Choice - Weighted Random Selector

Created by Hiroya Aramaki (Makihiro)

What is Weighted Random Selector ?

Weighted Random Selector is an algorithm for randomly selecting elements based on their weights.

For example.

• Drop items based on rarity.
• Events that occur with a certain probability

It can be used to determine things with probability.

Choice is a library that was created to make it easier to implement.

// This is the simplest usage.
var randomSelectedItem = items
	.ToWeightedSelector(item => item.weight)
	.SelectItemWithUnityRandom();

Great introduction article on Weighted Random Select: https://blog.bruce-hill.com/a-faster-weighted-random-choice

Table of Contents

• 📥 Installation
• 🔰 Usage
  • ToWeightedSelector Overloads
    • from weighted entry pattern
    • from weighted item pattern
    • from Dictionary<Item,float> pattern
  • LINQ
  • Algorithms
    • Linear Scan
    • Binary Search
    • Alias Method
    • Speed Measurement
• 📔 Author Info
• 📜 License

📥 Installation

Download any version from releases.

Releases: https://github.com/mackysoft/Choice/releases

Install via git URL

Or, you can add this package by opening PackageManager and entering

https://github.com/mackysoft/Choice.git?path=Assets/MackySoft/MackySoft.Choice

from the Add package from git URL option.

Install via Open UPM

Or, you can install this package from the Open UPM registry.

More details here.

openupm add com.mackysoft.choice

🔰 Usage

// To use Choice, add this namespace.
using MackySoft.Choice;

public class WeightedItem {
	public string id;
	public float weight;
}

public WeightedItem SelectItem () {
	// Prepare weighted items.
	var items = new WeightedItem[] {
		new WeightedItem { id = "🍒", weight = 8f },
		new WeightedItem { id = "🍏", weight = 4f },
		new WeightedItem { id = "🍍", weight = 0f },
		new WeightedItem { id = "🍇", weight = 6f },
		new WeightedItem { id = "🍊", weight = -1f }
	};
	
	// Create the WeightedSelector.
	var weightedSelector = items.ToWeightedSelector(item => item.weight);
	
	// The probability of each item being selected,
	// 🍒 is 44%, 🍏 is 22%, and 🍇 is 33%.
	// 🍍 and 🍊 will never be selected because their weights are less or equal to 0.
	return weightedSelector.SelectItemWithUnityRandom();
	// Same as weightedSelector.SelectItem(UnityEngine.Random.value);
}

ToWeightedSelector Overloads

The ToWeightedSelector method has many overloads and can be used for a variety of patterns.

from weighted entry pattern

public struct ItemEntry {
	public Item item;
	public float weight;
}

public IWeightedSelector<Item> WeightedEntryPattern () {
	var entries = new ItemEntry[] {
		new ItemEntry { item = new Item { id = "🍒" }, weight = 1f },
		new ItemEntry { item = new Item { id = "🍏" }, weight = 5f },
		new ItemEntry { item = new Item { id = "🍍" }, weight = 3f }
	};

	// Create a WeightedSelector by selecting item and weight from entry respectively.
	return entries.ToWeightedSelector(
		itemSelector: entry => entry.item,
		weightSelector: entry => entry.weight
	);
}

from weighted item pattern

public class WeightedItem {
	public string id;
	public float weight;
}

public IWeightedSelector<WeightedItem> WeightedItemPattern () {
	var items = new WeightedItem[] {
		new WeightedItem { id = "🍒", weight = 1f },
		new WeightedItem { id = "🍏", weight = 5f },
		new WeightedItem { id = "🍍", weight = 3f }
	};

	// Create a WeightedSelector using the weight of the WeightedItem.
	return fromWeightedItem = items.ToWeightedSelector(weightSelector: item => item.weight);
}

from Dictionary<TItem,float> pattern

public class Item {
	public string id;
}

public IWeightedSelector<Item> DictionaryPattern () {
	// This need a Dictionary<TItem,float>. (Strictly speaking, IEnumerable<KeyValuePair<TItem,float>>)
	var dictionary = new Dictionary<Item,float>(
		{ new Item { id = "🍒" }, 1f },
		{ new Item { id = "🍏" }, 5f },
		{ new Item { id = "🍍" }, 3f }
	);

	// Create a WeightedSelector with the dictionary key as item and value as weight.
	return dictionary.ToWeightedSelector();
}

LINQ

Since the ToWeightedSelector method is defined as an extension of IEnumerable<T>, it can be connected from the LINQ query operators.

var randomSelectedItem = items
	.Where(item => item != null) // null check
	.ToWeightedSelector(item => item.weight)
	.SelectItemWithUnityRandom();

Algorithms

When creating a WeightedSelector, you can specify the IWeightedSelectMethod.

var weightedSelector = items.ToWeightedSelector(
	item => item.weight,
	WeightedSelectMethod.Binary // Use the binary search algorithm.
);

All ToWeightedSelector methods can specify IWeightedSelectMethod.

If this is not specified, the linear scan algorithm will be used automatically.

Linear Scan (WeightedSelectMethod.Linear)

The simplest algorithm that walks linearly along the weights. This method is an O(n) operation, where n is number of weights.

Binary Search (WeightedSelectMethod.Binary)

The binary search algorithm that is faster than linear scan by preprocessing to store the current sum of weights.

It has an additional storage cost of O(n), but is accelerated by up to O(log(n)) for each selection, where n is number of weights.

Alias Method (WeightedSelectMethod.Alias)

The fastest algorithm.

It takes O(n) run time to set up, but the selection is performed in O(1) run time, where n is number of weights.

Therefore, this is a very effective algorithm for selecting multiple items.

Speed Measurement

1 items

Iterations	1	10	100	1000	10000
Linear Scan	0.0104ms	0.0055ms	0.0081ms	0.0393ms	0.3408ms
Binary Search	0.0091ms	0.0083ms	0.0126ms	0.0659ms	0.5944ms
Alias Method	0.0069ms	0.0065ms	0.01ms	0.0459ms	0.4094ms

Iterations	1	10	100	1000	10000
Linear Scan	0.0155ms	0.0064ms	0.0077ms	0.0381ms	0.353ms
Binary Search	0.0077ms	0.008ms	0.0123ms	0.0659ms	0.5919ms
Alias Method	0.0062ms	0.0065ms	0.01ms	0.0462ms	0.41ms

Iterations	1	10	100	1000	10000
Linear Scan	0.009ms	0.0053ms	0.0081ms	0.0378ms	0.3388ms
Binary Search	0.0073ms	0.0079ms	0.0129ms	0.0653ms	0.5927ms
Alias Method	0.0054ms	0.0062ms	0.0104ms	0.0461ms	0.4194ms

10 items

Iterations	1	10	100	1000	10000
Linear Scan	0.0113ms	0.0077ms	0.0182ms	0.1219ms	1.19ms
Binary Search	0.0109ms	0.0114ms	0.0237ms	0.158ms	1.4975ms
Alias Method	0.0136	0.022ms	0.0151ms	0.0601ms	0.5041ms

Iterations	1	10	100	1000	10000
Linear Scan	0.012ms	0.0072ms	0.0174ms	0.1272ms	1.1738ms
Binary Search	0.0095ms	0.0099ms	0.023ms	0.16ms	1.5503ms
Alias Method	0.0141ms	0.0104ms	0.0148ms	0.0618ms	0.5235ms

Iterations	1	10	100	1000	10000
Linear Scan	0.0095ms	0.009ms	0.0179ms	0.1216ms	1.1503ms
Binary Search	0.0096ms	0.0103ms	0.0225ms	0.1572ms	1.4991ms
Alias Method	0.0129ms	0.0105ms	0.015ms	0.0607ms	0.5176ms

100 items

Iterations	1	10	100	1000	10000
Linear Scan	0.0201ms	0.024ms	0.0822ms	0.741ms	7.2211ms
Binary Search	0.0212ms	0.0211ms	0.0433ms	0.3118ms	2.6434ms
Alias Method	0.0717ms	0.0364ms	0.0395ms	0.086ms	0.5462ms

Iterations	1	10	100	1000	10000
Linear Scan	0.0231ms	0.0247ms	0.0855ms	0.7027ms	7.0025ms
Binary Search	0.0224ms	0.0231ms	0.0441ms	0.2776ms	2.6521ms
Alias Method	*0.039ms	0.0358ms	0.0405ms	0.0861ms	0.5561ms

Iterations	1	10	100	1000	10000
Linear Scan	0.0194ms	0.0232ms	0.0892ms	0.7582ms	7.1886ms
Binary Search	0.0206ms	0.0218ms	0.0447ms	0.2804ms	2.6375ms
Alias Method	0.0376ms	0.0381ms	0.0413ms	0.0871ms	0.5728ms

1000 items

Iterations	1	10	100	1000	10000
Linear Scan	0.1147ms	0.1672ms	0.7792ms	6.7539ms	66.8329ms
Binary Search	0.1205ms	0.1183ms	0.1504ms	0.4758ms	3.7755ms
Alias Method	0.2783ms	0.2722ms	0.2925ms	0.3238ms	0.7824ms

Iterations	1	10	100	1000	10000
Linear Scan	0.1068ms	0.1717ms	0.8331ms	6.8282ms	68.455ms
Binary Search	0.1217ms	0.1173ms	0.1499ms	0.5026ms	3.7627ms
Alias Method	0.2785ms	0.2889ms	0.2876ms	0.3318ms	0.908ms

Iterations	1	10	100	1000	10000
Linear Scan	0.102ms	0.1636ms	0.7271ms	6.743ms	66.4393ms
Binary Search	0.1241ms	0.1208ms	0.1501ms	0.5216ms	4.0165ms
Alias Method	0.2782ms	0.2755ms	0.2777ms	0.3454ms	0.8068ms

10000 items

Iterations	1	10	100	1000	10000
Linear Scan	1.1885ms	1.7971ms	8.0482ms	69.1749ms	664.8696ms
Binary Search	1.3329ms	1.3181ms	1.3454ms	1.7735ms	6.1215ms
Alias Method	2.8859ms	2.8719ms	2.8832ms	2.9779ms	3.4764ms

Iterations	1	10	100	1000	10000
Linear Scan	1.1676ms	1.6953ms	8.0905ms	70.1629ms	668.3197ms
Binary Search	1.3118ms	1.3361ms	1.3407ms	1.786ms	6.1105ms
Alias Method	2.8833ms	2.934ms	2.951ms	2.9845ms	3.6259ms

Iterations	1	10	100	1000	10000
Linear Scan	1.3098ms	1.9826ms	8.063ms	68.9301ms	666.9364ms
Binary Search	1.4456ms	1.3787ms	4.6233ms	1.7861ms	6.0783ms
Alias Method	2.9751ms	2.9144ms	2.9236ms	2.9851ms	3.5149ms

10000 items without setup

Iterations	1	10	100	1000	10000
Linear Scan	0.0207ms	0.7364ms	6.5433ms	67.3963ms	671.3184ms
Binary Search	0.0015ms	0.0055ms	0.0492ms	0.496ms	4.828ms
Alias Method	0.0005ms	0.0011ms	0.0066ms	0.0579ms	0.5559ms

📔 Author Info

Hiroya Aramaki is a indie game developer in Japan.

• Blog: https://mackysoft.net/blog
• Twitter: https://twitter.com/makihiro_dev

📜 License

This library is under the MIT License.