Initial data commit

Task/Zeckendorf-number-representation/Python/zeckendorf-number-representation-1.py

@@ -0,0 +1,34 @@
+def fib():
+    memo = [1, 2]
+    while True:
+        memo.append(sum(memo))
+        yield memo.pop(0)
+
+def sequence_down_from_n(n, seq_generator):
+    seq = []
+    for s in seq_generator():
+        seq.append(s)
+        if s >= n: break
+    return seq[::-1]
+
+def zeckendorf(n):
+    if n == 0: return [0]
+    seq = sequence_down_from_n(n, fib)
+    digits, nleft = [], n
+    for s in seq:
+        if s <= nleft:
+            digits.append(1)
+            nleft -= s
+        else:
+            digits.append(0)
+    assert nleft == 0, 'Check all of n is accounted for'
+    assert sum(x*y for x,y in zip(digits, seq)) == n, 'Assert digits are correct'
+    while digits[0] == 0:
+        # Remove any zeroes padding L.H.S.
+        digits.pop(0)
+    return digits
+
+n = 20
+print('Fibonacci digit multipliers: %r' % sequence_down_from_n(n, fib))
+for i in range(n + 1):
+    print('%3i: %8s' % (i, ''.join(str(d) for d in zeckendorf(i))))

Task/Zeckendorf-number-representation/Python/zeckendorf-number-representation-2.py

@@ -0,0 +1,15 @@
+n = 20
+def z(n):
+    if n == 0 : return [0]
+    fib = [2,1]
+    while fib[0] < n: fib[0:0] = [sum(fib[:2])]
+    dig = []
+    for f in fib:
+        if f <= n:
+            dig, n = dig + [1], n - f
+        else:
+            dig += [0]
+    return dig if dig[0] else dig[1:]
+
+for i in range(n + 1):
+    print('%3i: %8s' % (i, ''.join(str(d) for d in z(i))))