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Minimum Number of Taps to Water Garden
Certification: Advanced Level
Accuracy: 100%
Submissions: 1
Points: 15
Write a Java program to determine the minimum number of taps needed to water an entire garden. You have a garden of length n where each position has a tap with a specific range. The range of a tap at position i is given by an array ranges, where ranges[i] represents the covering range of the tap at position i. A tap at position i can water the area from [i - ranges[i], i + ranges[i]]. The garden needs to be watered from position 0 to position n. Return the minimum number of taps that need to be turned on to water the entire garden. If it is impossible to water the entire garden, return -1.
Example 1
- Input: n = 5, ranges = [3,4,1,1,0,0]
- Output: 1
- Explanation:
The tap at position 0 has a range of 3, covering positions [0-3, 0+3] = [0, 3].
The tap at position 1 has a range of 4, covering positions [1-4, 1+4] = [0, 5].
The tap at position 1 can water the entire garden [0, 5], so we only need 1 tap.
Example 2
- Input: n = 3, ranges = [0,0,0,0]
- Output: -1
- Explanation:
The tap at position 0 has a range of 0, covering only position 0.
The tap at position 1 has a range of 0, covering only position 1.
The tap at position 2 has a range of 0, covering only position 2.
The tap at position 3 has a range of 0, covering only position 3.
It's impossible to cover the entire garden [0, 3] with these taps.
Constraints
- 1 <= n <= 10^4
- ranges.length == n + 1
- 0 <= ranges[i] <= 100
- Time Complexity: O(n)
- Space Complexity: O(n)
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Solution Hints
- Convert the problem to the "Jump Game" format by calculating the intervals each tap can cover
- For each tap at position i, calculate the leftmost position start = max(0, i - ranges[i]) and the rightmost position end = min(n, i + ranges[i])
- Sort the intervals by their start positions
- Use a greedy approach to find the minimum number of taps needed
- Iterate through the sorted intervals and find the interval that extends furthest to the right from the current position