Minimum Number Of Taps To Water Garden

Hard

0/120

Average time to solve is 15m

Contributed by

31 upvotes

Asked in companies

Problem statement

The gardener wants to water the garden by opening the minimum number of taps. The garden is one-dimensional along the x-axis of length N i.e. the garden starts from point 0 and ends at point N. There are N + 1 tap located at points [0, 1, 2, …, N] in the garden.

You are given an integer N, and an array named “ranges” of size N + 1(0-indexed). The ith tap, if opened, can water the gardener from point (i - ranges[i]) to (i + ranges[i]) including both. The task is to find the minimum number of taps that should be open to water the whole garden, return -1 if the garden can not be watered.

Example :

Follow Up:

Can you solve the problem in O(N) time?

Detailed explanation ( Input/output format, Notes, Images )

Input Format:

The first line contains a single integer T representing the number of test cases. 

The first line of each test case will contain the integer N.

The second and the last line of each test case will contain N single space-separated integers representing the elements of the array “ranges”.

Output format :

For each test case, print a single integer representing the value of the minimum number of taps needed to open by the gardener to fill the whole garden.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 10
1 <= N <= 10^4
0 <= ranges[i] <= 100

Time Limit: 1 sec

Sample Input 1 :

2
3
0 0 0 0
7
1 2 1 0 2 1 0 1

Sample Output 1 :

-1
3

Explanation For Sample Input 1 :

In test case 1, the ranges of taps are as follows : [ [ 0, 0 ], [ 1, 1 ], [ 2, 2 ] ]. So in the worst case, if we open all the taps, then it’s impossible to fill the gaps i.e (0-1), (1,2), (2,3). So it’s impossible to fill the garden.

In test case 2, the ranges of taps are as follows : [ [ -1, 1 ],[ -1, 3 ],[ 1, 3 ],[ 3, 3 ],[ 2, 6 ],[ 4, 6 ],[ 6, 6 ],[ 6, 8 ] ]. To fill the garden i.e [ 0, 7 ] , the gardener needs to open a minimum of three taps i.e. tap 2: [ -1, 3 ] , tap 5: [ 2, 6 ], tap 8: [ 6, 8 ] to fill the whole garden.

Sample Input 2 :

2
8
4 0 0 0 0 0 0 0 4
8
4 0 0 0 4 0 0 0 4

Sample Output 2 :

2
1

Console