Add Zeckendorf in Algol68

archive/a/algol68/zeckendorf.alg

@@ -0,0 +1,152 @@
+# Number of Fibonacci numbers before the math overflows #
+INT max fibonaccis = 43;
+
+MODE PARSEINT_RESULT = STRUCT(BOOL valid, INT value, STRING leftover);
+
+PROC parse int = (REF STRING s) PARSEINT_RESULT:
+(
+    BOOL valid := FALSE;
+    REAL r := 0.0;
+    INT n := 0;
+    STRING leftover;
+
+    # Associate string with a file #
+    FILE f;
+    associate(f, s);
+
+    # On end of input, exit if valid number not seen. Otherwise ignore it #
+    on logical file end(f, (REF FILE dummy) BOOL:
+        (
+            IF NOT valid THEN done FI;
+            TRUE
+        )
+    );
+
+    # Exit if value error #
+    on value error(f, (REF FILE dummy) BOOL: done);
+
+    # Convert string to real number #
+    get(f, r);
+
+    # If real number is in range of an integer, convert to integer. Indicate integer is valid if same as real #
+    IF ABS r <= max int
+    THEN
+        n := ENTIER(r);
+        valid := (n = r)
+    FI;
+
+    # Get leftover string #
+    get(f, leftover);
+
+done:
+    close(f);
+    PARSEINT_RESULT(valid, n, leftover)
+);
+
+PROC usage = VOID: printf(($gl$, "Usage: please input a non-negative integer"));
+
+COMMENT
+fib(n) = fib(n - 1) + fib(n - 2)
+where:
+- fib(0) = 0
+- fib(1) = 1
+- fib(2) = 1
+- fib(3) = 2
+COMMENT
+MODE FIBSTATE = STRUCT(INT prev, INT result);
+PROC init fib = FIBSTATE: FIBSTATE(1, 2);
+OP FIB = (FIBSTATE state) FIBSTATE: (result OF state, prev OF state + result OF state);
+OP FIBRESULT = (FIBSTATE state) INT: prev OF state;
+
+PROC fibonacci up to = (INT n) REF [] INT:
+(
+    # Temporary array that can handle Fibonacci numbers #
+    REF [] INT temp results = HEAP [1:max fibonaccis] INT;
+
+    # Initialize Fibonacci state #
+    FIBSTATE state := init fib;
+
+    # Collect all Fibonacci numbers up to the specified value #
+    INT idx := 0;
+    WHILE FIBRESULT state <= n AND idx < max fibonaccis
+    DO
+        idx +:= 1;
+        temp results[idx] := FIBRESULT state;
+        state := FIB state
+    OD;
+
+    # Resize results #
+    REF [] INT results := HEAP [1:idx] INT;
+    results := temp results[1:idx];
+    results
+);
+
+PROC zeckendorf = (INT n) REF [] INT:
+(
+    # Get Fibonacci numbers up to and including n #
+    REF [] INT fibs = fibonacci up to(n);
+
+    # Allocate temporary space for Zeckendorf values #
+    INT num fibs := UPB fibs;
+    REF [] INT temp results := HEAP [1:ENTIER((num fibs + 1) / 2)] INT;
+
+    # Going from largest to smallest, repeat until no more Fibonacci numbers #
+    # left or sum of Fibonacci numbers is equal to n #
+    INT fib idx := num fibs;
+    INT zeck idx := 0;
+    INT remaining := n;
+    WHILE fib idx > 0 AND remaining > 0
+    DO
+        # If this Fibonacci number is less than or equal to n, use it and skip the #
+        # previous Fibonacci number. Otherwise, go to previous Fibonacci number #
+        INT fib = fibs[fib idx];
+        IF fib <= remaining
+        THEN
+            zeck idx +:= 1;
+            temp results [zeck idx] := fib;
+            fib idx -:= 2;
+            remaining -:= fib
+        ELSE
+            fib idx -:= 1
+        FI
+    OD;
+
+    # Resize results #
+    REF [] INT results := HEAP [1:zeck idx] INT;
+    results := temp results[1:zeck idx];
+    results
+);
+
+PROC show list values = (REF []INT values) VOID:
+(
+    INT n = UPB values;
+    FOR k TO n
+    DO
+        IF k > 1
+        THEN
+            print(", ")
+        FI;
+
+        print(whole(values[k], 0))
+    OD;
+
+    IF n > 0
+    THEN
+        print(newline)
+    FI
+);
+
+# Parse 1st command-line argument #
+STRING s := argv(4);
+PARSEINT_RESULT result := parse int(s);
+
+# If invalid or extra characters or negative number, exit #
+INT n := value OF result;
+IF NOT (valid OF result) OR (leftover OF result) /= "" OR n < 0
+THEN
+    usage;
+    stop
+FI;
+
+REF [] INT results := zeckendorf(n);
+show list values(results)