1st order markov chain of the melody to "Mary Had A Little Lamb".

markov1.swift

//
//  main.swift
//  MarkovTest
//
//  Created by Peter Kos on 4/20/19.
//  Copyright © 2019 UW. All rights reserved.
//

import Foundation


// Enum for each of our notes
// @TODO: Allow for better comparisons with raw Strings?
// (May have to do in acutal algo below)
enum Note: Int {
	case C
	case D
	case E
	case F
	case G
	case A
	case B
}

// This lets us subscript strings like a NORMAL LANGUAGE
extension String {
	subscript (i: Int) -> Character {
		return self[index(startIndex, offsetBy: i)]
	}
}


// Raw input note string
let input = "EDCDEEEDDDEGGEDCDEEEEDDEDC"

// 1st order transition probability matrix
var matrix = Array(repeating: Array(repeating: 0.0, count: 5), count: 5)
var noteProbability = Array(repeating: 0.0, count: 5)

// We want to store notes in our own type, see above.
var notes = [Note]()

// Convert input to enum
for letter in input {
	switch letter {
	case "C": notes.append(.C)
	case "D": notes.append(.D)
	case "E": notes.append(.E)
	case "F": notes.append(.F)
	case "G": notes.append(.G)
	case "A": notes.append(.A)
	case "B": notes.append(.B)
	default: print("Unable to parse letter \(letter) in string \(input).")
	}
}



// Compute the next events of each note.
// For example, if "CD" appeared 3 times, matrix[.C][.D] == 3.
// This sets up the probability calcualtion later on, using
// the total number of occurences also calcualted in this function.
for noteIndex in 0..<notes.count {

	// Grab the current note and increment its overall probability
	let note = notes[noteIndex]
	noteProbability[note.rawValue] += 1


	// Grab the NEXT note in the sequence.
	// Since we're looking one ahead, and always want to keep track
	// of every node (i.e., not ignroe the last), this if statemnt
	// is necessecary to keep bounds under control.
	if (noteIndex + 1 < notes.count) {
		let nextNote = notes[noteIndex + 1]
		matrix[note.rawValue][nextNote.rawValue] += 1

		// Wrap around case
		// If we reach the end of the list,
		// set the next probability to point to the first note
		if (noteIndex + 1 == notes.count - 1) {
			matrix[nextNote.rawValue][notes[0].rawValue] += 1
		}

	}

}

print("-------------")

// Finally, compute the probabilities of each note occuring.
for row in 0..<matrix.count {
	for col in 0..<matrix[row].count {

		// The Magic Magics
		var probability = matrix[row][col] / noteProbability[row]

		// Remove pesky garbage
		if (probability.isNaN) {
			probability = 0
		}

		// Assign it back
		matrix[row][col] = probability
	}
}

// Print it all out!
for row in matrix {
	print(row)
}