Update triangle.py

Updated the format

Author: ananya-research

dynamic_programming/triangle.py

@@ -1,11 +1,42 @@
-class Solution:
-    def minimumTotal(self, triangle: List[List[int]]) -> int:
-        for row in range(1, len(triangle)):
-            for col in range(row + 1):
-                smallest_above = math.inf
-                if col > 0:
-                    smallest_above = triangle[row - 1][col - 1]
-                if col < row:
-                    smallest_above = min(smallest_above, triangle[row - 1][col])
-                triangle[row][col] += smallest_above
-        return min(triangle[-1])
+from __future__ import annotations
+
+
+def minimum_total(triangle: list[list[int]]) -> int:
+    """
+    Return the minimum path sum from top to bottom of a triangle.
+
+    Each step you may move to adjacent numbers on the row below.
+    The input must be a proper triangle: len(row i) == i + 1.
+
+    >>> minimum_total([[2],[3,4],[6,5,7],[4,1,8,3]])
+    11
+    >>> minimum_total([[-10]])
+    -10
+    >>> minimum_total([[1],[2,3]])
+    3
+    >>> minimum_total([])  # doctest: +IGNORE_EXCEPTION_DETAIL
+    Traceback (most recent call last):
+    ValueError: triangle must be non-empty and well-formed
+    >>> minimum_total([[1],[2]])  # malformed (second row length not 2)  # doctest: +IGNORE_EXCEPTION_DETAIL
+    Traceback (most recent call last):
+    ValueError: triangle must be non-empty and well-formed
+    """
+    # Basic validation: non-empty and proper "triangle" shape
+    if not triangle or any(len(row) != i + 1 for i, row in enumerate(triangle)):
+        raise ValueError("triangle must be non-empty and well-formed")
+
+    # Start from the last row and fold upwards.
+    # dp[j] will store the minimum path sum from row r to the bottom starting at column j.
+    dp = triangle[-1][:]  # copy so we don't mutate the input
+
+    for r in range(len(triangle) - 2, -1, -1):
+        for c in range(r + 1):
+            dp[c] = triangle[r][c] + min(dp[c], dp[c + 1])
+
+    return dp[0]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()