From 027aceb3ad8eedb5b2db9ab1aec16b3ca200301e Mon Sep 17 00:00:00 2001
From: Saurav <sauravgc33@gmail.com>
Date: Thu, 9 Apr 2026 17:21:52 +0545
Subject: [PATCH 1/2] Add Z-score normalization algorithm for data
 standardization

---
 data_structures/z_score_normalization.py | 68 ++++++++++++++++++++++++
 1 file changed, 68 insertions(+)
 create mode 100644 data_structures/z_score_normalization.py

diff --git a/data_structures/z_score_normalization.py b/data_structures/z_score_normalization.py
new file mode 100644
index 000000000000..34bb6ebbff91
--- /dev/null
+++ b/data_structures/z_score_normalization.py
@@ -0,0 +1,68 @@
+"""
+Z-Score Normalization: Standardizes data by converting each value to the number
+of standard deviations it is from the mean. The result has a mean of 0 and a
+standard deviation of 1.
+
+Formula: z = (x - mean) / standard_deviation
+
+Z-score normalization is widely used in machine learning preprocessing,
+statistics, and data analysis to bring features to the same scale.
+
+Reference: https://en.wikipedia.org/wiki/Standard_score
+"""
+
+
+def z_score_normalization(data: list[float]) -> list[float]:
+    """
+    Normalize a list of numbers using Z-score normalization.
+
+    Parameters
+    ----------
+    data: list[float], the input list of numbers
+
+    Returns
+    -------
+    list[float]: list of z-scores for each element
+
+    >>> z_score_normalization([2, 4, 4, 4, 5, 5, 7, 9])
+    [-1.5, -0.5, -0.5, -0.5, 0.0, 0.0, 1.0, 2.0]
+    >>> z_score_normalization([1, 1, 1, 1])
+    Traceback (most recent call last):
+        ...
+    ValueError: standard deviation is zero — all elements are identical
+    >>> z_score_normalization([])
+    Traceback (most recent call last):
+        ...
+    ValueError: data cannot be empty
+    >>> z_score_normalization([10])
+    Traceback (most recent call last):
+        ...
+    ValueError: data must contain at least two elements
+    >>> z_score_normalization([0, 0, 1, 1])
+    [-1.0, -1.0, 1.0, 1.0]
+    >>> z_score_normalization([-5, 0, 5])
+    [-1.2247448714, 0.0, 1.2247448714]
+    """
+    if not data:
+        raise ValueError("data cannot be empty")
+    if len(data) < 2:
+        raise ValueError("data must contain at least two elements")
+
+    mean = sum(data) / len(data)
+    variance = sum((x - mean) ** 2 for x in data) / len(data)
+    std_dev = variance ** 0.5
+
+    if std_dev == 0:
+        raise ValueError("standard deviation is zero — all elements are identical")
+
+    return [round((x - mean) / std_dev, 10) for x in data]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    data = [2, 4, 4, 4, 5, 5, 7, 9]
+    print(f"Original data: {data}")
+    print(f"Z-score normalized: {z_score_normalization(data)}")

From 2df83ecbc1be26cbc8e6ec9d41a68b9e1c78ef32 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Thu, 9 Apr 2026 11:37:53 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 data_structures/z_score_normalization.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/data_structures/z_score_normalization.py b/data_structures/z_score_normalization.py
index 34bb6ebbff91..37e24a15f538 100644
--- a/data_structures/z_score_normalization.py
+++ b/data_structures/z_score_normalization.py
@@ -50,7 +50,7 @@ def z_score_normalization(data: list[float]) -> list[float]:
 
     mean = sum(data) / len(data)
     variance = sum((x - mean) ** 2 for x in data) / len(data)
-    std_dev = variance ** 0.5
+    std_dev = variance**0.5
 
     if std_dev == 0:
         raise ValueError("standard deviation is zero — all elements are identical")