From 429154af2f63a39be346ca43fa5b3000690b51bc Mon Sep 17 00:00:00 2001
From: darshan totagi <darshantotagi7975@gmail.com>
Date: Tue, 28 Oct 2025 12:32:55 +0530
Subject: [PATCH 1/2] feat: add Meta Binary Search algorithm in Python

---
 searches/interpolation_search_recursive.py | 17 +++++++++++++++++
 searches/meta_binary_search.py             | 18 ++++++++++++++++++
 2 files changed, 35 insertions(+)
 create mode 100644 searches/interpolation_search_recursive.py
 create mode 100644 searches/meta_binary_search.py

diff --git a/searches/interpolation_search_recursive.py b/searches/interpolation_search_recursive.py
new file mode 100644
index 000000000000..dfb5c0f6d4c1
--- /dev/null
+++ b/searches/interpolation_search_recursive.py
@@ -0,0 +1,17 @@
+def interpolation_search_recursive(arr, low, high, x):
+    """Recursive implementation of Interpolation Search."""
+    if low <= high and arr[low] <= x <= arr[high]:
+        pos = low + ((high - low) * (x - arr[low])) // (arr[high] - arr[low])
+        if arr[pos] == x:
+            return pos
+        if arr[pos] < x:
+            return interpolation_search_recursive(arr, pos + 1, high, x)
+        return interpolation_search_recursive(arr, low, pos - 1, x)
+    return -1
+
+
+if __name__ == "__main__":
+    arr = [10, 20, 30, 40, 50, 60, 70]
+    x = 50
+    result = interpolation_search_recursive(arr, 0, len(arr) - 1, x)
+    print(f"Element {x} found at index: {result}" if result != -1 else "Element not found.")
diff --git a/searches/meta_binary_search.py b/searches/meta_binary_search.py
new file mode 100644
index 000000000000..29ecfb4e38b4
--- /dev/null
+++ b/searches/meta_binary_search.py
@@ -0,0 +1,18 @@
+def meta_binary_search(arr, target):
+    """Meta Binary Search using bit manipulation."""
+    n = len(arr)
+    pos = -1
+    for i in reversed(range(n.bit_length())):
+        new_pos = pos + (1 << i)
+        if new_pos < n and arr[new_pos] <= target:
+            pos = new_pos
+    if pos != -1 and arr[pos] == target:
+        return pos
+    return -1
+
+
+if __name__ == "__main__":
+    arr = [2, 5, 7, 9, 14, 18, 21, 25]
+    target = 18
+    result = meta_binary_search(arr, target)
+    print(f"Element {target} found at index: {result}" if result != -1 else "Element not found.")

From e16910be417cb973aafb616e055e0bf0ecaa69cb Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 28 Oct 2025 07:05:43 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 searches/interpolation_search_recursive.py | 6 +++++-
 searches/meta_binary_search.py             | 6 +++++-
 2 files changed, 10 insertions(+), 2 deletions(-)

diff --git a/searches/interpolation_search_recursive.py b/searches/interpolation_search_recursive.py
index dfb5c0f6d4c1..bb1a4be4821f 100644
--- a/searches/interpolation_search_recursive.py
+++ b/searches/interpolation_search_recursive.py
@@ -14,4 +14,8 @@ def interpolation_search_recursive(arr, low, high, x):
     arr = [10, 20, 30, 40, 50, 60, 70]
     x = 50
     result = interpolation_search_recursive(arr, 0, len(arr) - 1, x)
-    print(f"Element {x} found at index: {result}" if result != -1 else "Element not found.")
+    print(
+        f"Element {x} found at index: {result}"
+        if result != -1
+        else "Element not found."
+    )
diff --git a/searches/meta_binary_search.py b/searches/meta_binary_search.py
index 29ecfb4e38b4..94319aec3fa6 100644
--- a/searches/meta_binary_search.py
+++ b/searches/meta_binary_search.py
@@ -15,4 +15,8 @@ def meta_binary_search(arr, target):
     arr = [2, 5, 7, 9, 14, 18, 21, 25]
     target = 18
     result = meta_binary_search(arr, target)
-    print(f"Element {target} found at index: {result}" if result != -1 else "Element not found.")
+    print(
+        f"Element {target} found at index: {result}"
+        if result != -1
+        else "Element not found."
+    )