Updated Fibonacci.

fibonacci/src/fibonacci/Main.java

@@ -6,11 +6,42 @@ class Examples {
 
     ISequence<Integer> f;
     ISequence<String> a;
+    ISequence<String> m;
     ISeqGen<String> aGen = new AGen();
 
+    ProbTab tab = new ProbTab(
+        new Cons<WordProb>(
+            new WordProb(
+                "never",
+                new Cons<ProbPair>(new ProbPair("gonna", 3), new Mt<ProbPair>())
+            ),
+            new Cons<WordProb>(
+                new WordProb(
+                    "gonna",
+                    new Cons<ProbPair>(
+                        new ProbPair("give", 3),
+                        new Mt<ProbPair>()
+                    )
+                ),
+                new Cons<WordProb>(
+                    new WordProb(
+                        "give",
+                        new Cons<ProbPair>(
+                            new ProbPair("you", 3),
+                            new Mt<ProbPair>()
+                        )
+                    ),
+                    new Mt<WordProb>()
+                )
+            )
+        )
+    );
+    ISeqGen<String> markov = new Markov(tab, "never");
+
     void init() {
         this.f = new Fibonacci();
         this.a = new GenSeq<String>("", aGen);
+        this.m = new GenSeq<String>("", markov);
     }
 
     void testFibonacci(Tester t) {
@@ -24,6 +55,16 @@ class Examples {
         t.checkExpect(f.get(), 8);
     }
 
+    void testFibonacciNth(Tester t) {
+        t.checkExpect(Fibonacci.nth(0), 0);
+        t.checkExpect(Fibonacci.nth(1), 1);
+        t.checkExpect(Fibonacci.nth(2), 1);
+        t.checkExpect(Fibonacci.nth(3), 2);
+        t.checkExpect(Fibonacci.nth(4), 3);
+        t.checkExpect(Fibonacci.nth(5), 5);
+        t.checkExpect(Fibonacci.nth(6), 8);
+    }
+
     void testASeq(Tester t) {
         init();
         t.checkExpect(a.get(), "");
@@ -33,10 +74,23 @@ class Examples {
         t.checkExpect(a.get(), "aaaa");
         t.checkExpect(a.get(), "aaaaa");
     }
+
+    void testMarkov(Tester t) {
+        init();
+        t.checkExpect(m.get(), "");
+        t.checkExpect(m.get(), "never");
+        t.checkExpect(m.get(), "never gonna");
+        t.checkExpect(m.get(), "never gonna give");
+    }
 }
 
 // A generic list.
 interface ILo<A> {
+    // Find the element that matches the string.
+    A findMatch(GenMatch<A> match, String a);
+    // Find the maximum of the list.
+    A findMax(IntVal<A> intVal);
+    A findMaxHelper(IntVal<A> intVal, A biggestSoFar, int biggestSoFarVal);
 }
 
 class Cons<A> implements ILo<A> {
@@ -48,9 +102,52 @@ class Cons<A> implements ILo<A> {
         this.first = first;
         this.rest = rest;
     }
+
+    public A findMatch(GenMatch<A> match, String s) {
+        if (match.match(s, this.first)) return this.first;
+        else return this.rest.findMatch(match, s);
+    }
+
+    public A findMax(IntVal<A> intVal) {
+        return this.findMaxHelper(intVal, this.first, intVal.apply(this.first));
+    }
+
+    public A findMaxHelper(
+        IntVal<A> intVal,
+        A biggestSoFar,
+        int biggestSoFarVal
+    ) {
+        int thisVal = intVal.apply(this.first);
+        if (thisVal > biggestSoFarVal) return this.rest.findMaxHelper(
+                intVal,
+                this.first,
+                thisVal
+            );
+        else return this.rest.findMaxHelper(
+                intVal,
+                biggestSoFar,
+                biggestSoFarVal
+            );
+    }
 }
 
 class Mt<A> implements ILo<A> {
+
+    public A findMatch(GenMatch<A> match, String s) {
+        throw new Error("Can't find a match: " + s);
+    }
+
+    public A findMax(IntVal<A> intVal) {
+        throw new Error("Can't find max of empty list.");
+    }
+
+    public A findMaxHelper(
+        IntVal<A> intVal,
+        A biggestSoFar,
+        int biggestSoFarVal
+    ) {
+        return biggestSoFar;
+    }
 }
 
 interface ISequence<X> {
@@ -86,8 +183,7 @@ class Fibonacci implements ISequence<Integer> {
          */
 
         // F(0) = 0; F(1) = 1
-        if (this.idx <= 1)
+        if (this.idx <= 1) ret = this.idx;
-            ret = this.idx;
         else { // F(n) = F(n-1) + F(n-2)
             ret = this.pre + this.pen;
 
@@ -98,6 +194,10 @@ class Fibonacci implements ISequence<Integer> {
         this.idx = this.idx + 1;
         return ret;
     }
+
+    static Integer nth(int n) {
+        return n <= 1 ? n : nth(n - 1) + nth(n - 2);
+    }
 }
 
 // A generic sequence.
@@ -119,10 +219,102 @@ class GenSeq<X> implements ISequence<X> {
     }
 }
 
-// A string of n "a"s.
+// A string of "a"s.
 class AGen implements ISeqGen<String> {
 
     public String gen(String state) {
         return state.concat("a");
     }
 }
+
+// A simple markov chain text generator, with a working memory of 1 word.
+class Markov implements ISeqGen<String> {
+
+    ProbTab tab;
+    String initState;
+
+    Markov(ProbTab tab, String initState) {
+        this.tab = tab;
+        this.initState = initState;
+    }
+
+    public String gen(String state) {
+        if (state.isEmpty()) return initState;
+        return state
+            .concat(" ")
+            .concat(
+                this.tab.nextWord(state.substring(state.lastIndexOf(" ") + 1))
+            );
+    }
+}
+
+// A generic match function.
+interface GenMatch<A> {
+    Boolean match(String s, A a);
+}
+
+class MatchWord implements GenMatch<WordProb> {
+
+    public Boolean match(String word, WordProb prob) {
+        return prob.word.equals(word);
+    }
+}
+
+// Get an integer value for a type.
+interface IntVal<A> {
+    int apply(A a);
+}
+
+class ProbPairIntVal implements IntVal<ProbPair> {
+
+    public int apply(ProbPair pair) {
+        return pair.count;
+    }
+}
+
+// Probability table.
+class ProbTab {
+
+    ILo<WordProb> wordProbs;
+
+    ProbTab(ILo<WordProb> wordProbs) {
+        this.wordProbs = wordProbs;
+    }
+
+    String nextWord(String state) {
+        // The completion probabilities for the current state.
+        WordProb stateCompletions = wordProbs.findMatch(new MatchWord(), state);
+        String bestWordCompletion = stateCompletions.select();
+        return bestWordCompletion;
+    }
+}
+
+// Word completion probability.
+class WordProb {
+
+    String word;
+    ILo<ProbPair> probs;
+
+    WordProb(String word, ILo<ProbPair> probs) {
+        this.word = word;
+        this.probs = probs;
+    }
+
+    String select() {
+        // Ran out of time, but this should really use a weighted random selection.
+        ProbPair bestFit = this.probs.findMax(new ProbPairIntVal());
+        return bestFit.word;
+    }
+}
+
+// A word and its probability (count).
+class ProbPair {
+
+    String word;
+    int count;
+
+    ProbPair(String word, int count) {
+        this.word = word;
+        this.count = count;
+    }
+}