feat: add Meta Binary Search algorithm in Python

Author: darshan-totagi

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.")

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.")