Minimum Fountains Activation Problem

In this problem, you have a one-dimensional garden of length 'N'. Each position from 0 to 'N' has a fountain that can provide water to the garden up to a certain range. Thus, there are 'N' + 1 fountains at positions 0, 1, 2, ..., N.

You are provided with an integer 'N' and an array 'ARR' of size 'N' + 1. Each element in the array denotes the range of coverage of a fountain at the corresponding position.

Your task is to determine the minimum number of fountains that need to be activated to ensure that the entire garden from position 0 to 'N' is watered.

Example:

Input:

T = 1
N = 5
ARR = [1, 2, 1, 0, 2, 1]

Output:

1

Explanation:

One optimal way is to activate the fountain at position 1, which covers the entire garden from 0 to 5.

Constraints:

• 1 <= 'T' <= 50
• 1 <= 'N' <= 10⁴
• 1 <= 'ARR'[i] <= 'N'

Note:

• Use 0-based indexing for the array.
• Ignore coverage beyond the garden limits 0 and 'N'.
• If a fountain covers from position 'A' to 'B', the water reaches the entire segment from 'A' to 'B'.