Ayende @ Rahien

Peter Morris commented on Challenge: probability based selection

Wed, 25 Mar 2009 08:22:40 GMT

Brian. Your original statement implied that my code was wrong because it doesn't assume the percentages add up to 100. My point is that it doesn't matter what the percentages add up to, my routine will work with the correct ratio anyway so there is no point in restricting it. Besides, when a customer says "Always" what they actually mean is "Mostly", and when they say "Never" they mean "Hardly ever".

Avish commented on Challenge: probability based selection

Tue, 24 Mar 2009 21:40:50 GMT

Matt's solution is pretty much what I had in mind, so +1 there.

Mathias commented on Challenge: probability based selection

Tue, 24 Mar 2009 19:59:23 GMT

Matt's solution looks correct to me, and is the standard approach used in simulation. You can even optimize it a bit, by sorting your pages by decreasing probability: starting with the highest probability will likely terminate your loop earlier. Most likely irrelevant, given the size of the problem, though!

James Curran commented on Challenge: probability based selection

Tue, 24 Mar 2009 18:07:28 GMT

The first question is "Why are you rebuilding the chance[] array every time?" If the answer is "Because the PercentageToShow values may change between calls", then you are better off with some variant of the code offered by Adam/Matt/Peter. They are O(N) versus your O(100) (where N must be <100, or the algorithm won't work). However, if the answer is "I'm not. It just looks that way in the snippet", then you probably better off with what you are doing. It's O(1) with a presumably amortizable O(100) one-time set-up.

Brian commented on Challenge: probability based selection

Tue, 24 Mar 2009 17:42:05 GMT

@Peter - Its probably a bit of a silly argument in this case, but the fact that it works for values that don't add to 100 is irrelevant. The spec specifically stated that they would sum to 100.

Peter Morris commented on Challenge: probability based selection

Tue, 24 Mar 2009 17:05:03 GMT

Sorry, that would be better as... public static Page ChoosePage(List p.PercentageToShow); int randomNumber = RND.Next(totalWeight); return pages.SkipWhile(p => (randomNumber -= p.PercentageToShow) > 0).First(); } >

Cory Foy commented on Challenge: probability based selection

Tue, 24 Mar 2009 17:03:10 GMT

Must...Test...First... I meant to have the Add method clear the list before redistributing the elements to it. Sorry about that.

Peter Morris commented on Challenge: probability based selection

Tue, 24 Mar 2009 17:03:01 GMT

Aha! It was the RND that was the problem, it was returning the same value because it was being created each time. Making it static fixed it. using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace ConsoleApplication45 { class Program { static void Main(string[] args) { var pages = new List p.PercentageToShow); int randomNumber = RND.Next(totalWeight); Console.Write("Chose RND " + randomNumber.ToString()); return pages.SkipWhile(p => (randomNumber -= p.PercentageToShow) > 0).Take(1).Single(); } } public class Page { public int PercentageToShow { get; set; } } } >

Cory Foy commented on Challenge: probability based selection

Tue, 24 Mar 2009 17:01:44 GMT

Subtext stripped out all the generic statements. Let's try again: public class WeightedString { public string aString { get; set; } public int Weight { get; set; } public WeightedString(string s, int weight) { aString = s; Weight = weight; } } public class WeightedStrings : List { List distributedStrings = new List(100); List weightedStrings = new List(); public new void Add(WeightedString ws) { weightedStrings.Add(ws); foreach (WeightedString weightedString in weightedStrings) { for (int i = 0; i < weightedString.Weight; i++) { distributedStrings.Add(weightedString); } } } public string GetNextString() { return distributedStrings[new Random().Next(0, 100)].aString; } } public class Weighted { public string GetNextString() { WeightedStrings strings = new WeightedStrings(); strings.Add(new WeightedString("Hello", 80)); strings.Add(new WeightedString("World", 20)); return strings.GetNextString(); } }

Yann Schwartz commented on Challenge: probability based selection

Tue, 24 Mar 2009 17:00:53 GMT

(me again) it's really useful for markov chains when you can have big probability differences between items, greater than 1%. Also, if you have a lot of items, you can implement a nice binary search to get to your value, but then you can kiss LINQ bye bye (because of its forward only streaming)

Cory Foy commented on Challenge: probability based selection

Tue, 24 Mar 2009 17:00:06 GMT

I think it's because you are combining the weighted distribution with the selection of the next page. I don't know if this is any better, but maybe something like: public class WeightedString { public string aString { get; set; } public int Weight { get; set; } public WeightedString(string s, int weight) { aString = s; Weight = weight; } } public class WeightedStrings : List

FallenGameR commented on Challenge: probability based selection

Tue, 24 Mar 2009 16:56:14 GMT

I have had a similar issue. There was a dictionary of elements (T) and there was a probability of choosing each element (double) [Dictionary Weights]: // Make sure that summ of probabilities = 1.0 Normalize( ); // All weights are on single tape with length 1.0 // Tape is divided by regions whose length equals to their probability // Revolve the rulette and stop somewhere on the tape double rouletteStop = Random.NextDouble( ); // Search for element that we stopped at T lastElement = default( T ); foreach( T key in Weights.Keys ) { lastElement = key; rouletteStop -= Weights[ key ]; if( rouletteStop <= 0.0 ) { return lastElement; } } // We are at the end of the tape or there was rounding error return lastElement;

Yann Schwartz commented on Challenge: probability based selection

Tue, 24 Mar 2009 16:51:02 GMT

(continued) read rnd instead of limit int rnd = new Random().Next(0, 100); pages.SkipWhile(p => p.PercentageToShow < rnd).Take(1); your weights must be ordered ascending, and it must be weights, not absolute pc. Going from absolutes to weighted percentages is trivial and could be done ahead of time, once and for all.

Peter Morris commented on Challenge: probability based selection

Tue, 24 Mar 2009 16:49:52 GMT

Brian, 100 is irrelevant, the code is functionally identical whether they add up to 100, 30, or 99. The ratio should still be 2 to 1.

Yann Schwartz commented on Challenge: probability based selection

Tue, 24 Mar 2009 16:48:33 GMT

This reminds me of my probability vectors when playing with Markov Chains. There are several ways, when you don't have a lot of items in your array, best way is to use some kind of sparse array int rnd = new Random().Next(0, 100); pages.SkipWhile(p => p.PercentageToShow < limit).Take(1); Note: percentage to show is actually a weighted percentage ( p.Percentage + every p.Percentage less than that. If you want to stick to absolute percentage, you have to massage your collection first, with a loop, a aggregate of some sort and a sort)

Brian commented on Challenge: probability based selection

Tue, 24 Mar 2009 16:40:20 GMT

@Peter - 10 + 20 != 100. "We are assured that the numbers will always match to a 100."

innesm commented on Challenge: probability based selection

Tue, 24 Mar 2009 16:39:38 GMT

Pseudocode: percent = 100.0 for each page in pages { if testprobability(page.percent / percent) return page percent -= page.percent } bool testprobability(probability) { // return true if random between 0 and 1.0 is less than probability } sample: page1 20% probability == 20/100 page2 50% probability == 50/80 page3 30% probability == 30/30

Peter Morris commented on Challenge: probability based selection

Tue, 24 Mar 2009 16:31:31 GMT

Matt, I tried that too but with 2 pages (10% and 20%) I didn't get anything near a 2 to 1 ratio, more of an 8 to 1.

innesm commented on Challenge: probability based selection

Tue, 24 Mar 2009 16:25:44 GMT

You could iterate through the pages and for each page generate a boolean value from the weighted probability of that page being selected (the 'percent' of the page over the 'percent' of all remaining pages including the page). If that value is true, return the page. Eg If you get to the last page, the probability will be 1.0 that you return that page.

Remco Ros commented on Challenge: probability based selection

Tue, 24 Mar 2009 16:10:17 GMT

@Matt that works too ! nice one.

Matt commented on Challenge: probability based selection

Tue, 24 Mar 2009 16:04:42 GMT

int rand = new Random().Next(0, 100); int percentSoFar = 0; foreach (var page in pages) { percentSoFar += page.PercentageToShow; if (percentSoFar >= rand) return page; } // error?

Peter Morris commented on Challenge: probability based selection

Tue, 24 Mar 2009 15:56:09 GMT

Importantly 1: It's fast enough 2: It's very easy to understand 3: It works So I wouldn't change it.

Remco Ros commented on Challenge: probability based selection

Tue, 24 Mar 2009 15:37:36 GMT

@Ayende sorry, didn't test it. This should work: replace the last loop with: foreach (var kv in pagesperc) { if (number <= kv.Value) { foundpage = kv.Key; break; } }

Adam commented on Challenge: probability based selection

Tue, 24 Mar 2009 15:34:17 GMT

I'm not sure about the language, but wouldn't this work? int index = new Random().Next(0, 100); foreach (var page in pages) { if (index < page.PercentageToShow) return page; index -= page.PercentageToShow; } ?

Brian commented on Challenge: probability based selection

Tue, 24 Mar 2009 15:32:03 GMT

Maybe the one loop approach (you'd have to use a different first loop then Remco) isn't more elegant, just thought you might be looking at the problem backwards.

Ayende Rahien commented on Challenge: probability based selection

Tue, 24 Mar 2009 15:20:35 GMT

I don't understand how this is suppose to work. Let us assume that you have 50% / 50%. And random returns 7.

Brian commented on Challenge: probability based selection

Tue, 24 Mar 2009 15:19:23 GMT

@Remco at that point, why don't you just put the random number selection before the first loop and do away with the second loop entirely?

Remco Ros commented on Challenge: probability based selection

Tue, 24 Mar 2009 15:16:52 GMT

Sorry, comment messed up. The dictionary should be generic {Page, int}

Remco Ros commented on Challenge: probability based selection

Tue, 24 Mar 2009 15:15:49 GMT

how about: var pagesperc = new Dictionary (); int total = 0; foreach(var page in pages) { pagesperc.Add(page, page.PercentageToShow + total) total += page.PercentageToShow; } int rnd = new Random().Next(0, 100); foreach(var kv in pagesperc) { if (kv.Value == rnd) { return kv.Key } }

Brian commented on Challenge: probability based selection

Tue, 24 Mar 2009 14:58:51 GMT

Maybe I'm missing the something, but aren't you just finding the page that has a percentage range (offset by the sum of previous percentages) in which a random number falls? If so, you should be able to remove at least one loop.