From 4cd7ea7c404f5b25cb42f800d15c224934b2c47d Mon Sep 17 00:00:00 2001
From: pralav-25 <174412353+pralav-25@users.noreply.github.com>
Date: Sun, 27 Sep 2026 13:51:39 +0530
Subject: [PATCH 1/2] fix(math): decode negative values emitted by int_to_base

---
 algorithms/math/base_conversion.py   | 10 ++++++++--
 tests/test_base_conversion_signed.py | 23 +++++++++++++++++++++++
 2 files changed, 31 insertions(+), 2 deletions(-)
 create mode 100644 tests/test_base_conversion_signed.py

diff --git a/algorithms/math/base_conversion.py b/algorithms/math/base_conversion.py
index f332dc6f6..2d1c17390 100644
--- a/algorithms/math/base_conversion.py
+++ b/algorithms/math/base_conversion.py
@@ -54,7 +54,8 @@ def base_to_int(str_to_convert: str, base: int) -> int:
     """Convert a string in a given base to a base-10 integer.
 
     Args:
-        str_to_convert: The string representation of the number.
+        str_to_convert: The string representation of the number, optionally
+            prefixed with a minus sign as produced by int_to_base.
         base: The base of the input string (2-36).
 
     Returns:
@@ -65,7 +66,12 @@ def base_to_int(str_to_convert: str, base: int) -> int:
         5
         >>> base_to_int('FF', 16)
         255
+        >>> base_to_int('-FF', 16)
+        -255
     """
+    is_negative = str_to_convert.startswith("-")
+    if is_negative:
+        str_to_convert = str_to_convert[1:]
     digit = {}
     for ind, char in enumerate(string.digits + string.ascii_uppercase):
         digit[char] = ind
@@ -74,4 +80,4 @@ def base_to_int(str_to_convert: str, base: int) -> int:
     for char in str_to_convert[::-1]:
         res += digit[char] * multiplier
         multiplier *= base
-    return res
+    return -res if is_negative else res
diff --git a/tests/test_base_conversion_signed.py b/tests/test_base_conversion_signed.py
new file mode 100644
index 000000000..e1b81a3a0
--- /dev/null
+++ b/tests/test_base_conversion_signed.py
@@ -0,0 +1,23 @@
+"""Check that signed encodings can be decoded in every supported base."""
+
+import pytest
+
+from algorithms.math.base_conversion import base_to_int, int_to_base
+
+
+@pytest.mark.parametrize("base", range(2, 37))
+def test_signed_conversion_matches_builtin(base):
+    """Use int as an independent oracle for positive and negative outputs."""
+    for number in [-2**128, -255, -31, -1, 0, 1, 31, 255, 2**128]:
+        encoded = int_to_base(number, base)
+        assert int(encoded, base) == number
+        assert base_to_int(encoded, base) == number
+
+
+@pytest.mark.parametrize(
+    "encoded,base,expected",
+    [("-101", 2, -5), ("-FF", 16, -255), ("-Z", 36, -35), ("-0", 10, 0)],
+)
+def test_decode_negative_literal(encoded, base, expected):
+    """Decoding also works on literals not produced by the encoder."""
+    assert base_to_int(encoded, base) == expected

From e364e5887f4c7f37eb4c68e9cf6f63764c0f3efd Mon Sep 17 00:00:00 2001
From: pralav-25 <174412353+pralav-25@users.noreply.github.com>
Date: Sun, 27 Sep 2026 13:57:27 +0530
Subject: [PATCH 2/2] fix(math): reject signed conversion inputs without digits

---
 algorithms/math/base_conversion.py   | 5 +++++
 tests/test_base_conversion_signed.py | 7 +++++++
 2 files changed, 12 insertions(+)

diff --git a/algorithms/math/base_conversion.py b/algorithms/math/base_conversion.py
index 2d1c17390..3ba3a2014 100644
--- a/algorithms/math/base_conversion.py
+++ b/algorithms/math/base_conversion.py
@@ -61,6 +61,9 @@ def base_to_int(str_to_convert: str, base: int) -> int:
     Returns:
         The base-10 integer value.
 
+    Raises:
+        ValueError: If the input contains no digits after removing its sign.
+
     Examples:
         >>> base_to_int('101', 2)
         5
@@ -72,6 +75,8 @@ def base_to_int(str_to_convert: str, base: int) -> int:
     is_negative = str_to_convert.startswith("-")
     if is_negative:
         str_to_convert = str_to_convert[1:]
+    if not str_to_convert:
+        raise ValueError("number must contain at least one digit")
     digit = {}
     for ind, char in enumerate(string.digits + string.ascii_uppercase):
         digit[char] = ind
diff --git a/tests/test_base_conversion_signed.py b/tests/test_base_conversion_signed.py
index e1b81a3a0..0916ddedf 100644
--- a/tests/test_base_conversion_signed.py
+++ b/tests/test_base_conversion_signed.py
@@ -21,3 +21,10 @@ def test_signed_conversion_matches_builtin(base):
 def test_decode_negative_literal(encoded, base, expected):
     """Decoding also works on literals not produced by the encoder."""
     assert base_to_int(encoded, base) == expected
+
+
+@pytest.mark.parametrize("encoded", ["", "-"])
+def test_missing_digits_are_rejected(encoded):
+    """Neither an empty string nor a sign alone represents zero."""
+    with pytest.raises(ValueError, match="at least one digit"):
+        base_to_int(encoded, 16)