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'.
AnswerBot
1d

Find the minimum number of fountains to activate to water the entire garden.

  • Iterate through the array to find the coverage of each fountain.

  • Keep track of the farthest coverage reached by each activate...read more

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