Related
Is there an intelligent way to identify the order of a Bitwise Enum?
Take this enum for example:
[System.FlagsAttribute()]
internal enum AnswersSort : int
{
None = 0,
Bounty = 1,
MarkedAnswer = 2,
MostVotes = 4
}
If I combine these in different ways:
var result = AnswersSort.MarkedAnswer | AnswersSort.MostVotes | AnswersSort.Bounty;
result = AnswersSort.MostVotes | AnswersSort.Bounty | AnswersSort.MarkedAnswer;
Both results are 7 and the order is lost. Is there a way to do this without using an array or a list? Ideally I'm looking for a solution using an enum but I'm not sure how or if it's possible.
If you have 10 values, you need 4 bits per item. You could treat the combination as a single 40-bit value, encoded with 4 bits per digit. So, given your two examples:
var result = AnswersSort.MarkedAnswer | AnswersSort.MostVotes | AnswersSort.Bounty;
result = AnswersSort.MostVotes | AnswersSort.Bounty | AnswersSort.MarkedAnswer;
The first would be encoded as
0010 0100 0001
---- ---- ----
| | - Bounty
| - MostVotes
- MarkedAnswer
You could build that in a 64-bit integer:
long first = BuildValue(AnswersSort.MarkedAnswer, AnswersSort.MostVotes, AnswersSort.Bounty);
long BuildValue(params AnswersSort[] values)
{
long result = 0;
foreach (var val in values)
{
result = result << 4;
result |= (int)val;
}
return result;
}
Given a list of opponent seeds (for example seeds 1 to 16), I'm trying to write an algorithm that will result in the top seed playing the lowest seed in that round, the 2nd seed playing the 2nd-lowest seed, etc.
Grouping 1 and 16, 2 and 15, etc. into "matches" is fairly easy, but I also need to make sure that the higher seed will play the lower seed in subsequent rounds.
An example bracket with the correct placement:
1 vs 16
1 vs 8
8 vs 9
1 vs 4
4 vs 13
4 vs 5
5 vs 12
1 vs 2
2 vs 15
2 vs 7
7 vs 10
2 vs 3
3 vs 14
3 vs 6
6 vs 11
As you can see, seed 1 and 2 only meet up in the final.
This JavaScript returns an array where each even index plays the next odd index
function seeding(numPlayers){
var rounds = Math.log(numPlayers)/Math.log(2)-1;
var pls = [1,2];
for(var i=0;i<rounds;i++){
pls = nextLayer(pls);
}
return pls;
function nextLayer(pls){
var out=[];
var length = pls.length*2+1;
pls.forEach(function(d){
out.push(d);
out.push(length-d);
});
return out;
}
}
> seeding(2)
[1, 2]
> seeding(4)
[1, 4, 2, 3]
> seeding(8)
[1, 8, 4, 5, 2, 7, 3, 6]
> seeding(16)
[1, 16, 8, 9, 4, 13, 5, 12, 2, 15, 7, 10, 3, 14, 6, 11]
With your assumptions, players 1 and 2 will play in the final, players 1-4 in the semifinals, players 1-8 in the quarterfinals and so on, so you can build the tournament recursively backwards from the final as AakashM proposed. Think of the tournament as a tree whose root is the final.
In the root node, your players are {1, 2}.
To expand the tree recursively to the next level, take all the nodes on the bottom layer in the tree, one by one, and create two children for them each, and place one of the players of the original node to each one of the child nodes created. Then add the next layer of players and map them to the game so that the worst newly added player plays against the best pre-existing player and so on.
Here first rounds of the algorithm:
{1,2} --- create next layer
{1, _}
/ --- now fill the empty slots
{1,2}
\{2, _}
{1, 4} --- the slots filled in reverse order
/
{1,2}
\{2, 3} --- create next layer again
/{1, _}
{1, 4}
/ \{4, _}
{1,2} --- again fill
\ /{2, _}
{2, 3}
\{3, _}
/{1, 8}
{1, 4}
/ \{4, 5} --- ... and so on
{1,2}
\ /{2, 7}
{2, 3}
\{3, 6}
As you can see, it produces the same tree you posted.
I've come up with the following algorithm. It may not be super-efficient, but I don't think that it really needs to be. It's written in PHP.
<?php
$players = range(1, 32);
$count = count($players);
$numberOfRounds = log($count / 2, 2);
// Order players.
for ($i = 0; $i < $numberOfRounds; $i++) {
$out = array();
$splice = pow(2, $i);
while (count($players) > 0) {
$out = array_merge($out, array_splice($players, 0, $splice));
$out = array_merge($out, array_splice($players, -$splice));
}
$players = $out;
}
// Print match list.
for ($i = 0; $i < $count; $i++) {
printf('%s vs %s<br />%s', $players[$i], $players[++$i], PHP_EOL);
}
?>
I also wrote a solution written in PHP. I saw Patrik Bodin's answer, but thought there must be an easier way.
It does what darkangel asked for: It returns all seeds in the correct positions. The matches are the same as in his example, but in a prettier order, seed 1 and seed number 16 are on the outside of the schema (as you see in tennis tournaments).
If there are no upsets (meaning a higher seeded player always wins from a lower seeded player), you will end up with seed 1 vs seed 2 in the final.
It actually does two things more:
It shows the correct order (which is a requirement for putting byes in the correct positions)
It fills in byes in the correct positions (if required)
A perfect explanation about what a single elimination bracket should look like: http://blog.playdriven.com/2011/articles/the-not-so-simple-single-elimination-advantage-seeding/
Code example for 16 participants:
<?php
define('NUMBER_OF_PARTICIPANTS', 16);
$participants = range(1,NUMBER_OF_PARTICIPANTS);
$bracket = getBracket($participants);
var_dump($bracket);
function getBracket($participants)
{
$participantsCount = count($participants);
$rounds = ceil(log($participantsCount)/log(2));
$bracketSize = pow(2, $rounds);
$requiredByes = $bracketSize - $participantsCount;
echo sprintf('Number of participants: %d<br/>%s', $participantsCount, PHP_EOL);
echo sprintf('Number of rounds: %d<br/>%s', $rounds, PHP_EOL);
echo sprintf('Bracket size: %d<br/>%s', $bracketSize, PHP_EOL);
echo sprintf('Required number of byes: %d<br/>%s', $requiredByes, PHP_EOL);
if($participantsCount < 2)
{
return array();
}
$matches = array(array(1,2));
for($round=1; $round < $rounds; $round++)
{
$roundMatches = array();
$sum = pow(2, $round + 1) + 1;
foreach($matches as $match)
{
$home = changeIntoBye($match[0], $participantsCount);
$away = changeIntoBye($sum - $match[0], $participantsCount);
$roundMatches[] = array($home, $away);
$home = changeIntoBye($sum - $match[1], $participantsCount);
$away = changeIntoBye($match[1], $participantsCount);
$roundMatches[] = array($home, $away);
}
$matches = $roundMatches;
}
return $matches;
}
function changeIntoBye($seed, $participantsCount)
{
//return $seed <= $participantsCount ? $seed : sprintf('%d (= bye)', $seed);
return $seed <= $participantsCount ? $seed : null;
}
?>
The output:
Number of participants: 16
Number of rounds: 4
Bracket size: 16
Required number of byes: 0
C:\projects\draw\draw.php:7:
array (size=8)
0 =>
array (size=2)
0 => int 1
1 => int 16
1 =>
array (size=2)
0 => int 9
1 => int 8
2 =>
array (size=2)
0 => int 5
1 => int 12
3 =>
array (size=2)
0 => int 13
1 => int 4
4 =>
array (size=2)
0 => int 3
1 => int 14
5 =>
array (size=2)
0 => int 11
1 => int 6
6 =>
array (size=2)
0 => int 7
1 => int 10
7 =>
array (size=2)
0 => int 15
1 => int 2
If you change 16 into 6 you get:
Number of participants: 6
Number of rounds: 3
Bracket size: 8
Required number of byes: 2
C:\projects\draw\draw.php:7:
array (size=4)
0 =>
array (size=2)
0 => int 1
1 => null
1 =>
array (size=2)
0 => int 5
1 => int 4
2 =>
array (size=2)
0 => int 3
1 => int 6
3 =>
array (size=2)
0 => null
1 => int 2
# Here's one in python - it uses nested list comprehension to be succinct:
from math import log, ceil
def seed( n ):
""" returns list of n in standard tournament seed order
Note that n need not be a power of 2 - 'byes' are returned as zero
"""
ol = [1]
for i in range( ceil( log(n) / log(2) ) ):
l = 2*len(ol) + 1
ol = [e if e <= n else 0 for s in [[el, l-el] for el in ol] for e in s]
return ol
For JavaScript code, use one of the two functions below. The former embodies imperative style & is much faster. The latter is recursive & neater, but only applicable to relatively small number of teams (<16384).
// imperative style
function foo(n) {
const arr = new Array(n)
arr[0] = 0
for (let i = n >> 1, m = 1; i >= 1; i >>= 1, m = (m << 1) + 1) {
for (let j = n - i; j > 0; j -= i) {
arr[j] = m - arr[j -= i]
}
}
return arr
}
Here you fill in the spots one by one by mirroring already occupied ones. For example, the first-seeded team (that is number 0) goes to the topmost spot. The second one (1) occupies the opposite spot in the other half of the bracket. The third team (2) mirrors 1 in their half of the bracket & so on. Despite the nested loops, the algorithm has a linear time complexity depending on the number of teams.
Here is the recursive method:
// functional style
const foo = n =>
n === 1 ? [0] : foo(n >> 1).reduce((p, c) => [...p, c, n - c - 1], [])
Basically, you do the same mirroring as in the previous function, but recursively:
For n = 1 team, it's just [0].
For n = 2 teams, you apply this function to the argument n-1 (that is,
1) & get [0]. Then you double the array by inserting mirrored
elements between them at even positions. Thus, [0] becomes [0, 1].
For n = 4 teams, you do the same operation, so [0, 1] becomes [0, 3,
1, 2].
If you want to get human-readable output, increase each element of the resulting array by one:
const readableArr = arr.map(i => i + 1)
At each round sort teams by seeding criteria
(If there are n teams in a round)team at ith position plays with team n-i+1
Since this comes up when searching on the subject, and it's hopeless to find another answer that solves the problem AND puts the seeds in a "prettier" order, I will add my version of the PHP code from darkangel. I also added the possibility to give byes to the higher seed players.
This was coded in an OO environment, so the number of participants are in $this->finalists and the number of byes are in $this->byes. I have only tested the code without byes and with two byes.
public function getBracket() {
$players = range(1, $this->finalists);
for ($i = 0; $i < log($this->finalists / 2, 2); $i++) {
$out = array();
$reverse = false;
foreach ($players as $player) {
$splice = pow(2, $i);
if ($reverse) {
$out = array_merge($out, array_splice($players, -$splice));
$out = array_merge($out, array_splice($players, 0, $splice));
$reverse = false;
} else {
$out = array_merge($out, array_splice($players, 0, $splice));
$out = array_merge($out, array_splice($players, -$splice));
$reverse = true;
}
}
$players = $out;
}
if ($this->byes) {
for ($i = 0; $i < $this->byes; $i++ ) {
for ($j = (($this->finalists / pow(2, $i)) - 1); $j > 0; $j--) {
$newPlace = ($this->finalists / pow(2, $i)) - 1;
if ($players[$j] > ($this->finalists / (pow(2 ,($i + 1))))) {
$player = $players[$j];
unset($players[$j]);
array_splice($players, $newPlace, 0, $player);
}
}
}
for ($i = 0; $i < $this->finalists / (pow(2, $this->byes)); $i++ ) {
$swap[] = $players[$i];
}
for ($i = 0; $i < $this->finalists /(pow(2, $this->byes)); $i++ ) {
$players[$i] = $swap[count($swap) - 1 - $i];
}
return array_reverse($players);
}
return $players;
}
I worked on a PHP / Laravel plugin that generates brackets with / without preliminary round robin. Maybe it can be useful to you, I don't know what tech you are using. Here is the github.
https://github.com/xoco70/kendo-tournaments
Hope it helps!
A C version.
int * pctournamentSeedArray(int PlayerCnt)
{
int * Array;
int * PrevArray;
int i;
Array = meAlloc(sizeof(int) * PlayerCnt);
if (PlayerCnt == 2)
{
Array[0] = 0;
Array[1] = 1;
return Array;
}
PrevArray = pctournamentSeedArray(PlayerCnt / 2);
for (i = 0; i < PlayerCnt;i += 2)
{
Array[i] = PrevArray[i / 2];
Array[i + 1] = (PlayerCnt - 1) - Array[i] ;
}
meFree(PrevArray);
return Array;
}
I have two sets of integers A and B (size of A less than or equal to B), and I want to answer the question, "How close is A to B?". The way I want to answer this question is by producing a measure of how far you have to go from a given a in A to find a b in B.
The specific measure I want to produce does the following: for each a, find the closest b, the only catch being that once I match a b with an a, I can no longer use that b to match any other a's. (EDIT: the algorithm I'm trying to implement will always prefer a shorter match. So if b is the nearest neighbor to more than one a, pick the a nearest to b. I'm not sure what to do if more than one a has the same distance to b, right now I'm picking the a that precedes b, but that's quite arbitrary and not necessarily optimal.) The measure that I'll for make these sets, the final product, is a histogram showing the number of pairs in the vertical axis and the distance of the pairs in the x-axis.
So if A = {1, 3, 4} and B = {1, 5, 6, 7}, I will get the following a,b pairs: 1,1, 4,5, 3,6. For these data, the histogram should show one pair with distance zero, one pair with distance 1, and one pair with distance 3.
(The actual size of these sets has an upper bound around 100,000 elements, and I read them in from disk already sorted low to high. The integers range from 1 to ~20,000,000. EDIT: also, the elements of A and B are unique, i.e. no repeated elements.)
The solution I've come up with feels a bit clunky. I'm using Perl, but the problem is more or less language agnostic.
First I make a hash, with one key for each number that appears in the union of A and B and values indicating whether each number appears in A, B, or both, e.g. $hash{5} = {a=>1, b=>1} if the number 5 appears in both data-sets. (If it only appeared in A, you'd have $hash{5} = {a=>1}.)
Next, I iterate over A to find all the hash elements that appear in A and B, mark them in the measure, and remove them from the hash.
Then, I sort all the hash keys and make each element of the hash point to its nearest neighbors, like a linked list, where a given hash element now looks like $hash{6} = {b=>1, previous=>4, next=>8}. The linked list doesn't know whether the next and previous elements are in A or B.
Then I loop over pair distances starting at d=1, and find all pairs with distance d, mark them, remove them from the hash, until there are no more elements of A to match.
The loop looks like this:
for ($d=1; #a > 0; $d++) {
#left = ();
foreach $a in #a {
$next = $a;
# find closest b ahead of $a, stop searching if you pass $d
while (exists $hash{$next}{next} && $next - $a < $d) {
$next = $hash{$next}{next};
}
if ($next is in B && $next - $a == $d) {
# found a pair at distance $d
mark_in_measure($a, $next);
remove_from_linked_list($next);
remove_from_linked_list($a);
next;
}
# do same thing looking behind $a
$prev = $a;
...
# you didn't find a match for $a
push #left, $a;
}
#a = #left;
}
This loop obviously prefers pairs that match b's that appear later than a's; I can't tell whether there's a sensible way to decide whether later is better than prior (better in terms of getting closer pairs). The main optimization I'm interested in is processing time.
Sounds like you have a particular case of the Assignment Problem (finding a minimum matching in a weighted bipartite graph).
The algorithm to solve the assignment problem is too slow for you at O(N^3) but I'm pretty sure there you can shave some of this complexity off by exploiting your particular weight function or how you only want a histogram instead of the exact matching.
#!/usr/bin/perl
use strict;
use warnings FATAL => 'all';
use diagnostics;
# http://www.hungarianalgorithm.com/solve.php?c=3-2-6-22--7-2-2-18--13-8-4-12--23-18-14-2&random=1
# https://www.topcoder.com/community/data-science/data-science-tutorials/assignment-problem-and-hungarian-algorithm/
# http://www.cse.ust.hk/~golin/COMP572/Notes/Matching.pdf
my #mat;
my #out_mat;
my $spaces = 6;
my $precision = 0;
my $N = 10;
my $M = 12;
my $r = 100;
my #array1; my #array2;
for my $i (1..$N) {
push #array1, sprintf( "%.${precision}f", rand($r) );
}
for my $i (1..$M) {
push #array2, sprintf( "%.${precision}f", rand($r) );
}
##array1 = ( 1, 3, 4); # $mat[i]->[j] = abs( array1[i] - array2[j] )
##array2 = ( 1, 5, 6, 7);
# 1 5 6 7
# 1 [ 0* 4 5 6 ]
# 3 [ 2 2* 3 4 ]
# 4 [ 3 1 2* 3 ]
my $min_size = $#array1 < $#array2 ? $#array1 : $#array2;
my $max_size = $#array1 > $#array2 ? $#array1 : $#array2;
for (my $i = 0; $i < #array1; $i++){
my #weight_function;
for (my $j = 0; $j < #array2; $j++){
my $dif = sprintf( "%.${precision}f", abs ($array1[$i] - $array2[$j]) );
#my $dif = sprintf( "%.${precision}f", ($array1[$i] - $array2[$j])**2 );
push #weight_function, $dif;
}
push #mat, \#weight_function;
}
# http://cpansearch.perl.org/src/TPEDERSE/Algorithm-Munkres-0.08/lib/Algorithm/Munkres.pm
Algorithm::Munkres::assign(\#mat,\#out_mat);
print "\n\#out_mat index = [";
for my $index (#out_mat) {
printf("%${spaces}d", $index);
}
print " ]\n";
print "\#out_mat values = [";
my %hash;
for my $i (0 .. $max_size){
my $j = $out_mat[$i];
last if ( $i > $min_size and $#array1 < $#array2 );
next if ( $j > $min_size and $#array1 > $#array2 );
my $dif = $mat[$i]->[$j];
printf( "%${spaces}.${precision}f", $dif );
$hash{ $dif } { $i } { 'index_array1' } = $i;
$hash{ $dif } { $i } { 'index_array2' } = $j;
$hash{ $dif } { $i } { 'value_array1' } = $array1[$i];
$hash{ $dif } { $i } { 'value_array2' } = $array2[$j];
}
print " ]\n\n";
my $soma_da_dif = 0;
foreach my $min_diferenca ( sort { $a <=> $b } keys %hash ){
foreach my $k ( sort { $a <=> $b } keys %{$hash{$min_diferenca}} ){
$soma_da_dif += $min_diferenca;
my $index_array1 = $hash{ $min_diferenca } { $k } { 'index_array1' };
my $index_array2 = $hash{ $min_diferenca } { $k } { 'index_array2' };
my $value_array1 = $hash{ $min_diferenca } { $k } { 'value_array1' };
my $value_array2 = $hash{ $min_diferenca } { $k } { 'value_array2' };
printf( " index (%${spaces}.0f,%${spaces}.0f), values (%${spaces}.${precision}f,%${spaces}.${precision}f), dif = %${spaces}.${precision}f\n",
$index_array1, $index_array2, $value_array1, $value_array2, $min_diferenca );
}
}
print "\n\nSum = $soma_da_dif\n";
#-------------------------------------------------#
#------------------ New-Package ------------------#
{ # start scope block
package Algorithm::Munkres;
use 5.006;
use strict;
use warnings;
require Exporter;
our #ISA = qw(Exporter);
our #EXPORT = qw( assign );
our $VERSION = '0.08';
...
... <---- copy all the 'package Algorithm::Munkres' here
...
return $minval;
}
1; # don't forget to return a true value from the file
} # end scope block
I've been trying to work out exactly how the TED Talk homepage works. Leaving aside all the animation rubbish, I find the way that the boxes are organised is really fascinating.
At first glance it looks like the jQuery masonry plugin, bu it quickly becomes clear that it tends to create several right angle triangle shapes, but has no fixed number of columns or rows, and the final shape produced is always completely solid (no hollow parts).
My initial assumption was that the boxes (their size is predetermined by some factor on the site) were sorted randomly and then sequentially added to the grid using a few simple rules, however I can't identify what those rules might be, or how they could prevent any hollows in the final shape.
Does anyone have any idea how this works?
Could be wrong but a few observations:
Each section has 19 videos
There are 4 sizes 1 (#1), 1/4 (#2), 1/16 (#3) and 1/32 (#4)
For a given section, there are always 4(#1). The number of (#2), (#3) and (#4) can be either:
4(#1), 10(#2), 4(#3), 1(#1) = 19
4(#1), 11(#2), 4(#3), 0(#1) = 19
4(#1), 11(#2), 3(#3), 1(#1) = 19
4(#1), 12(#2), 2(#3), 1(#1) = 19
4(#1), 13(#2), 1(#3), 1(#1) = 19
As for the order:
The first row always contains 2(#1) and 4(#2)
(#4) are always at the bottom of a column
Here is the javascript code which does it (you need a html page with a div#container):
function ted_layout(settings, coordinates_array, num_elements, start_x, start_y, arrangement, remaining_elements, is_child){
var num_columns = arrangement.length;
var col = 0;
var current_x = start_x;
while( col < num_columns){
var column_x_scale = 100 / arrangement[col];
var current_column_arrangement;
if(is_child){
if(num_elements > 14){
if(column_x_scale == 50){
current_column_arrangement = random_shuffle([1, 2, 2]);
} else {
current_column_arrangement = random_shuffle([1, 2]);
}
} else if(num_elements > 10){
if(column_x_scale == 50){
current_column_arrangement = [1];
} else {
current_column_arrangement = random_shuffle([1, 2]);
}
} else{
current_column_arrangement = random_shuffle([1, 2]);
}
} else {
if(num_elements > 14){
if(column_x_scale == 25){
current_column_arrangement = [1, 1];
} else {
current_column_arrangement = [1];
}
} else if(column_x_scale == 25){
current_column_arrangement = [1, 1];
} else {
current_column_arrangement = [1];
}
}
var num_rows = current_column_arrangement.length;
var current_y = start_y;
var row = 0;
while(row < num_rows){
var numRects = current_column_arrangement[row];
var current_rectangle = 0;
var current_rectangle_x = current_x;
while( current_rectangle < numRects){
if(remaining_elements == 0){
return coordinates_array;
}
var currScale = column_x_scale/numRects;
var height = settings.height * currScale*0.01;
var width = settings.width * currScale*0.01;
if(current_rectangle == numRects-1 && row == num_rows-1 && is_child && Math.random() > 0.5){
coordinates_array.push({x: current_rectangle_x, y:current_y, w:width/2, h:height/2, scale:currScale/2*0.01*2})
}
else{
coordinates_array.push({x: current_rectangle_x, y:current_y, w:width, h:height, scale:currScale*0.01*2})
}
current_rectangle_x += width;
remaining_elements--;
current_rectangle++;
}
row++;
current_y += height;
}
current_x = current_rectangle_x;
col++;
}
if( remaining_elements > 0){
coordinates_array = ted_layout(settings, coordinates_array, num_elements, start_x, current_y, random_shuffle([2, 4, 4, 2]), remaining_elements, true);
}
return coordinates_array;
}
function generate_ted_layout(num_elements){
var settings = {
width: 640,
height: 480,
};
var coordinates_array=[];
returned = ted_layout(settings, coordinates_array, num_elements, 0, 0, random_shuffle([2, 4, 4, 2]), num_elements, false);
console.log("Returned", returned)
return returned;
}
function random_shuffle(array){
var temp;
for(var i = array.length - 1; i >= 1; i--){
var elem = Math.floor(Math.random() * (i + 1));
temp = array[elem];
array[elem] = array[i];
array[i] = temp;
}
return array;
}
function initAndLayout() {
var items = generate_ted_layout(20);
var container = $('#container'); // cache jquery object
console.log(items);
for (var i = 0; i < items.length; i++)
{
var item = items[i];
console.log(item);
$('#container').append($('<div class="item"></div>').css({'left': item.x, 'top': item.y, 'width': item.w, 'height': item.h}));
}
}
I think I've worked it out.
First of all the number of items varies substantially, I'm currently viewing a page with only 13 boxes.
To start I'll name each of the 4 sizes of blocks from largest to smallest as:
A,B,C,D
As we know the first 'row' contains two As and two vertical stacks of Bs, for example:
_______________________
| A | B | A | B |
| |___| |___|
| | B | | B |
|_______|___|_______|___|
The arrangement of these appears to be random, but the Bs are always in the same vertical pattern. Looking at this just now I realised that there are only two rows, and the second row works in the same way.
The second row is twice the height of the first, taking up the rest of the page. It is built of horizontally stacked patterns of shapes, which are (at least in part) selected randomly.
I've found 9 of these patterns of shapes, two of which are a single A or B and the rest are:
_______ _______ _______ ___ ___ _______ ___
| B | B | | A | | B | B | |C|C| | B | | A | |C|C|
|___|___| | | |___|___| | B | |___| | |
| A | | | | B | B | |___| |C|D | |
| | |_______| |___|___| |_______|
| | | B | B | | A | | B |
|_______| |___|___| | | |___|
|B |C| |B |C| | |
|___| |___| |_______|
The next question is how are these selected? There may be some clever searching to find the best configuration: for example if there are X items to be displayed we need to find a configuration with a total of X which does not exceed the width of the row.
This could be done with a metric of pattern density, which would be number of blocks divided by the width of the pattern.
I'm looking for some algorithm that for a given record with n properties with n possible values each (int, string etc) searches a number of existing records and gives back the one that matches the most properties.
Example:
A = 1
B = 1
C = 1
D = f
A | B | C | D
----+-----+-----+----
1 | 1 | 9 | f <
2 | 3 | 1 | g
3 | 4 | 2 | h
2 | 5 | 8 | j
3 | 6 | 5 | h
The first row would be the one I'm looking for, as it has the most matching values. I think it doesn't need to calculate any closeness to the values, because then row 2 might be more matching.
Loop through each row, add one to the row score of a field matches (field one has a score of 2) and when that's done, you have a resultset of scores which you can sort.
The basic algorithm could look like (in java pseudo code):
int bestMatchIdx = -1;
int currMatches = 0;
int bestMatches = 0;
for ( int row = 0 ; row < numRows ; row++ ) {
currMatches = 0;
for ( int col = 0 ; col < numCols ; col++ ) {
if ( search[col].equals( rows[ row ][ cols] ))
currMatches++;
}
if ( currMatches > bestMatches ) {
bestMatchIdx = row;
bestMatches = currMatches;
}
}
This assumes that you have an equals function to compare, and the data stored in a 2D array. 'search' is the reference row to compare all other rows against it.