Minimum Number of Taps to Water the Garden
Given a garden that extends along a one-dimensional x-axis from point 0 to point N, your task is to determine the minimum number of taps needed to water the entire garden. The garden has N+1 taps located at positions [0, 1, 2, ..., N].
Each tap, once opened, waters a range from (i - ranges[i]) to (i + ranges[i]), inclusive. You must find the fewest number of taps required to water every part of the garden from point 0 to point N. Return -1 if it's not possible to water the entire garden.
Input:
Integer T, the number of test cases
For each test case:
- Integer N, the range of the garden.
- Array ranges of size N+1, where ranges[i] indicates the water coverage radius a tap at point i can achieve.
Output:
For each test case, a single integer representing the minimum number of taps required. If the garden cannot be fully watered, return -1.
Example:
Consider an input where T = 1, N = 5, and ranges = [3,4,1,1,0,0].
Input:
T = 1
N = 5
ranges = [3, 4, 1, 1, 0, 0]
Output:
1
Explanation:
By opening the tap at position 1, which covers points from -3 to 5, the entire garden from 0 to 5 is watered.
Constraints:
1 <= T <= 10
1 <= N <= 104
0 <= ranges[i] <= 100
- Time Limit: 1 sec
Find the minimum number of taps needed to water the entire garden with given tap ranges.
Iterate over each tap and find the maximum range it can cover.
Sort the taps based on their starting point and en...read more
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