Step 16: Dynamic Programming [Patterns and Problems]›2D/3D DP and DP on Grids
Minimum Falling Path Sum
MediumFunction: minimumFallingPathSum()
ASCI Mission Breakdown • Simple as Hell
"Master Minimum Falling Path Sum: Take `nums` (number[]), execute an optimal 2d/3d dp and dp on grids strategy, and return number with clean edge-case handling."
Real-World Metaphor:
Think of Minimum Falling Path Sum as an everyday real-world challenge: you receive input data, inspect its elements in sequence without making unnecessary duplicate passes, and transform the collection to reach the exact target without wasting computer memory.
Interactive Visual WalkthroughDP-GRID
Step 1 / 3
StatusInitialized
ModeScanning
Evaluating
1. Initialize State for Minimum Falling Path Sum
Load inputs and initialize algorithmic registers.
How to Think About This (Mental Model)
Unpack the problem parameters (`nums` (number[])) and clarify what is given vs what must be returned.
Identify the optimal data structure or pattern (e.g. pointers, hash map, or stack) to avoid redundant recalculations.
Walk through state transitions, handle edge cases (empty collections, single items, negative numbers), and return the verified result.
### The Mission
Welcome to **Minimum Falling Path Sum**! In this challenge, your goal is to write a high-performance, clean solution in your chosen programming language.
You are given `nums` (number[]). Your job is to process this input using optimal logic and return number.
### How to Approach It
- Read through the inputs carefully and look for patterns.
- Think about what state you need to track as you examine each element.
- Strive for optimal time complexity and keep your code readable and structured.
Examples
Example 1
Input: nums = [1,2,3,4,5]
Output: 15
Constraints
1 <= nums.length <= 10^5
-10^9 <= nums[i] <= 10^9
Topic Tags:
Dynamic Programming [Patterns and Problems]2D/3D DP and DP on GridsminimumFallingPathSum