How to find the path of robot if it can only move in 3 directions:right, down, diagonally down.

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Imagine a robot sitting on the upper left hand corner of an NxN grid. The robot can only move in three directions: right , down and diagonally down. The robot has to reach the lower right hand corner of the NxN grid. Imagine certain squares are “off limits” or “offsets”, such that the robot cannot step on them. Write a program to determine the number of possible paths for the robot.The entry of offset points ends when the user enters the coordinates as (-1,-1).
Input:
Enter the size of the grid
3
Enter the grid points that are offsets
0 1
-1 -1
output:
The paths for the robot are

( 0 , 0 ) - ( 1 , 0 ) - ( 2 , 0 ) - ( 2 , 1 ) - ( 2 , 2 )
( 0 , 0 ) - ( 1 , 0 ) - ( 1 , 1 ) - ( 2 , 1 ) - ( 2 , 2 )
( 0 , 0 ) - ( 1 , 0 ) - ( 1 , 1 ) - ( 1 , 2 ) - ( 2 , 2 )
( 0 , 0 ) - ( 1 , 0 ) - ( 1 , 1 ) - ( 2 , 2 )
( 0 , 0 ) - ( 1 , 0 ) - ( 2 , 1 ) - ( 2 , 2 )
( 0 , 0 ) - ( 1 , 1 ) - ( 2 , 1 ) - ( 2 , 2 )
( 0 , 0 ) - ( 1 , 1 ) - ( 1 , 2 ) - ( 2 , 2 )
( 0 , 0 ) - ( 1 , 1 ) - ( 2 , 2 )

What I have tried:

C++

#include <iostream>
using namespace std;
int numberOfPaths(int m, int n)
{
	int count[m][n];
	for (int i = 0; i < m; i++)
		count[i][0] = 1;
        for (int j = 0; j < n; j++)
		count[0][j] = 1;
	for (int i = 1; i < m; i++)
	{
		for (int j = 1; j < n; j++)
                   count[i][j] = count[i-1][j] + count[i][j-1]; 
	}
	return count[m-1][n-1];
}
int main()
{
	cout << numberOfPaths(3, 3);
	return 0;
}

//This is what I found to count the path if it can move only in 2 directions:right,down.

Posted 2-Jul-17 5:48am

Member 13289075

Updated 1-Jun-19 18:34pm

PIEBALDconsult

v2

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PIEBALDconsult 2-Jul-17 12:32pm

We won't do your homework for you.

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Patrice T · Answer 1 · 2017-07-02T08:36:00

Looks like to need to learn some analyze methods.
You need to proceed in order

Quote:
Imagine a robot sitting on the upper left hand corner of an NxN grid.
The robot has to reach the lower right hand corner of the NxN grid.
Imagine certain squares are “off limits” or “offsets”, such that the robot cannot step on them.

You need a grid of size NxN where you will remember positions that are off limits.

Quote:
The robot can only move in three directions: right , down and diagonally down.
Write a program to determine the number of possible paths for the robot.

You need to count all paths. which means that the robot can choose one of the 3 directions as long as the move do not hit a border of the grid or an off limit position.
This is a typical recursive problem: you need to write a function with actual position, if position is final position, it is a new path, otherwise for each moves, you check if move is allowed, and if allowed, call this same function with new position.
Either you do it with an explicit recursive function, or with implicit recursion using backtracking.
We do not do your HomeWork.
HomeWork is not set to test your skills at begging other people to do your work, it is set to make you think and to help your teacher to check your understanding of the courses you have taken and also the problems you have at applying them.
Any failure of you will help your teacher spot your weaknesses and set remedial actions.
Any failure of you will help you to learn what works and what don't, it is called 'trial and error' learning.

As programmer, your job is to create algorithms that solve specific problems and you can't rely on someone else to eternally do it for you, so there is a time where you will have to learn how to.
Creating an algorithm is basically finding the maths and make necessary adaptation to fit your actual problem.

Member 13402059 · Answer 2 · 2017-09-09T22:02:00

Solution 2

( 0 , 0 ) - ( 1 , 1 ) - ( 1 , 2 ) - ( 2 , 2 )

( 0 , 0 ) - ( 1 , 1 ) - ( 2 , 2 )

Posted 9-Sep-17 22:02pm

Member 13402059

Member 14477856 · Answer 3 · 2019-06-01T18:34:00

#include <stdio.h>
int pospaths(int m, int n)
{
int count[m][n];
for (int i = 0; i < m; i++)
count[i][0] = 1;
for (int j = 0; j < n; j++)
count[0][j] = 1;
for (int i = 1; i < m; i++)
{
for (int j = 1; j < n; j++)
count[i][j] = count[i-1][j] + count[i][j-1] + count[i-1][j-1];
}
return count[m-1][n-1];
}
int main()
{
int size;
printf("Enter the size of the grid\n");
scanf("%d",&size);
printf("The number of paths is %d",pospaths(size, size));
return 0;
}

How to find the path of robot if it can only move in 3 directions:right, down, diagonally down.

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