"""
There is a one-dimensional garden on the x-axis. The garden starts at the point 0 and ends at the point n. (i.e The length of the garden is n).

There are n + 1 taps located at points [0, 1, ..., n] in the garden.

Given an integer n and an integer array ranges of length n + 1 where ranges[i] (0-indexed) means the i-th tap can water the area [i - ranges[i], i + ranges[i]] if it was open.

Return the minimum number of taps that should be open to water the whole garden, If the garden cannot be watered return -1.

Example 1:
Input: n = 5, ranges = [3,4,1,1,0,0]
Output: 1
Explanation: The tap at point 0 can cover the interval [-3,3]
The tap at point 1 can cover the interval [-3,5]
The tap at point 2 can cover the interval [1,3]
The tap at point 3 can cover the interval [2,4]
The tap at point 4 can cover the interval [4,4]
The tap at point 5 can cover the interval [5,5]
Opening Only the second tap will water the whole garden [0,5]

Example 2:
Input: n = 3, ranges = [0,0,0,0]
Output: -1
Explanation: Even if you activate all the four taps you cannot water the whole garden.

Constraints:
1 <= n <= 104
ranges.length == n + 1
0 <= ranges[i] <= 100

hint:
1 Create intervals of the area covered by each tap, sort intervals by the left end.
2 We need to cover the interval [0, n]. we can start with the first interval and out of all intervals that intersect with it we choose the one that covers the farthest point to the right.
3 What if there is a gap between intervals that is not covered ? we should stop and return -1 as there is some interval that cannot be covered.
"""
from typing import List

class MinimumNumberOfTapsToOpenToWateraGarden:
    def minTaps(self, n: int, ranges: List[int]) -> int:
        intervals = []
        for i, r in enumerate(ranges):
            intervals.append((i - r, i + r))
        intervals.sort(key=lambda x: x[0])
        cnt, end, i, right_most = 0, 0, 0, 0
        while i < len(intervals):
            if end < intervals[i][0]:
                return -1
            while i < len(intervals) and intervals[i][0] <= end:
                right_most = max(right_most, intervals[i][1])
                i += 1
            cnt += 1
            end = right_most
            if n <= end:
                return cnt
        return -1