Median "algorithm" for two ordered arrays

Source: Internet
Author: User

There are two ordered arrays A and b, and the design algorithm evaluates the median of a and b.


Situation 1. Arrays A and B are equal in length and set to N.

1) Calculate the median M1 and m2 of A and B, respectively.

2) Compare M1 and M2. If M1 equals M2, then the end result is M1 (M2).

3) If M1 is greater than M2, then the median must be in and two sub-arrays.

4) If M1 is less than M2, then the median must be in and two sub-arrays.

5) Repeat the above steps until the two sub-arrays are 2 in size, then the end result is.


Situation 2. Arrays A and B are unequal in length and are set to M,n (M <= N) respectively.

The assumption is the median, so since the array is ordered,Must be larger than the first number in array a. Moreover, ifis the median, which is bound to be larger than the first number in array B. If and, then is the median, otherwise can be based on and, relationship judgment than the median number or small. Because array a is ordered, it can be found in time with a binary search . The pseudo code is as follows:

Imin, Imax = 0, mwhile imin <= imax    i = (imin + IMAX)/2    j = ((M + n + 1)/2)-I    if J > 0 and I < M and b[j-1] > a[i]        imin = i + 1    else if i > 0 and J < N and a[i-1] > b[j]        imax = i-1    El Se        if i = = 0            num1 = b[j-1]        elif j = = 0            num1 = a[i-1]        else            NUM1 = max (a[i-1], b[j-1]) if (M + N) & 1:    return num1if i = = m    num2 = B[j]else if J = = n     num2 = a[i]else     num2 = min (A[i], b[j]) Return (NUM1 + num2)/2.0

Reference: http://www.geeksforgeeks.org/median-of-two-sorted-arrays/

Https://oj.leetcode.com/discuss/15790/share-my-o-log-min-m-n-solution-with-explanation

http://ocw.alfaisal.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-046JFall-2005/ 30c68118-e436-4fe3-8c79-6bafbb07d935/0/ps9sol.pdf

Https://oj.leetcode.com/discuss/11174/share-my-iterative-solution-with-o-log-min-n-m

http://www.geeksforgeeks.org/median-of-two-sorted-arrays-of-different-sizes/

Median "algorithm" for two ordered arrays

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