Package g2801_2900.s2818_apply_operations_to_maximize_score

Class Solution

java.lang.Object
g2801_2900.s2818_apply_operations_to_maximize_score.Solution
public class Solution extends java.lang.Object
2818 - Apply Operations to Maximize Score.

Hard

You are given an array nums of n positive integers and an integer k.

Initially, you start with a score of 1. You have to maximize your score by applying the following operation at most k times:

  • Choose any non-empty subarray nums[l, ..., r] that you haven’t chosen previously.
  • Choose an element x of nums[l, ..., r] with the highest prime score. If multiple such elements exist, choose the one with the smallest index.
  • Multiply your score by x.

Here, nums[l, ..., r] denotes the subarray of nums starting at index l and ending at the index r, both ends being inclusive.

The prime score of an integer x is equal to the number of distinct prime factors of x. For example, the prime score of 300 is 3 since 300 = 2 * 2 * 3 * 5 * 5.

Return the maximum possible score after applying at most k operations.

Since the answer may be large, return it modulo 109 + 7.

Example 1:

Input: nums = [8,3,9,3,8], k = 2

Output: 81

Explanation:

To get a score of 81, we can apply the following operations:

  • Choose subarray nums[2, …, 2]. nums[2] is the only element in this subarray. Hence, we multiply the score by nums[2]. The score becomes 1 * 9 = 9.

  • Choose subarray nums[2, …, 3]. Both nums[2] and nums[3] have a prime score of 1, but nums[2] has the smaller index. Hence, we multiply the score by nums[2]. The score becomes 9 * 9 = 81.

It can be proven that 81 is the highest score one can obtain.

Example 2:

Input: nums = [19,12,14,6,10,18], k = 3

Output: 4788

Explanation:

To get a score of 4788, we can apply the following operations:

  • Choose subarray nums[0, …, 0]. nums[0] is the only element in this subarray. Hence, we multiply the score by nums[0]. The score becomes 1 * 19 = 19.

  • Choose subarray nums[5, …, 5]. nums[5] is the only element in this subarray. Hence, we multiply the score by nums[5]. The score becomes 19 * 18 = 342.

  • Choose subarray nums[2, …, 3]. Both nums[2] and nums[3] have a prime score of 2, but nums[2] has the smaller index. Hence, we multipy the score by nums[2]. The score becomes 342 * 14 = 4788. It can be proven that 4788 is the highest score one can obtain.

Constraints:

  • 1 <= nums.length == n <= 105
  • 1 <= nums[i] <= 105
  • 1 <= k <= min(n * (n + 1) / 2, 109)

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    maximumScore(java.util.List<java.lang.Integer> nums, int k)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • maximumScore

      public int maximumScore(java.util.List<java.lang.Integer> nums, int k)