Solution 3 for Scaler Topics Fortnightly Contest - 6

This article is part of the Scaler Topics Fortnightly Contest - 6.

Transform Your Career

Choose from our industry-leading programs designed for career success

NSDC Certified

Modern Software and AI Engineering Program

Master full-stack development with AI integration

12 MonthsDuration

AI-LedCurriculum

Career SupportSupport

+1000 more

Go to Program

NSDC Certified

Modern Data Science and ML with specialisation in AI

Advanced data science techniques with AI specialization

12 MonthsDuration

AI-LedCurriculum

Career SupportSupport

+1000 more

Go to Program

NSDC Certified

Advanced AIML with Specialisation in Agentic AI

Deep dive into AIML with focus on Agentic systems

12 MonthsDuration

AI-LedCurriculum

Career SupportSupport

+1000 more

Go to Program

NSDC Certified

DevOps, Cloud & AI Platform Engineering

Build and manage AI-powered cloud infrastructure

12 MonthsDuration

AI-LedCurriculum

Career SupportSupport

+1000 more

Go to Program

NSDC Certified

AI Engineering Advanced Certification by IIT-Roorkee

Premier AI engineering certification from IIT-Roorkee

3 MonthsDuration

AI-LedCurriculum

Career SupportSupport

Go to Program

Solution Approach

• We can use Dynamic Programming here to solve this problem, as we have reached some cell we only care about the last move used to reach this cell.
• There are 5 kinds of moves possible in the game so we can keep track of the moves by assigning them a value.
• Let DP[i][j][k] represent the number of ways to reach the destination if we start at (i, j) cell, with the last move being represented by k, from state (i, j, k) we can make all possible moves not equal to k.

Time Complexity: O(A × B × K × K) where K represents the possible number of moves which is 5 in our case.

Space Complexity:- O(A × B × K)

C++ Implementation

Java Implementation

Hiring Partners:

GoogleAmazonMicrosoftFlipkartAdobe1200+ more

Python Implementation