Base case: dp[0] = 1 (one way to make sum 0)
- → Time: O(target * n), Space: O(target)
🧭 Prerequisites
🛠️ Hints & Pitfalls
Hints
- •Use DP where dp[i] = number of combinations to sum to i
- •For each target sum, consider adding each number from nums
- •dp[i] = sum(dp[i - num] for all num in nums where num <= i)
Common Pitfalls
- •Base case: dp[0] = 1 (one way to make sum 0)
- •Time: O(target * n), Space: O(target)
🧪 Test Cases
Hidden tests on submit: 1
Test Case 1
Not run Input:
combinationSum3([1,2,3], 4); Expected:
4 Test Case 2
Not run Input:
combinationSum3([9], 3); Expected:
0 Test Case 3
Not run Input:
combinationSum3([2], 1); Expected:
0 📝 Code Editor
📤 Output