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mp_20200515.php

puggan May 15th, 2020 1,053 Never
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  1. <?php
  2.  
  3. /*
  4.  * a & b is positive integers
  5.  * f(0) = a;
  6.  * f(1) = a + b;
  7.  * f(n) = f(n-1) + f(n-2)
  8.  * f(x) = 1e6, find a & b so that x get as high as posible
  9.  *
  10.  * g(0,a,b) = a
  11.  * g(1,a,b) = a+b
  12.  * g(n,a,b) = g(n-1,a,b) + g(n-2,a,b)
  13.  *
  14.  * g(n,0,1) => fibinatchii => g(31,0,1) > 1e6 => n < 31
  15.  * best found; g(18,144,154) = 1e6
  16.  * g(18,a,b) = 4181a + 2584b
  17.  * g(19,a,b) = 6765a + 4181b, x > 18 => 4181b < 1e6 => b < 240
  18.  */
  19.  
  20. function fibMaker($a, $b) {
  21.     yield $a;
  22.     while(true) {
  23.         yield $b += $a;
  24.         yield $a += $b;
  25.     }
  26. }
  27.  
  28. function serie($n = 0, $max = 240) {
  29.     while($n < $max) {
  30.         yield $n++;
  31.     }
  32. }
  33.  
  34. function getX($a, $b, $goal = 1e6, $limit = 31) {
  35.     $fib = fibMaker($a,$b);
  36.     $index = 0;
  37.     foreach($fib as $n) {
  38.         if($n == $goal) {
  39.             return $index;
  40.         }
  41.         if($n > $goal) {
  42.             return 0;
  43.         }
  44.         if($index > $limit) {
  45.             return 0;
  46.         }
  47.         $index++;
  48.     }
  49.     return 0;
  50. }
  51.  
  52. $best = 1;
  53. foreach(serie(1) as $n1) {
  54.     echo $n1, "\r";
  55.     foreach(serie(0) as $n2) {
  56.         $x = getX($n1, $n2);
  57.         if($x >= $best) {
  58.             echo 'g(', $x, ',', $n1, ',', $n2, ') = 1e6', PHP_EOL;
  59.             $best = $x;
  60.         }
  61.     }
  62. }
  63. echo '    ', PHP_EOL;
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