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bigjoyints/divmod.py

@@ -16,22 +16,39 @@ def div_mod(A, B):
     if not B:
         raise ZeroDivisionError()
     a_len, b_len = len(A), len(B)
-    if a_len < b_len or A[-1] < B[-1]:
+    if a_len < b_len or (a_len == b_len and  A[-1] < B[-1]):
         return [], A
 
     # Whew! Okay, we got all that out of the way.
     # A > B
 
-    A_digits = A[-b_len:]
+    A, A_digits = A[:-b_len], A[-b_len:]
     if -1 == cmp_digits(A_digits, B):
         # Because we know
         #   A > B  AND a_len >= b_len (aka len(A_digits))
         # if A_digits < B there must be at least one more
         # digit in A:
         assert a_len > b_len
-        A_digits = A[-(b_len + 1):]
+        A_digits.insert(0, A.pop())
         assert -1 < cmp_digits(A_digits, B)
-    q, r = lil_divmod(A_digits, B)
+    q, R = lil_divmod(A_digits, B)
+    # So we have divided a prefix of A by B
+    # resulting in a digit q of the answer Q
+    # and a remainder R that must be extended
+    # with the rest of the digits of A to make
+    # a new number N
+
+    N = A + R
+
+    # which then must either be the remainder of
+    # the whole thing if N < B...
+    if -1 == cmp_digits(N, B):
+        return [q], N
+    # Otherwise, we find the rest of the digits
+    # by
+    Q, R = div_mod(N, B)
+    Q.append(digit)
+    return Q, R
 
 def lil_divmod(A, B):
     assert -1 < cmp_digits(A, B)
@@ -60,6 +77,7 @@ def int_to_list(i):
     return list(map(int, str(i)[::-1]))
 
 def list_to_int(A):
+    if not A: return 0
     i = int(''.join(map(str, A[::-1])))
     assert i >= 0
     return i
@@ -88,9 +106,19 @@ def subtract(A, B):
 
 A = int_to_list(145)
 B = int_to_list(72)
-q, R = lil_divmod(A, B)
+
-print(f'divmod({list_to_int(A)}, {list_to_int(B)}) = ',
+##q, R = lil_divmod(A, B)
-      q, list_to_int(R))
+##print(f'divmod({list_to_int(A)}, {list_to_int(B)}) = ',
+##      q, list_to_int(R))
+
+def try_it(a, b):
+    A = int_to_list(a)
+    B = int_to_list(b)
+    Q, R = div_mod(A, B)
+    print(f'divmod({list_to_int(A)}, {list_to_int(B)}) = {list_to_int(Q)}, {list_to_int(R)}')
+
+try_it(145, 72)
+try_it(1450, 72)
 
 
 ##print(cmp_digits([], []))