Initial data commit

Task/Partition-function-P/Python/partition-function-p-1.py

@@ -0,0 +1,51 @@
+from itertools import islice
+
+def posd():
+    "diff between position numbers. 1, 2, 3... interleaved with  3, 5, 7..."
+    count, odd = 1, 3
+    while True:
+        yield count
+        yield odd
+        count, odd = count + 1, odd + 2
+
+def pos_gen():
+    "position numbers. 1 3 2 5 7 4 9 ..."
+    val = 1
+    diff = posd()
+    while True:
+        yield val
+        val += next(diff)
+
+def plus_minus():
+    "yield (list_offset, sign) or zero for Partition calc"
+    n, sign = 0, [1, 1]
+    p_gen = pos_gen()
+    out_on = next(p_gen)
+    while True:
+        n += 1
+        if n == out_on:
+            next_sign = sign.pop(0)
+            if not sign:
+                sign = [-next_sign] * 2
+            yield -n, next_sign
+            out_on = next(p_gen)
+        else:
+            yield 0
+
+def part(n):
+    "Partition numbers"
+    p = [1]
+    p_m = plus_minus()
+    mods = []
+    for _ in range(n):
+        next_plus_minus = next(p_m)
+        if next_plus_minus:
+            mods.append(next_plus_minus)
+        p.append(sum(p[offset] * sign for offset, sign in mods))
+    return p[-1]
+
+print("(Intermediaries):")
+print("    posd:", list(islice(posd(), 10)))
+print("    pos_gen:", list(islice(pos_gen(), 10)))
+print("    plus_minus:", list(islice(plus_minus(), 15)))
+print("\nPartitions:", [part(x) for x in range(15)])

Task/Partition-function-P/Python/partition-function-p-2.py

@@ -0,0 +1,18 @@
+def par_primes():
+    "Prime number generator from the partition machine"
+    p = [1]
+    p_m = plus_minus()
+    mods = []
+    n = 0
+    while True:
+        n += 1
+        next_plus_minus = next(p_m)
+        if next_plus_minus:
+            mods.append(next_plus_minus)
+        p.append(sum(p[offset] * sign for offset, sign in mods))
+        if p[0] + 1 == p[-1]:
+            yield p[0]
+        p[0] += 1
+    yield p
+
+print("\nPrimes:", list(islice(par_primes(), 15)))

Task/Partition-function-P/Python/partition-function-p-3.py

@@ -0,0 +1,30 @@
+from typing import List
+
+
+def partitions(n: int) -> int:
+    """Count partitions."""
+    p: List[int] = [1] + [0] * n
+    for i in range(1, n + 1):
+        k: int = 0
+        while True:
+            k += 1
+            j: int = (k * (3*k - 1)) // 2
+            if (j > i):
+                break
+            if (k & 1):
+                p[i] += p[i - j]
+            else:
+                p[i] -= p[i - j]
+            j = (k * (3*k + 1)) // 2
+            if (j > i):
+                break
+            if (k & 1):
+                p[i] += p[i - j]
+            else:
+                p[i] -= p[i - j]
+
+    return p[n]
+
+
+if __name__ == '__main__':
+    print("\nPartitions:", [partitions(x) for x in range(15)])