Question

I have a perfectly square 64×64 2D array of integers that will never have a value greater than 64. I was wondering if there is a really fast way to compare all of the elements with each other and display the ones that are the same, in a unique way.

At the current moment I have this

2D int array named array
loop from i = 0 to 64
    loop from j = 0 to 64
        loop from k = (j+1) to 64
            loop from z = 0 to 64
                if(array[i][j] == array[k][z])
                    print "element [i][j] is same as [k][z]

As you see having 4 nested loops is quite a stupid thing that I would like not to use. Language does not matter at all whatsoever, I am just simply curious to see what kind of cool solutions it is possible to use. Since value inside any integer will not be greater than 64, I guess you can only use 6 bits and transform array into something fancier. And that therefore would require less memory and would allow for some really fancy bitwise operations. Alas I am not quite knowledgeable enough to think in that format, and therefore would like to see what you guys can come up with.

Thanks to anyone in advance for a really unique solution.

Answer 1

There’s no need to sort the array via an O(m log m) algorithm; you can use an O(m) bucket sort. (Letting m = n*n = 64*64).

An easy O(m) method using lists is to set up an array H of n+1 integers, initialized to -1; also allocate an array L of m integers each, to use as list elements. For the i‘th array element, with value A[i], set k=A[i] and L[i]=H[k] and H[k]=i. When that’s done, each H[k] is the head of a list of entries with equal values in them. For 2D arrays, treat array element A[i,j] as A[i+n*(j-1)].

Here’s a python example using python lists, with n=7 for ease of viewing results:

import random
n = 7
m = n*n
a=[random.randint(1,n) for i in range(m)]
h=[[] for i in range(n+1)]
for i in range(m):
    k = a[i]
    h[k].append(i)
for i in range(1,n+1):
    print 'With value %2d:  %s' %(i, h[i])

Its output looks like:

With value  1:  [1, 19, 24, 28, 44, 45]
With value  2:  [3, 6, 8, 16, 27, 29, 30, 34, 42]
With value  3:  [12, 17, 21, 23, 32, 41, 47]
With value  4:  [9, 15, 36]
With value  5:  [0, 4, 7, 10, 14, 18, 26, 33, 38]
With value  6:  [5, 11, 20, 22, 35, 37, 39, 43, 46, 48]
With value  7:  [2, 13, 25, 31, 40]