MediumNo. 2189LeetCode Premium
Number of Ways to Build House of Cards — LeetCode 2189 Python Solution
- Pattern
- Dynamic Programming
- Topics
- Math, Dynamic Programming
- Reading time
- 2 min
- Source
- leetcode.com
The problem
You are given an integer n representing the number of playing cards you have. A house of cards meets the following conditions: A house of cards consists of one or more rows of triangles and horizontal cards.
Example
- Input
- n = 16
- Output
- 2
- Explanation
- The two valid houses of cards are shown.
Python solution
class Solution:
def houseOfCards(self, n: int) -> int:
@cache
def dfs(n: int, k: int) -> int:
x = 3 * k + 2
if x > n:
return 0
if x == n:
return 1
return dfs(n - x, k + 1) + dfs(n, k + 1)
return dfs(n, 0)Complexity
- Time
- O(n2)
- Space · auxiliary
- O(n2)
Pattern: Dynamic Programming
Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2189. Number of Ways to Build House of Cards is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.
The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.
Related problems
| No. | Problem | Difficulty |
|---|---|---|
| 0062 | Unique Paths | Medium |
| 0070 | Climbing Stairs | Easy |
| 0096 | Unique Binary Search Trees | Medium |
| 0233 | Number of Digit One | Hard |
| 0241 | Different Ways to Add Parentheses | Medium |
| 0279 | Perfect Squares | Medium |
Frequently asked questions
- How hard is LeetCode 2189. Number of Ways to Build House of Cards?
LeetCode 2189. Number of Ways to Build House of Cards is rated Medium on LeetCode.
- What is the time complexity of LeetCode 2189. Number of Ways to Build House of Cards?
The Python solution on this page runs in O(n2).
- What is the space complexity of LeetCode 2189. Number of Ways to Build House of Cards?
The Python solution on this page uses O(n2) auxiliary space.
- What topics does LeetCode 2189. Number of Ways to Build House of Cards cover?
LeetCode 2189. Number of Ways to Build House of Cards is tagged Math and Dynamic Programming on LeetCode.
- Is LeetCode 2189. Number of Ways to Build House of Cards a premium problem?
Yes. LeetCode 2189. Number of Ways to Build House of Cards is a LeetCode Premium problem, so the full statement and test cases require a paid LeetCode subscription.