Create binary_search_matrix.py (#6995)

* Create binary_search_matrix.py

Added an algorithm to search in matrix

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* Update binary_search_matrix.py

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* fix Indentation

* Update matrix/binary_search_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

matrix/binary_search_matrix.py

@@ -0,0 +1,57 @@
+def binary_search(array: list, lower_bound: int, upper_bound: int, value: int) -> int:
+    """
+    This function carries out Binary search on a 1d array and
+    return -1 if it do not exist
+    array: A 1d sorted array
+    value : the value meant to be searched
+    >>> matrix = [1, 4, 7, 11, 15]
+    >>> binary_search(matrix, 0, len(matrix) - 1, 1)
+    0
+    >>> binary_search(matrix, 0, len(matrix) - 1, 23)
+    -1
+    """
+
+    r = int((lower_bound + upper_bound) // 2)
+    if array[r] == value:
+        return r
+    if lower_bound >= upper_bound:
+        return -1
+    if array[r] < value:
+        return binary_search(array, r + 1, upper_bound, value)
+    else:
+        return binary_search(array, lower_bound, r - 1, value)
+
+
+def mat_bin_search(value: int, matrix: list) -> list:
+    """
+    This function loops over a 2d matrix and calls binarySearch on
+    the selected 1d array and returns [-1, -1] is it do not exist
+    value : value meant to be searched
+    matrix = a sorted 2d matrix
+    >>> matrix = [[1, 4, 7, 11, 15],
+    ...           [2, 5, 8, 12, 19],
+    ...           [3, 6, 9, 16, 22],
+    ...           [10, 13, 14, 17, 24],
+    ...           [18, 21, 23, 26, 30]]
+    >>> target = 1
+    >>> mat_bin_search(target, matrix)
+    [0, 0]
+    >>> target = 34
+    >>> mat_bin_search(target, matrix)
+    [-1, -1]
+    """
+    index = 0
+    if matrix[index][0] == value:
+        return [index, 0]
+    while index < len(matrix) and matrix[index][0] < value:
+        r = binary_search(matrix[index], 0, len(matrix[index]) - 1, value)
+        if r != -1:
+            return [index, r]
+        index += 1
+    return [-1, -1]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()