1326. Minimum Number of Taps to Open to Water a Garden

Problem

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.

  Constraints:

• 1 <= n <= 10^4

• ranges.length == n + 1

• 0 <= ranges[i] <= 100

Solution

class Solution {
    public int minTaps(int n, int[] ranges) {
        if (n == 0 || ranges.length == 0) {
            return n == 0 ? 0 : -1;
        }
        int[] dp = new int[n + 1];

        int nxtLargest = 0;
        int current = 0;
        int amount = 0;
        for (int i = 0; i < ranges.length; i++) {
            if (ranges[i] > 0) {
                int ind = Math.max(0, i - ranges[i]);
                dp[ind] = Math.max(dp[ind], i + ranges[i]);
            }
        }
        for (int i = 0; i <= n; i++) {
            nxtLargest = Math.max(nxtLargest, dp[i]);
            if (i == current && i < n) {
                current = nxtLargest;
                amount++;
            }
            if (current < i) {
                return -1;
            }
        }
        return amount;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).