<p>There is a one-dimensional garden on the x-axis. The garden starts at the point <code>0</code> and ends at the point <code>n</code>. (i.e., the&nbsp;length of the garden is <code>n</code>).</p>

<p>There are <code>n + 1</code> taps located at points <code>[0, 1, ..., n]</code> in the garden.</p>

<p>Given an integer <code>n</code> and an integer array <code>ranges</code> of length <code>n + 1</code> where <code>ranges[i]</code> (0-indexed) means the <code>i-th</code> tap can water the area <code>[i - ranges[i], i + ranges[i]]</code> if it was open.</p>

<p>Return <em>the minimum number of taps</em> that should be open to water the whole garden, If the garden cannot be watered return <strong>-1</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/01/16/1685_example_1.png" style="width: 525px; height: 255px;" />
<pre>
<strong>Input:</strong> n = 5, ranges = [3,4,1,1,0,0]
<strong>Output:</strong> 1
<strong>Explanation:</strong> 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]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 3, ranges = [0,0,0,0]
<strong>Output:</strong> -1
<strong>Explanation:</strong> Even if you activate all the four taps you cannot water the whole garden.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
	<li><code>ranges.length == n + 1</code></li>
	<li><code>0 &lt;= ranges[i] &lt;= 100</code></li>
</ul>

class Solution:
    def minTaps(self, n: int, ranges: List[int]) -> int:
        intervals = sorted([(max(0, i - x), i + x) for i, x in enumerate(ranges) if x > 0], key=lambda v:v[0])
        if not intervals or intervals[0][0] > 0: 
            return -1

        cur = (-1, 0)
        i, m, res = 0, len(intervals), 0
        print(intervals, cur)
        while i < m and cur[1] < n:
            j = i
            tr = cur[1]
            while j < m and intervals[j][0] <= cur[1]:
                tr = max(tr, intervals[j][1])
                j += 1
               
            if j == i:
                return -1
            else:
                res += (cur[0] < intervals[j - 1][0])
                cur = (cur[1], tr)
                i = j

        
        return res if cur[1] >= n else -1
18300