Question

In a program I’m writing in an unnamed language, I have a block of text for which the width is unknown, and all I know is the maximum width that this block of text could be. Given this information, I need to find out the smallest possible width that this text could be (assume that I can’t use the metrics of the characters / glyphs or the character count). So far I just have a brute force solution which looks like follows:

for (int i = .1; i < maxTextWidth; i += .1)
{
       if (textFitsInGivenWidth(text, i))
       {
             textWidth = i;
             break;
       }
}

I’d like to try and optimize this as much as I can. My first thought was to use a binary search, but I’m having trouble implementing this in the proper way (and am not sure if it’s even possible). Does anyone have any suggestions on what I could do here to improve the run time using only what I’ve given in the above solution?

Answer 1

Binary Search is the answer indeed.

http://en.wikipedia.org/wiki/Binary_search_algorithm

for integer binary search, it can be:

minW=0, maxW=maxTextWidth
while(minW<=maxW){

  mid=(minW+maxW)/2;
  if (textFitsInGivenWidth(text, mid)){
    maxW=mid-1;
  }else{
    minW=mid+1;
  }
}
textWidth=minW

The idea is, if you have textFitsInGivenWidth(text, mid) == True,

then you must have textFitsInGivenWidth(text, i) == True for all i>=mid,

and if it’s False, then you have textFitsInGivenWidth(text, i) == False for all i<=mid

so each time we check the middle of the interval to be checked, and reduce the interval into half . The time is O(logN), in which N=maxTextWidth

update: for float support, see the example below :

float minW=0, maxW=maxTextWidth
while(1){
  if (maxW-minW<0.05)
    break;
  float mid=(minW+maxW)/2;
  if (textFitsInGivenWidth(text, mid)){
    maxW=mid;
  }else{
    minW=mid;
  }
}

textWidth=minW

and to get a precision of .1, simply change the last line to :

textWidth=int(minW*10)/10.0