Program 002: LeetCode Problem | There is an array A of N integers sorted in ... | Step By Step

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Problem Statement: There is an array A of N integers sorted in non-decreasing order. In one move, you can either remove
an integer from A or insert an integer before or after any element of A. The goal is to achieve an array
in which all values X that are present in the array occur exactly X times.
For example, given A = [1, 1, 3, 4, 4, 4], value 1 occurs twice, value 3 occurs once and value 4 occurs
three times. You can remove one occurrence each of both 1 and 3, and insert one occurrence 4,
resulting in the array [1, 4, 4, 4, 4]. In this array, every element X occurs exactly X times.
What is the minimum number of moves after which every value X in the array occurs exactly X times?
Write a function:
class Solution { public int solution(int[] A); }
that, given an array A, returns the minimum number of moves after which every value X in the array
occurs exactly X times. Note that it is permissible to remove some values entirely, if appropriate.
Examples:

Given A = [1, 1, 3, 4, 4, 4], your function should return 3, as described above.
Given A = [1, 2, 2, 2, 5, 5, 5, 8], your function should return 4. You can delete the 8 and one
occurrence of 2, and insert 5 twice, resulting in [1, 2, 2, 5, 5, 5, 5, 5] after four moves. Notice that after
the removals, there is no occurrence of 8 in the array anymore.
Given A = [1, 1, 1, 1, 3, 3, 4, 4, 4, 4, 4], your function should return 5.
Given A = [10, 10, 10], your function should return 3. You can remove all elements, resulting in an
empty array.
Write an efficient algorithm for the following assumptions:
N is an integer within the range [1..100,000];
each element of array A is an integer within the range [1..100,000,000];
elements of array A are sorted in non-decreasing order.

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