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g2601_2700.s2601_prime_subtraction_operation.readme.md Maven / Gradle / Ivy

2601\. Prime Subtraction Operation

Medium

You are given a **0-indexed** integer array `nums` of length `n`.

You can perform the following operation as many times as you want:

*   Pick an index `i` that you haven’t picked before, and pick a prime `p` **strictly less than** `nums[i]`, then subtract `p` from `nums[i]`.

Return _true if you can make `nums` a strictly increasing array using the above operation and false otherwise._

A **strictly increasing array** is an array whose each element is strictly greater than its preceding element.

**Example 1:**

**Input:** nums = [4,9,6,10]

**Output:** true

**Explanation:** In the first operation: Pick i = 0 and p = 3, and then subtract 3 from nums[0], so that nums becomes [1,9,6,10]. In the second operation: i = 1, p = 7, subtract 7 from nums[1], so nums becomes equal to [1,2,6,10]. After the second operation, nums is sorted in strictly increasing order, so the answer is true.

**Example 2:**

**Input:** nums = [6,8,11,12]

**Output:** true

**Explanation:** Initially nums is sorted in strictly increasing order, so we don't need to make any operations.

**Example 3:**

**Input:** nums = [5,8,3]

**Output:** false

**Explanation:** It can be proven that there is no way to perform operations to make nums sorted in strictly increasing order, so the answer is false.

**Constraints:**

*   `1 <= nums.length <= 1000`
*   `1 <= nums[i] <= 1000`
*   `nums.length == n`