Recursion/DP - Grid Traveller - Memoized | C# Online Compiler

Recursion/DP - Grid Traveller - Memoized by SuckingFlayer

using System;
using System.Collections.Generic;
					
public class Program
{
	public static void Main()
	{
		Console.WriteLine("Hello World");
		Dictionary<string,long> map=new Dictionary<string,long>();
		//The problem is to count all the possible paths from top left to bottom right of a mXn matrix with the constraints that from each cell you can either move only to right or down
		//Time complexity of non optimized version becomes O(2^n/2) as for evrry level of recursion, we are doubling our number of operations. Same for Fibonacci sequence
		Console.WriteLine(GridTraveller_1(2,3,map));
	}
	
	public static long GridTraveller(int m,int n,Dictionary<string,long> map)
	{
		string key=String.Concat(m.ToString(),',',n.ToString());
		
		if(map!=null) {if(map.ContainsKey(key)) return map[key];}
		if(m==0 || n==0) 	return 0;
		if (m==n && m==1)	return 1;
		map[key]=GridTraveller(m-1,n,map)+GridTraveller(m,n-1,map);
		return map[key];
	}
	
	public static long GridTraveller_1(int m,int n,Dictionary<string,long> map)
	{
		//Possible traversals are RU,RD and R
		string key=String.Concat(m.ToString(),',',n.ToString());
		
		if(map!=null) {if(map.ContainsKey(key)) return map[key];}
		if(m==0 || n==0) 	return 0;
		if (m==n && m==1)	return 1;
		//Traversing Right means decreasing the grid columns by 1..so m,n-1
		//Traversing Right Up means decreasing the grid columns by 1 and grid rows by 1...so m-1,n-1
		map[key]=GridTraveller_1(m+1,n-1,map)+GridTraveller_1(m,n-1,map)+GridTraveller_1(m-1,n-1,map);
		return map[key];
	}
}

 
using System;
using System.Collections.Generic;
                    
public class Program
{
    public static void Main()
    {
        Console.WriteLine("Hello World");
        Dictionary<string,long> map=new Dictionary<string,long>();
        //The problem is to count all the possible paths from top left to bottom right of a mXn matrix with the constraints that from each cell you can either move only to right or down
        //Time complexity of non optimized version becomes O(2^n/2) as for evrry level of recursion, we are doubling our number of operations. Same for Fibonacci sequence
        Console.WriteLine(GridTraveller_1(2,3,map));
    }
    
    public static long GridTraveller(int m,int n,Dictionary<string,long> map)
    {
        string key=String.Concat(m.ToString(),',',n.ToString());
        
        if(map!=null) {if(map.ContainsKey(key)) return map[key];}
        if(m==0 || n==0)    return 0;
        if (m==n && m==1)   return 1;
        map[key]=GridTraveller(m-1,n,map)+GridTraveller(m,n-1,map);
        return map[key];
    }
    
    public static long GridTraveller_1(int m,int n,Dictionary<string,long> map)
    {
        //Possible traversals are RU,RD and R
        string key=String.Concat(m.ToString(),',',n.ToString());
        
        if(map!=null) {if(map.ContainsKey(key)) return map[key];}
        if(m==0 || n==0)    return 0;
        if (m==n && m==1)   return 1;
        //Traversing Right means decreasing the grid columns by 1..so m,n-1
        //Traversing Right Up means decreasing the grid columns by 1 and grid rows by 1...so m-1,n-1
        map[key]=GridTraveller_1(m+1,n-1,map)+GridTraveller_1(m,n-1,map)+GridTraveller_1(m-1,n-1,map);
        return map[key];
    }
} 

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Last Run:	9:41:44 pm
Compile:	0s
Execute:	0.189s
Memory:	0b
CPU:	0s

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