Question

Suppose I have a database table with 3 fields: string title, int A, int B.
A range of both A and B is 1 to 500.
I want to represent part of the values as a matrix 5×5.
So that (1, 1) will be string which has lowest both A and B;
(5, 5) will have highest both A and B;
(1, 5) will have lowest A and highest B. And so on.
Which algorithm should I use?

Answer 1

I have set up a simulation here and comments will describe the steps.

First I generate some data: a series of tuples each containing a string and two random numbers representing score A and B.

Next I divide the ranges of A and B into five equally spaced bins, each representing the minimum and maximum for a cell.

Then I serially query the data set to extract the strings in each cell.

There are a hundred ways of optimizing this, based on the actual data structure and storage you are using.

from random import random

# Generate data and keep record of scores
data = []
a_list = []
b_list = []
for i in range(50):
    a = int(random()*500)+1
    b = int(random()*500)+1
    rec = { 's' : 's%s' % i,
            'a' : a,
            'b' : b
             }
    a_list.append(a)
    b_list.append(b)
    data.append(rec)

# divide A and B ranges into five bins

def make_bins(f_list):
    f_min = min(f_list)
    f_max = max(f_list)
    f_step_size = (f_max - f_min) / 5.0
    f_steps = [ (f_min + i * f_step_size,
                 f_min + (i+1) * f_step_size)
                for i in range(5) ]
    # adjust top bin to be just larger than maximum
    top = f_steps[4]
    f_steps[4] = ( top[0], f_max+1 )
    return f_steps

a_steps = make_bins(a_list)
b_steps = make_bins(b_list)

# collect the strings that fit into any of the bins
# thus all the strings in cell[4,3] of your matrix
# would fit these conditions:
# string would have a Score A that is
# greater than or equal to the first element in a_steps[3]
# AND less than the second element in a_steps[3]
# AND it would have a Score B that is
# greater than or equal to the first element in b_steps[2]
# AND less than the second element in a_steps[2]
# NOTE: there is a need to adjust the pointers due to
#       the way you have numbered the cells of your matrix

def query_matrix(ptr_a, ptr_b):
    ptr_a -= 1
    from_a = a_steps[ptr_a][0]
    to_a = a_steps[ptr_a][1]

    ptr_b -= 1
    from_b = b_steps[ptr_b][0]
    to_b = b_steps[ptr_b][1]

    results = []
    for rec in data:
        s = rec['s']
        a = rec['a']
        b = rec['b']
        if (a >= from_a and
            a < to_a and
            b >= from_b and
            b < to_b):
            results.append(s)
    return results

# Print out the results for a visual check
total = 0
for i in range(5):
    for j in range(5):
        print '=' * 80
        print 'Cell: ', i+1, j+1, ' contains: ',
        hits = query_matrix(i+1,j+1)
        total += len(hits)
        print hits
print '=' * 80
print 'Total number of strings found: ', total