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. 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