title: median of two sorted arrays
body: <p>My question is with reference to Method 2 of <a href="http://www.geeksforgeeks.org/median-of-two-sorted-arrays/">this</a> link. Here two equal length sorted arrays are given and we have to find the median of the two arrays merged. </p>
  
  <pre><code>Algorithm:
  
  1) Calculate the medians m1 and m2 of the input arrays ar1[] 
     and ar2[] respectively.
  2) If m1 and m2 both are equal then we are done.
       return m1 (or m2)
  3) If m1 is greater than m2, then median is present in one 
     of the below two subarrays.
      a)  From first element of ar1 to m1 (ar1[0...|_n/2_|])
      b)  From m2 to last element of ar2  (ar2[|_n/2_|...n-1])
  4) If m2 is greater than m1, then median is present in one    
     of the below two subarrays.
     a)  From m1 to last element of ar1  (ar1[|_n/2_|...n-1])
     b)  From first element of ar2 to m2 (ar2[0...|_n/2_|])
  5) Repeat the above process until size of both the subarrays 
     becomes 2.
  6) If size of the two arrays is 2 then use below formula to get 
    the median.
      Median = (max(ar1[0], ar2[0]) + min(ar1[1], ar2[1]))/2
  
  Example:
  
     ar1[] = {1, 12, 15, 26, 38}
     ar2[] = {2, 13, 17, 30, 45}
  
  For above two arrays m1 = 15 and m2 = 17
  
  For the above ar1[] and ar2[], m1 is smaller than m2. So median is present in one of the following two subarrays.
  
     [15, 26, 38] and [2, 13, 17]
  Let us repeat the process for above two subarrays:
  
      m1 = 26 m2 = 13.
  m1 is greater than m2. So the subarrays become
  
    [15, 26] and [13, 17]
  Now size is 2, so median = (max(ar1[0], ar2[0]) + min(ar1[1], ar2[1]))/2
                         = (max(15, 13) + min(26, 17))/2 
                         = (15 + 17)/2
                         = 16
  </code></pre>
  
  <p><strong>I understand</strong> how they exclude halves of the arrays and say that the median element would be in particular halves of the arrays i.e. <strong>steps 1, 2, 3, 4, 5</strong>. </p>
  
  <p>But what I can't fathom, <strong>how can they say</strong> that the median of the merged arrays would be the median of the merged arrays resulting after pruning the halves of the arrays i.e. <strong>the median of merge array of {1, 12, 15, 26, 38} and {2, 13, 17, 30, 45} would be the median of the merge array of {2,13,17} and {15, 26, 38}.</strong></p>
  
  <p>Please explain. Thanks in advance.</p>