1326 - Minimum Number of Taps to Open to Water a Garden.

Hard

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:

• <code>1 <= n <= 10⁴</code>

• ranges.length == n + 1

• 0 <= ranges[i] <= 100