Is Minimum Falling Path Sum II easy or hard?

LeetCode classifies Minimum Falling Path Sum II as a Hard problem. The challenge comes from recognizing how to optimize the DP transition by tracking two minimum values instead of scanning every column.

Minimum Falling Path Sum II Python/Java solution

Python and Java implementations typically maintain an array for the previous row's DP values and compute the smallest and second smallest entries before updating the next row. The algorithm runs in O(n^2) time and can be implemented with either a full DP matrix or a space-optimized single array.

How to solve Minimum Falling Path Sum II in O(n^2)?

Maintain the smallest and second smallest DP values from the previous row along with their column indices. For each column in the current row, use the smallest value unless it came from the same column; otherwise use the second smallest. This removes the need for scanning all columns during transitions.

What is the best approach for Minimum Falling Path Sum II?

The best approach uses dynamic programming with tracking of the smallest and second smallest values from the previous row. This avoids scanning all columns for each transition and reduces the complexity to O(n^2). It processes the grid row by row while ensuring the chosen column differs from the previous row.

Is Minimum Falling Path Sum II asked at Google/Amazon/Meta?

Variants of constrained grid dynamic programming problems frequently appear in interviews at companies like Google, Amazon, and Meta. The key skill tested is optimizing DP transitions using tracked minimum values instead of brute-force scanning.

What data structure is used in Minimum Falling Path Sum II?

The solution primarily uses arrays to store dynamic programming states for each row. Additional variables track the smallest and second smallest values from the previous row to enable efficient transitions.

What is the time complexity of Minimum Falling Path Sum II?

The optimized dynamic programming solution runs in O(n^2) time for an n x n grid. Each row is processed once, and transitions are constant time because the smallest and second smallest values from the previous row are precomputed.

Description Hints 3 Solution Video 31:44

1289. Minimum Falling Path Sum II

Hard63.2% acceptance3 companies

Given an n x n integer matrix grid, return the minimum sum of a falling path with non-zero shifts.

A falling path with non-zero shifts is a choice of exactly one element from each row of grid such that no two elements chosen in adjacent rows are in the same column.

Example 1:

Input: grid = [[1,2,3],[4,5,6],[7,8,9]]
Output: 13
Explanation: 
The possible falling paths are:
[1,5,9], [1,5,7], [1,6,7], [1,6,8],
[2,4,8], [2,4,9], [2,6,7], [2,6,8],
[3,4,8], [3,4,9], [3,5,7], [3,5,9]
The falling path with the smallest sum is [1,5,7], so the answer is 13.

Example 2:

Input: grid = [[7]]
Output: 7

Constraints:

n == grid.length == grid[i].length
1 <= n <= 200
-99 <= grid[i][j] <= 99

Asked at 3 companies

Google Meta Bloomberg

Topics

Hints open one at a time

Hint 1

Use dynamic programming.

Hint 2

Let dp[i][j] be the answer for the first i rows such that column j is chosen from row i.

Hint 3

Use the concept of cumulative array to optimize the complexity of the solution.

31:44

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