<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:
#         dp = [float('inf')]*(n+1)
#         dp[0] = 0 

#         for i, r in enumerate(ranges):
#             start, end = max(0, i -r), min(n, i+r) 
#             for j in range(start+1, end+1):
#                 dp[j] = min(dp[j], dp[start] + 1) 

#         return dp[-1] if dp[-1] != float('inf') else -1 

class Solution:
    def minTaps(self, n: int, ranges: List[int]) -> int:
        arr = [0] * (n + 1)
        for i, r in enumerate(ranges):
            if r == 0:
                continue
            left = max(0, i - r)
            arr[left] = max(arr[left], i + r)

        end, far_can_reach, cnt = 0, 0, 0
        
        for i, reach in enumerate(arr):
            if i > end:
                if far_can_reach <= end:
                    return -1
                end, cnt = far_can_reach, cnt + 1
            far_can_reach = max(far_can_reach, reach)
        print(arr)
        return cnt

17100