Number of Great Partitions — LeetCode 2518 Python Solution

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) % mod

Complexity

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.

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