HardNo. 2518
Number of Great Partitions — LeetCode 2518 Python Solution
- Pattern
- Dynamic Programming
- Topics
- Array, Dynamic Programming
- Reading time
- 3 min
- Source
- leetcode.com
The problem
You are given an array nums consisting of positive integers and an integer k. Partition the array into two ordered groups such that each element is in exactly one group.
Example
- Input
- nums = [1,2,3,4], k = 4
- Output
- 6
- Explanation
- The great partitions are: ([1,2,3], [4]), ([1,3], [2,4]), ([1,4], [2,3]), ([2,3], [1,4]), ([2,4], [1,3]) and ([4], [1,2,3]).
Python solution
class Solution:
def countPartitions(self, nums: List[int], k: int) -> int:
if sum(nums) < k * 2:
return 0
mod = 10**9 + 7
n = len(nums)
f = [[0] * k for _ in range(n + 1)]
f[0][0] = 1
ans = 1
for i in range(1, n + 1):
ans = ans * 2 % mod
for j in range(k):
f[i][j] = f[i - 1][j]
if j >= nums[i - 1]:
f[i][j] = (f[i][j] + f[i - 1][j - nums[i - 1]]) % mod
return (ans - sum(f[-1]) * 2 + mod) % modComplexity
- Time
- O(n·m) (typical)
- Space · auxiliary
- O(n·m)or optimized
Pattern: Dynamic Programming
Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2518. Number of Great Partitions 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 |
|---|---|---|
| 0045 | Jump Game II | Medium |
| 0053 | Maximum Subarray | Medium |
| 0055 | Jump Game | Medium |
| 0063 | Unique Paths II | Medium |
| 0064 | Minimum Path Sum | Medium |
| 0085 | Maximal Rectangle | Hard |
Frequently asked questions
- How hard is LeetCode 2518. Number of Great Partitions?
LeetCode 2518. Number of Great Partitions is rated Hard on LeetCode.
- What topics does LeetCode 2518. Number of Great Partitions cover?
LeetCode 2518. Number of Great Partitions is tagged Array and Dynamic Programming on LeetCode.