Minimum Number of Taps to Open to Water a Garden

arraydynamic programminggreedy

Problem Statement

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 .

Examples

Example 1

Input: n = 5, ranges = [3,4,1,1,0,0]
Output: 1
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
Even if you activate all the four taps you cannot water the whole garden.

Constraints

1 <= n <= 10 ^4

ranges.length == n + 1

0 <= ranges[i] <= 100

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming