README_EN.md

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

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Description

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 <= 104
• ranges.length == n + 1
• 0 <= ranges[i] <= 100

Solutions

Python3

class Solution:
    def minTaps(self, n: int, ranges: List[int]) -> int:
        last = [0] * (n + 1)
        for i, v in enumerate(ranges):
            l, r = max(0, i - v), min(n, i + v)
            last[l] = max(last[l], r)

        ans = mx = pre = 0
        for i in range(n):
            mx = max(mx, last[i])
            if mx <= i:
                return -1
            if pre == i:
                ans += 1
                pre = mx
        return ans

Java

class Solution {
    public int minTaps(int n, int[] ranges) {
        int[] last = new int[n + 1];
        for (int i = 0; i < n + 1; ++i) {
            int v = ranges[i];
            int l = Math.max(0, i - v), r = Math.min(n, i + v);
            last[l] = Math.max(last[l], r);
        }
        int ans = 0, mx = 0, pre = 0;
        for (int i = 0; i < n; ++i) {
            mx = Math.max(mx, last[i]);
            if (mx <= i) {
                return -1;
            }
            if (pre == i) {
                ++ans;
                pre = mx;
            }
        }
        return ans;
    }
}

C++

class Solution {
public:
    int minTaps(int n, vector<int>& ranges) {
        vector<int> last(n + 1);
        for (int i = 0; i < n + 1; ++i) {
            int v = ranges[i];
            int l = max(0, i - v), r = min(n, i + v);
            last[l] = max(last[l], r);
        }
        int ans = 0, mx = 0, pre = 0;
        for (int i = 0; i < n; ++i) {
            mx = max(mx, last[i]);
            if (mx <= i) {
                return -1;
            }
            if (pre == i) {
                ++ans;
                pre = mx;
            }
        }
        return ans;
    }
};

Go

func minTaps(n int, ranges []int) int {
	last := make([]int, n+1)
	for i, v := range ranges {
		l, r := max(0, i-v), min(n, i+v)
		last[l] = max(last[l], r)
	}
	ans, mx, pre := 0, 0, 0
	for i := 0; i < n; i++ {
		mx = max(mx, last[i])
		if mx <= i {
			return -1
		}
		if pre == i {
			ans++
			pre = mx
		}
	}
	return ans
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

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