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g2501_2600.s2518_number_of_great_partitions.readme.md Maven / Gradle / Ivy

2518\. Number of Great Partitions

Hard

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. A partition is called great if the **sum** of elements of each group is greater than or equal to `k`.

Return _the number of **distinct** great partitions_. Since the answer may be too large, return it **modulo** 109 + 7.

Two partitions are considered distinct if some element `nums[i]` is in different groups in the two partitions.

**Example 1:**

**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]).

**Example 2:**

**Input:** nums = [3,3,3], k = 4

**Output:** 0

**Explanation:** There are no great partitions for this array.

**Example 3:**

**Input:** nums = [6,6], k = 2

**Output:** 2

**Explanation:** We can either put nums[0] in the first partition or in the second partition. The great partitions will be ([6], [6]) and ([6], [6]).

**Constraints:**

*   `1 <= nums.length, k <= 1000`
*   1 <= nums[i] <= 109