commit cdca6df82121ada4d864b2cbaa1b9fe5cb1a36bc
Author: Nikolai Hartmann <nikoladze@posteo.de>
Date:   Tue Sep 19 07:02:45 2023 +0200

    initial commit

diff --git a/splitbill.py b/splitbill.py
new file mode 100755
index 0000000..4284f52
--- /dev/null
+++ b/splitbill.py
@@ -0,0 +1,68 @@
+#!/usr/bin/env python3
+from itertools import chain, combinations
+from typing import Generator
+
+balances = {
+    # "A": -20,
+    # "B": 10,
+    # "C": 3,
+    # "D": -43,
+    # should be possible with 3 transactions (A, B, C balance excactly)
+    "A": 50,
+    "B": -30,
+    "C": -20,
+    "D": -40,
+}
+balances["E"] = -sum(balances.values())
+
+
+def find_zerosum_subgroups(
+    balances: dict[str, int],
+) -> Generator[tuple[str, ...], None, None]:
+    for n in range(2, len(balances)):
+        for combination in combinations(balances, n):
+            if sum(balances[key] for key in combination) == 0:
+                yield combination
+
+
+def solve_greedily(balances: dict[str, int]) -> dict[tuple[str, str], int]:
+    creditors = {}
+    debitors = {}
+    for k, v in balances.items():
+        if v > 0:
+            creditors[k] = v
+        else:
+            debitors[k] = v
+
+    txn = {}
+    while not all(value == 0 for value in chain(creditors.values(), debitors.values())):
+        for debitor, debit_value in sorted(debitors.items(), key=lambda x: x[1]):
+            for creditor, credit_value in sorted(
+                creditors.items(), key=lambda x: x[1], reverse=True
+            ):
+                sum_value = credit_value + debit_value
+                if abs(debit_value) <= credit_value:
+                    del debitors[debitor]
+                    creditors[creditor] = sum_value
+                    txn[debitor, creditor] = abs(debit_value)
+                else:
+                    debitors[debitor] = sum_value
+                    del creditors[creditor]
+                    txn[debitor, creditor] = credit_value
+                break
+
+    return txn
+
+
+def solve(balances: dict[str, int]) -> dict[tuple[str, str], int]:
+    possibilities = []
+    for subgroup in find_zerosum_subgroups(balances):
+        txn_sub = solve({k: balances[k] for k in subgroup})
+        txn_other = solve({k: balances[k] for k in balances if not k in subgroup})
+        possibilities.append(txn_sub | txn_other)
+    if not possibilities:
+        possibilities.append(solve_greedily(balances))
+    return min(possibilities, key=lambda x: len(x))
+
+
+print(solve(balances))