Minimum Falling Path Sum

Author: anantkaushik

931-minimum-falling-path-sum.py

@@ -0,0 +1,48 @@
+"""
+Problem Link: https://leetcode.com/problems/minimum-falling-path-sum/
+
+Given an n x n array of integers matrix, return the minimum sum of any falling path through matrix.
+A falling path starts at any element in the first row and chooses the element in the next row that 
+is either directly below or diagonally left/right. Specifically, the next element from position 
+(row, col) will be (row + 1, col - 1), (row + 1, col), or (row + 1, col + 1).
+
+Example 1:
+Input: matrix = [[2,1,3],[6,5,4],[7,8,9]]
+Output: 13
+Explanation: There are two falling paths with a minimum sum as shown.
+
+Example 2:
+Input: matrix = [[-19,57],[-40,-5]]
+Output: -59
+Explanation: The falling path with a minimum sum is shown.
+
+Constraints:
+n == matrix.length == matrix[i].length
+1 <= n <= 100
+-100 <= matrix[i][j] <= 100
+"""
+class Solution:
+ def minFallingPathSum(self, matrix: List[List[int]]) -> int:
+ if len(matrix) == 1:
+ return min(matrix[0])
+ 
+ dp = matrix[0].copy()
+ min_path = float('inf')
+ 
+ for row in range(1, len(matrix)):
+ temp = []
+ for col in range(len(matrix[0])):
+ min_val = dp[col] + matrix[row][col]
+ if col - 1 >= 0:
+ min_val = min(min_val, matrix[row][col] + dp[col-1])
+ if col + 1 < len(matrix[0]):
+ min_val = min(min_val, matrix[row][col] + dp[col+1])
+ 
+ temp.append(min_val)
+ 
+ if row == len(matrix) - 1:
+ min_path = min(min_path, temp[col])
+ 
+ dp = temp
+ 
+ return min_path