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.
Example 3:
Input: n = 7, ranges = [1,2,1,0,2,1,0,1]
Output: 3
Example 4:
Input: n = 8, ranges = [4,0,0,0,0,0,0,0,4]
Output: 2
Example 5:
Input: n = 8, ranges = [4,0,0,0,4,0,0,0,4]
Output: 1
Constraints:
1 <= n <= 10^4
ranges.length == n + 1
0 <= ranges[i] <= 100
class Solution:
    def minTaps(self, n: int, ranges: List[int]) -> int:
        if not ranges: return 0
        N = len(ranges)
        # For all location of taps, store the largest right reach point
        max_right_end = list(range(N))
        for i, a in enumerate(ranges):
            max_right_end[max(i - a, 0)] = min(i + a, N-1)
        print(max_right_end)
        res, l, r = 0, 0, max_right_end[0]
        while True:
            res += 1
            # if r can reach to the end of the whole garden, return res
            if r>=N-1:return res
            new_r = max(max_right_end[l:r+1])
            # if next r is same as current r, it means we can not move forward, return -1
            if new_r == r:return -1
            l, r = r, new_r

class Solution:
    def minTaps(self, n: int, ranges: List[int]) -> int:
        if not ranges: return 0
        N = len(ranges)
        # For all location of taps, store the largest right reach point
        max_right_end = list(range(N))
        for i, a in enumerate(ranges):
            max_right_end[max(i - a, 0)] = min(i + a, N-1)
        print(max_right_end)
        res, l, r = 0, 0, max_right_end[0]
        while True:
            res += 1
            # if r can reach to the end of the whole garden, return res
            if r>=N-1:return res
            new_r = max(max_right_end[l:r+1])
            # if next r is same as current r, it means we can not move forward, return -1
            if new_r == r:return -1
            l, r = r, new_r
