How do you solve Minimum Falling Path Sum on LeetCode?

Minimum Falling Path Sum (LeetCode #931) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n²) time complexity and O(1) space complexity. Key insight: Dynamic programming can significantly reduce redundant calculations.

What is the brute force solution for Minimum Falling Path Sum?

The brute force approach for Minimum Falling Path Sum is Brute Force, with O(n²) time complexity and O(n) space complexity. The brute-force approach explores all possible falling paths from the first row to the last row. It recursively checks each potential path, calculating the sum of the values along the way. The optimal Optimal Solution approach improves this to O(n²).

What algorithm or data structure is used to solve Minimum Falling Path Sum?

Minimum Falling Path Sum uses the following concepts: Array, Dynamic Programming, Matrix. The recommended patterns to study are: Dynamic Programming, Matrix Traversal.

What are the interview tips for Minimum Falling Path Sum?

Explain your thought process clearly while coding. Consider edge cases and discuss them with the interviewer. Practice both recursive and iterative approaches to build confidence.

What are common mistakes when solving Minimum Falling Path Sum?

Not considering edge cases like single row/column matrices. Failing to understand the recursive nature of the brute-force solution.

#931

Minimum Falling Path Sum

Medium

ArrayDynamic ProgrammingMatrixDynamic ProgrammingMatrix Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n²)
Space	O(n)	O(1)

💡

Intuition

Time O(n²)Space O(1)

The optimal solution uses dynamic programming to build the minimum falling path sum from the bottom row up to the top. By storing the minimum sums in the same matrix, we avoid redundant calculations.

⚙️

Algorithm

3 steps

1Step 1: Start from the second last row and move upwards.
2Step 2: For each element, update it to be the sum of itself and the minimum of the three possible elements in the row below.
3Step 3: After processing all rows, the minimum value in the first row will be the answer.

solution.py10 lines

1# Full working Python code
2
3def minFallingPathSum(matrix):
4    n = len(matrix)
5    for row in range(n - 2, -1, -1):
6        for col in range(n):
7            matrix[row][col] += min(matrix[row + 1][col - 1] if col > 0 else float('inf'),
8                                   matrix[row + 1][col],
9                                   matrix[row + 1][col + 1] if col < n - 1 else float('inf'))
10    return min(matrix[0])

ℹ

Complexity note: The time complexity remains O(n²) because we still iterate through all elements of the matrix. However, the space complexity is O(1) since we are modifying the input matrix in place.

1Dynamic programming can significantly reduce redundant calculations.
2In-place updates can save space while solving the problem.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.