title: Find if a path exists in a grid covered with circles of same radius
body: <p>I was asked this question in an interview and I couldn't solve it. </p>
  
  <p>I would be really grateful if you could help me solve it. </p>
  
  <p>The problem is as follows:-</p>
  
  <p>You are given a <strong>rectangular region</strong> whose left and <strong>bottom-most co-ordinate</strong> is <strong>(0,0)</strong> and <strong>right-most</strong> and <strong>top-most</strong> co-ordinate is <strong>(x,y)</strong>. </p>
  
  <p>There are <strong>n</strong> circles with given center <strong>co-ordinates</strong> that exist inside the region all having the same radius <strong>'r'</strong>. </p>
  
  <p>You are currently standing at <strong>(0,0)</strong> and want to reach <strong>(x,y)</strong> without touching any circle. </p>
  
  <p>You have to tell if it is possible or not. </p>
  
  <p>He told me that you can move between <strong>2 points</strong> freely and it is not necessary to move along the <strong>x or y-axis</strong>. </p>
  
  <p>The solution I thought of involved taking a matrix of <strong>x*y</strong> dimension and for each circle, mark the points which lie inside it or touch it. </p>
  
  <p>After that apply <code>BFS</code> starting from <strong>(0,0)</strong> to check if we can reach <strong>(x,y)</strong>. </p>
  
  <p>He told me <code>BFS</code> will be wrong which I couldn't figure out why. </p>
  
  <p>I had assumed that circles are having <strong>integer radius</strong> and have <strong>integer co-ordinates</strong>. </p>
  
  <p>He also asked me to solve the question without these assumptions. </p>
  
  <p>I couldn't. When asked, he told me it's a standard problem and <strong>I should be able to find it on google</strong>. </p>
  
  <p>I couldn't, again. Please help!</p>