[Matrix] Max area of island problem solved DFS algorithm (#6918)

* Maximum area of island program added

* Update matrix/max_area_of_island.py

Co-authored-by: Caeden <caedenperelliharris@gmail.com>

* Update matrix/max_area_of_island.py

Co-authored-by: Caeden <caedenperelliharris@gmail.com>

* Update matrix/max_area_of_island.py

Co-authored-by: Caeden <caedenperelliharris@gmail.com>

* Review's comment resolved

* max area of island

* PR Comments resolved

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* Update matrix/max_area_of_island.py

Co-authored-by: Caeden Perelli-Harris <caedenperelliharris@gmail.com>

* Update matrix/max_area_of_island.py

Co-authored-by: Caeden Perelli-Harris <caedenperelliharris@gmail.com>

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* Update matrix/max_area_of_island.py

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* Update matrix/max_area_of_island.py

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* PR, comments resolved

* Update max_area_of_island.py

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Co-authored-by: Caeden <caedenperelliharris@gmail.com>
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matrix/max_area_of_island.py

@@ -0,0 +1,112 @@
+"""
+Given an two dimensional binary matrix grid. An island is a group of 1's (representing
+land) connected 4-directionally (horizontal or vertical.) You may assume all four edges
+of the grid are surrounded by water.  The area of an island is the number of cells with
+a value 1 in the island. Return the maximum area of an island in a grid. If there is no
+island, return 0.
+"""
+
+matrix = [
+    [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
+    [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
+    [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
+    [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0],
+    [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0],
+    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
+    [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
+    [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0],
+]
+
+
+def is_safe(row: int, col: int, rows: int, cols: int) -> bool:
+    """
+    Checking whether coordinate (row, col) is valid or not.
+
+    >>> is_safe(0, 0, 5, 5)
+    True
+    >>> is_safe(-1,-1, 5, 5)
+    False
+    """
+    return 0 <= row < rows and 0 <= col < cols
+
+
+def depth_first_search(row: int, col: int, seen: set, mat: list[list[int]]) -> int:
+    """
+    Returns the current area of the island
+
+    >>> depth_first_search(0, 0, set(), matrix)
+    0
+    """
+    rows = len(mat)
+    cols = len(mat[0])
+    if is_safe(row, col, rows, cols) and (row, col) not in seen and mat[row][col] == 1:
+        seen.add((row, col))
+        return (
+            1
+            + depth_first_search(row + 1, col, seen, mat)
+            + depth_first_search(row - 1, col, seen, mat)
+            + depth_first_search(row, col + 1, seen, mat)
+            + depth_first_search(row, col - 1, seen, mat)
+        )
+    else:
+        return 0
+
+
+def find_max_area(mat: list[list[int]]) -> int:
+    """
+    Finds the area of all islands and returns the maximum area.
+
+    >>> find_max_area(matrix)
+    6
+    """
+    seen: set = set()
+
+    max_area = 0
+    for row, line in enumerate(mat):
+        for col, item in enumerate(line):
+            if item == 1 and (row, col) not in seen:
+                # Maximizing the area
+                max_area = max(max_area, depth_first_search(row, col, seen, mat))
+    return max_area
+
+
+if __name__ == "__main__":
+    import doctest
+
+    print(find_max_area(matrix))  # Output -> 6
+
+    """
+    Explanation:
+    We are allowed to move in four directions (horizontal or vertical) so the possible
+    in a matrix if we are at x and y position the possible moving are
+
+    Directions are [(x, y+1), (x, y-1), (x+1, y), (x-1, y)] but we need to take care of
+    boundary cases as well which are x and y can not be smaller than 0 and greater than
+    the number of rows and columns respectively.
+
+    Visualization
+    mat = [
+        [0,0,A,0,0,0,0,B,0,0,0,0,0],
+        [0,0,0,0,0,0,0,B,B,B,0,0,0],
+        [0,C,C,0,D,0,0,0,0,0,0,0,0],
+        [0,C,0,0,D,D,0,0,E,0,E,0,0],
+        [0,C,0,0,D,D,0,0,E,E,E,0,0],
+        [0,0,0,0,0,0,0,0,0,0,E,0,0],
+        [0,0,0,0,0,0,0,F,F,F,0,0,0],
+        [0,0,0,0,0,0,0,F,F,0,0,0,0]
+    ]
+
+    For visualization, I have defined the connected island with letters
+    by observation, we can see that
+        A island is of area 1
+        B island is of area 4
+        C island is of area 4
+        D island is of area 5
+        E island is of area 6 and
+        F island is of area 5
+
+    it has 6 unique islands of mentioned areas
+    and the maximum of all of them is 6 so we return 6.
+    """
+
+    doctest.testmod()