<p>You are given two positive integers <code>xCorner</code> and <code>yCorner</code>, and a 2D array <code>circles</code>, where <code>circles[i] = [x<sub>i</sub>, y<sub>i</sub>, r<sub>i</sub>]</code> denotes a circle with center at <code>(x<sub>i</sub>, y<sub>i</sub>)</code> and radius <code>r<sub>i</sub></code>.</p>

<p>There is a rectangle in the coordinate plane with its bottom left corner at the origin and top right corner at the coordinate <code>(xCorner, yCorner)</code>. You need to check whether there is a path from the bottom left corner to the top right corner such that the <strong>entire path</strong> lies inside the rectangle, <strong>does not</strong> touch or lie inside <strong>any</strong> circle, and touches the rectangle <strong>only</strong> at the two corners.</p>

<p>Return <code>true</code> if such a path exists, and <code>false</code> otherwise.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">xCorner = 3, yCorner = 4, circles = [[2,1,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">true</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/05/18/example2circle1.png" style="width: 346px; height: 264px;" /></p>

<p>The black curve shows a possible path between <code>(0, 0)</code> and <code>(3, 4)</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">xCorner = 3, yCorner = 3, circles = [[1,1,2]]</span></p>

<p><strong>Output:</strong> <span class="example-io">false</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/05/18/example1circle.png" style="width: 346px; height: 264px;" /></p>

<p>No path exists from <code>(0, 0)</code> to <code>(3, 3)</code>.</p>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">xCorner = 3, yCorner = 3, circles = [[2,1,1],[1,2,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">false</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/05/18/example0circle.png" style="width: 346px; height: 264px;" /></p>

<p>No path exists from <code>(0, 0)</code> to <code>(3, 3)</code>.</p>
</div>

<p><strong class="example">Example 4:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">xCorner = 4, yCorner = 4, circles = [[5,5,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">true</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/08/04/rectangles.png" style="width: 346px; height: 264px;" /></p>
</div>

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

<ul>
	<li><code>3 &lt;= xCorner, yCorner &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= circles.length &lt;= 1000</code></li>
	<li><code>circles[i].length == 3</code></li>
	<li><code>1 &lt;= x<sub>i</sub>, y<sub>i</sub>, r<sub>i</sub> &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:

    def circle_horiz(self,x,y0,y1,circle):
        if y0 <= circle[1] <= y1:
            return abs(x-circle[0]) <= circle[2]
        if y0 > circle[1]:
            return (y0-circle[1])**2 + (x-circle[0])**2 <= circle[2]**2
        return (y1-circle[1])**2 + (x-circle[0])**2 <= circle[2]**2
    def circle_vert(self,x0,x1,y,circle):
        return self.circle_horiz(y,x0,x1,[circle[1],circle[0],circle[2]])

    def canReachCorner(self, X: int, Y: int, circles: List[List[int]]) -> bool:
        adj = [[] for i in range(len(circles))]

        for i in range(len(circles)):
            for j in range(len(circles)):
                if i != j and (circles[i][0]-circles[j][0])**2 + (circles[i][1]-circles[j][1])**2 <= (circles[i][2]+circles[j][2])**2:
                    adj[i].append(j)
        
        reachb = set()
        bottoms = [i for i,x in enumerate(circles) if self.circle_vert(0,X,0,x)]
        while len(bottoms):
            i = bottoms.pop()
            if i in reachb: continue
            reachb.add(i)
            bottoms += adj[i]
        

        reachr = set()
        rights = [i for i,x in enumerate(circles) if self.circle_horiz(X,0,Y,x)]
        while len(rights):
            i = rights.pop()
            if i in reachr: continue
            reachr.add(i)
            rights += adj[i]
        
        print(reachb,reachr)

        for x in reachb.union(reachr):
            if self.circle_vert(0,X,Y,circles[x]) or self.circle_horiz(0,0,Y,circles[x]): return False
        
        return True

50484