LeetCode 1326: Minimum Number of Taps to Open to Water a Garden Solution

Master LeetCode problem 1326 (Minimum Number of Taps to Open to Water a Garden), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

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

Hard

Array Dynamic Programming Greedy

Problem Explanation

Explanation:

To solve this problem, we can think of each tap as an interval on the garden that it can water. Our goal is to find the minimum number of taps that need to be opened such that the entire garden is watered.

We can iterate through each tap and calculate the leftmost and rightmost points it can cover.
We can then sort these intervals based on their starting points.
We can then start from the leftmost point and keep track of the farthest point we can reach using the currently opened taps.
As we move along, we open the tap that covers the farthest distance and update our coverage.
If we can reach the end of the garden (n) before opening all taps, we return the count of taps opened. Otherwise, we return -1.

Time Complexity: O(nlogn) - sorting the intervals Space Complexity: O(n) - to store the intervals

Solution Code

class Solution {
    public int minTaps(int n, int[] ranges) {
        int[] maxRanges = new int[n + 1];
        for (int i = 0; i <= n; i++) {
            int left = Math.max(0, i - ranges[i]);
            int right = Math.min(n, i + ranges[i]);
            maxRanges[left] = Math.max(maxRanges[left], right);
        }

        int openTaps = 0;
        int curEnd = 0;
        int nextEnd = 0;

        for (int i = 0; i <= n; i++) {
            if (i > curEnd) {
                return -1;
            }
            if (i > nextEnd) {
                openTaps++;
                curEnd = nextEnd;
            }
            nextEnd = Math.max(nextEnd, maxRanges[i]);
        }

        return openTaps;
    }
}

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