Add reversible binary strings. Format python code in format recipe

Author: cullback

content/2023-06-10-watsky-words/watsky.py

@@ -14,4 +14,4 @@ def starts_with(words: list[str], prefix: str) -> Iterator[str]:
     for third in starts_with(words, first[6:]):
         for second in starts_with(words, first[3:6]):
             if second.endswith(third[3:6]):
-                print(f"{first},{second},{third}")
+                print(f"{first},{second},{third}")

content/2025-08-14-reversible-binary-strings/binary.py

@@ -0,0 +1,63 @@
+def find_different(text: str) -> int:
+    """Returns the index of mirrored pairs that hold different values."""
+    indexed_pairs = enumerate(zip(text, text[::-1]))
+    i = next((i for i, (a, b) in indexed_pairs if a != b), len(text) // 2)
+    return i
+
+
+def encode(msg: str) -> str:
+    i = find_different(msg)
+    n = len(msg) // 2
+
+    if len(msg) % 2 == 0:
+        return msg[:n] + msg[i] + msg[n:]
+
+    middle = msg[n] if msg[i] == "0" else ["1", "0"][int(msg[n])]
+    head = msg[: n + 1]
+    tail = msg[n + 1 :]
+    return head + middle + tail
+
+
+def decode(msg: str) -> str:
+    i = find_different(msg)
+    n = len(msg) // 2
+
+    if len(msg) % 2 == 1:
+        received = msg[:n] + msg[n + 1 :]
+        if msg[i] != msg[n]:
+            return received[::-1]
+        return received
+
+    head = msg[: n - 1]
+    mid1 = msg[n - 1]
+    mid2 = msg[n]
+    tail = msg[n + 1 :]
+    expected = ["0", "1"][mid1 != mid2]
+    if msg[i] != expected:
+        return (head + mid2 + tail)[::-1]
+    return head + mid1 + tail
+
+
+def test_protocol():
+    for n in range(1, 7):
+        for i in range(2**n):
+            bits = f"{i:0{n}b}"
+            assert len(bits) == n
+            test_string(bits)
+
+
+def test_string(original):
+    encoded = encode(original)
+    decoded = decode(encoded)
+
+    if original != decoded:
+        print(f"FAIL {original} -> {encoded} -> {decoded}")
+
+    decoded = decode(encoded[::-1])
+
+    if original != decoded:
+        print(f"FAIL {original} -> {encoded[::-1]} -> {decoded}")
+
+
+if __name__ == "__main__":
+    test_protocol()

content/2025-08-14-reversible-binary-strings/index.md

@@ -0,0 +1,13 @@
++++
+title = "Reversible binary strings"
++++
+
+We want to send a binary string from a to b, but there's a chance that the string will be reversed during transmission, i.e. `101011` becomes `110101`.
+
+We want a protocol such that we can figure out which orientation is correct.
+
+Information theory suggests we should be able to do this with only one additional bit.
+
+{{ code_block(path="content/2025-08-14-reversible-binary-strings/binary.py", code="python") }}
+
+<!-- - <https://www.astralcodexten.com/p/open-thread-385/comment/124990517> -->

justfile

@@ -6,4 +6,4 @@ run:
 
 format:
     mdformat content
-    # fd -e md | xargs sd '\\\\\\\\' '\\'
+    ruff format content