from __future__ import division
from random import random
from math import floor

def fractionize(R, n, d):
    error = abs(n/d - R)
    return (n, d, error)  # (numerator, denominator, absolute difference to R)

def better(a, b):
    return a if a[2] < b[2] else b

def approximate(R, n, m):
    best = (0, 1, R)
    for d in xrange(1, m+1):
        n1 = min(n, int(floor(R * d)))
        n2 = min(n, n1 + 1) # ceil(R*d)
        best = better(best, fractionize(R, n1, d))
        best = better(best, fractionize(R, n2, d))
    return best

if __name__ == '__main__':
    def main():
        R = random()
        n = 30
        m = 100
        print R, approximate(R, n, m)
    main()

best_x,best_y=(1,1)
for x in 1...n:
    y=max(1,min(m,round(x/R)))
    #optional optimization (if you have a fast gcd)
    if gcd(x,y)>1:
        continue

    if abs(R-x/y)<abs(R-bestx/besty):
        best_x,best_y=(x,y)
return (best_x,best_y)

r: input number to search.
n,m: the ranges.

for (int i=1;i<=m;i++)
{
    minVal = min(Search(i,1,n,r), minVal);
}

//x and y are start and end of array:
decimal Search(i,x,y,r)
{
   if (i/x > r)
      return i/x - r;

   decimal middle1 = i/Cill((x+y)/2);
   decimal middle2 = i/Roof((x+y)/2);

   decimal dist = min(middle1,middle2)

   decimal searchResult = 100000;

   if( middle > r)
     searchResult = Search (i, x, cill((x+y)/2),r)
  else
     searchResult = Search(i, roof((x+y)/2), y,r)

  if  (searchResult < dist)
     dist = searchResult;

  return dist;
}