How do you solve Minimum Falling Path Sum II on LeetCode?

Minimum Falling Path Sum II (LeetCode #1289) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n²) time complexity and O(n) space complexity. Key insight: Dynamic programming is a powerful technique for optimization problems.

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

The brute force approach for Minimum Falling Path Sum II is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach tries every possible combination of elements from each row while ensuring that no two elements are from the same column in adjacent rows. This is like trying every possible path down a staircase where you can only step on certain stairs. The optimal Optimal Solution approach improves this to O(n²).

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

Minimum Falling Path Sum II 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 II?

Always clarify constraints before starting to code. Think about how you can break down the problem into smaller subproblems. Practice explaining your thought process out loud as you code.

What are common mistakes when solving Minimum Falling Path Sum II?

Not considering the constraint of non-zero shifts between adjacent rows. Overcomplicating the problem by trying to generate all paths instead of using DP.

#1289

Minimum Falling Path Sum II

Hard

ArrayDynamic ProgrammingMatrixDynamic ProgrammingMatrix Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n²)Space O(n)

The optimal solution uses dynamic programming to build the minimum falling path sum iteratively. It keeps track of the minimum sums for each row while ensuring that no two elements from adjacent rows are in the same column. This is like building a path down a staircase, where you remember the best way to get to each step.

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Algorithm

3 steps

1Step 1: Create a DP array initialized to the first row of the grid.
2Step 2: For each subsequent row, calculate the minimum sum for each column while ensuring that the same column from the previous row is not chosen.
3Step 3: Return the minimum value from the last row of the DP array.

solution.py15 lines

1# Full working Python code
2
3def minFallingPathSum(grid):
4    n = len(grid)
5    dp = grid[0][:]
6    for i in range(1, n):
7        new_dp = [0] * n
8        for j in range(n):
9            min_val = float('inf')
10            for k in range(n):
11                if k != j:
12                    min_val = min(min_val, dp[k])
13            new_dp[j] = grid[i][j] + min_val
14        dp = new_dp
15    return min(dp)

ℹ

Complexity note: The time complexity is O(n²) because we iterate through each row and for each column, we check all other columns in the previous row. The space complexity is O(n) since we only keep track of the current and previous row sums.

1Dynamic programming is a powerful technique for optimization problems.
2Understanding how to track previous states can simplify complex problems.

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