You are given an array A of N positive integers. In one move, you can pick a segment (a contiguous fragment) of A and a positive integer X and then increase all elements within that segment by X. An array is strictly increasing if each element (except for the last one) is smaller than the next element. I need a Java code for this.
Write a function:
int solution(vector &A);
that, given an array A of N integers, returns the minimum number of moves needed to make the array strictly increasing.
Examples:
1. Given A = {14, 2, 4, 1, 3, 5}, the function should return 2. One possible solution is to add X = 3 to the segment [2, 4], and then add X = 8 to the segment [1, 3, 5]. As a result of these two moves, A is now strictly increasing.
2. Given A = {3, 5, 7, 71}, the function should return 1.
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.