Initial data commit

Task/Sailors-coconuts-and-a-monkey-problem/Python/sailors-coconuts-and-a-monkey-problem-1.py

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+def monkey_coconuts(sailors=5):
+    "Parameterised the number of sailors using an inner loop including the last mornings case"
+    nuts = sailors
+    while True:
+        n0, wakes = nuts, []
+        for sailor in range(sailors + 1):
+            portion, remainder = divmod(n0, sailors)
+            wakes.append((n0, portion, remainder))
+            if portion <= 0 or remainder != (1 if sailor != sailors else 0):
+                nuts += 1
+                break
+            n0 = n0 - portion - remainder
+        else:
+            break
+    return nuts, wakes
+
+if __name__ == "__main__":
+    for sailors in [5, 6]:
+        nuts, wake_stats = monkey_coconuts(sailors)
+        print("\nFor %i sailors the initial nut count is %i" % (sailors, nuts))
+        print("On each waking, the nut count, portion taken, and monkeys share are:\n ",
+              ',\n  '.join(repr(ws) for ws in wake_stats))

Task/Sailors-coconuts-and-a-monkey-problem/Python/sailors-coconuts-and-a-monkey-problem-2.py

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+def wake_and_split(n0, sailors, depth=None):
+    if depth is None:
+        depth = sailors
+    portion, remainder = divmod(n0, sailors)
+    if portion <= 0 or remainder != (1 if depth else 0):
+        return None
+    else:
+        return n0 if not depth else wake_and_split(n0 - portion - remainder, sailors, depth - 1)
+
+
+def monkey_coconuts(sailors=5):
+    "Parameterised the number of sailors using recursion including the last mornings case"
+    nuts = sailors
+    while True:
+        if wake_and_split(n0=nuts, sailors=sailors) is None:
+            nuts += 1
+        else:
+            break
+    return nuts
+
+if __name__ == "__main__":
+    for sailors in [5, 6]:
+        nuts = monkey_coconuts(sailors)
+        print("For %i sailors the initial nut count is %i" % (sailors, nuts))

Task/Sailors-coconuts-and-a-monkey-problem/Python/sailors-coconuts-and-a-monkey-problem-3.py

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+# gives one solution of (x,y) for a x + by = c
+def dioph(a, b, c):
+	aa,bb,x,y = a, b, 0, 1
+
+	while True:
+		q,a,b = a//b, b, a%b
+		x,y = y - q*x, x
+		if abs(a) == 1: break
+
+	if y*aa % bb != 1: y = -y
+	x,y = y*c, (c - aa*y*c)//bb
+	#assert(x*aa + y*bb == c)
+	return x,y
+
+# rems: what monkey got each turn
+# min_share: each sailor needs to get at least this many in the final round
+def calcnuts(rems, min_share = 0):
+	n, r = len(rems) - 1, 0
+	c = (n - 1)**n
+	for x in rems: r,c = r + x*c, c//(n-1)*n
+
+	a, b = (n-1)**n, n**(n+1)
+	x, y = dioph(a, -b, r)
+	k = (min_share - y + a - 1)//a
+	return x + k*b, y + k*a
+
+def distribute(nuts, monkey_nuts):
+	n = len(monkey_nuts) - 1
+	print("\n%d sailors, %d nuts:"%(n, nuts))
+	for r in monkey_nuts[:-1]:
+		p = (nuts - r)//n
+		print("\tNuts %d, hide %d, monkey gets %d" % (nuts, p, r))
+		nuts = p*(n - 1)
+
+	r = monkey_nuts[-1]
+	p = (nuts - r)//n
+	print("Finally:\n\tNuts %d, each share %d, monkey gets %d" % (nuts, p, r))
+
+for sailors in range(2, 10):
+	monkey_loot = [1]*sailors + [0]
+	distribute(calcnuts(monkey_loot, 1)[0], monkey_loot)
+
+# many sailors, many nuts
+#for i in range(1, 5): print(10**i, calcnuts([1]*10**i + [0])[0])