Check if the robot is within the bounds of the grid after given moves

Given a grid of size N X M and a robot is placed at cell (N – 1, M – 1). Also, given string str which consists only of the characters ‘U’ (Up), ‘D’ (Down), ‘L’ (Left) and ‘R’ (Right) representing the moves the robot is going to perform within the grid. The task is to find whether the robot will be safe at the end of the last move. Robot is said to be safe if it is within the bounds of the grid.

Note: Consider that the rectangular grid is present below the number line with the top-left corner lying on the origin.

Examples:



Input: N = 1, M = 1, str = “R”
Output: No
As there is only 1 cell, no movement is allowed.

Input: N = 2, M = 3, str = “LLRU”
Output: Yes

Approach: For every move, update the position of the robot inside the grid. if at any move the position of the robot is outside the grid then the output will be No else print Yes if for all the moves, the robot is within the bounds of the grid.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function that returns true if the robot is safe
bool isSafe(int N, int M, string str)
{
  
    int coll = 0, colr = 0, rowu = 0, rowd = 0;
  
    for (int i = 0; i < str.length(); i++) {
  
        // If current move is "L" then
        // increase the counter of coll
        if (str[i] == 'L') {
            coll++;
            if (colr > 0) {
                colr--;
            }
  
            // If value of coll is equal to
            // column then break
            if (coll == M) {
                break;
            }
        }
  
        // If current move is "R" then
        // increase the counter of colr
        else if (str[i] == 'R') {
            colr++;
            if (coll > 0) {
                coll--;
            }
  
            // If value of colr is equal to
            // column then break
            if (colr == M) {
                break;
            }
        }
  
        // If current move is "U" then
        // increase the counter of rowu
        else if (str[i] == 'U') {
            -rowu++;
            if (rowd > 0) {
                rowd--;
            }
  
            // If value of rowu is equal to
            // row then break
            if (rowu == N) {
                break;
            }
        }
  
        // If current move is "D" then
        // increase the counter of rowd
        else if (str[i] == 'D') {
            rowd++;
            if (rowu > 0) {
                rowu--;
            }
  
            // If value of rowd is equal to
            // row then break
            if (rowd == N) {
                break;
            }
        }
    }
  
    // If robot is within the bounds of the grid
    if (abs(rowd) < N && abs(rowu) < N
        && abs(coll) < M && abs(colr) < M) {
        return true;
    }
  
    // Unsafe
    return false;
}
  
// Driver code
int main()
{
    int N = 1, M = 1;
    string str = "R";
  
    if (isSafe(N, M, str))
        cout << "Yes";
    else
        cout << "No";
  
    return 0;
}

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Java

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// Java implementation of the approach
class GFG {
  
    // Function that returns true if the robot is safe
    static boolean isSafe(int N, int M, char[] str)
    {
  
        int coll = 0, colr = 0, rowu = 0, rowd = 0;
  
        for (int i = 0; i < str.length; i++) {
  
            // If current move is "L" then
            // increase the counter of coll
            if (str[i] == 'L') {
                coll++;
                if (colr > 0) {
                    colr--;
                }
  
                // If value of coll is equal to
                // column then break
                if (coll == M) {
                    break;
                }
            }
  
            // If current move is "R" then
            // increase the counter of colr
            else if (str[i] == 'R') {
                colr++;
                if (coll > 0) {
                    coll--;
                }
  
                // If value of colr is equal to
                // column then break
                if (colr == M) {
                    break;
                }
            }
  
            // If current move is "U" then
            // increase the counter of rowu
            else if (str[i] == 'U') {
                rowu++;
                if (rowd > 0) {
                    rowd--;
                }
  
                // If value of rowu is equal to
                // row then break
                if (rowu == N) {
                    break;
                }
            }
  
            // If current move is "D" then
            // increase the counter of rowd
            else if (str[i] == 'D') {
                rowd++;
                if (rowu > 0) {
                    rowu--;
                }
  
                // If value of rowd is equal to
                // row then break
                if (rowd == N) {
                    break;
                }
            }
        }
  
        // If robot is within the bounds of the grid
        if (Math.abs(rowd) < N && Math.abs(rowu) < N
            && Math.abs(coll) < M && Math.abs(colr) < M) {
            return true;
        }
  
        // Unsafe
        return false;
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int N = 1, M = 1;
        String str = "R";
  
        if (isSafe(N, M, str.toCharArray()))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}
  
// This code is contributed by 29AjayKumar

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Python3

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# Python 3 implementation of the approach
  
# Function that returns true 
# if the robot is safe
def isSafe(N, M, str):
    coll = 0
    colr = 0
    rowu = 0
    rowd = 0
  
    for i in range(len(str)):
          
        # If current move is "L" then
        # increase the counter of coll
        if (str[i] == 'L'):
            coll += 1
            if (colr > 0):
                colr -= 1
  
            # If value of coll is equal to
            # column then break
            if (coll == M):
                break
  
        # If current move is "R" then
        # increase the counter of colr
        elif (str[i] == 'R'):
            colr += 1
            if (coll > 0):
                coll -= 1
  
            # If value of colr is equal to
            # column then break
            if (colr == M):
                break
  
        # If current move is "U" then
        # increase the counter of rowu
        elif (str[i] == 'U'):
            rowu += 1
            if (rowd > 0):
                rowd -= 1
  
            # If value of rowu is equal to
            # row then break
            if (rowu == N):
                break
  
        # If current move is "D" then
        # increase the counter of rowd
        elif (str[i] == 'D'):
            rowd += 1
            if (rowu > 0):
                rowu -= 1
  
            # If value of rowd is equal to
            # row then break
            if (rowd == N):
                break
  
    # If robot is within the bounds of the grid
    if (abs(rowd) < N and abs(rowu) < N and 
        abs(coll) < M and abs(colr) < M):
        return True
  
    # Unsafe
    return False
  
# Driver code
if __name__ == '__main__':
    N = 1
    M = 1
    str = "R"
  
    if (isSafe(N, M, str)):
        print("Yes")
    else:
        print("No")
  
# This code is contributed by
# Surendra_Gangwar

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C#

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// C# implementation of the approach
using System;
  
class GFG {
  
    // Function that returns true if the robot is safe
    static bool isSafe(int N, int M, char[] str)
    {
  
        int coll = 0, colr = 0, rowu = 0, rowd = 0;
  
        for (int i = 0; i < str.Length; i++) {
  
            // If current move is "L" then
            // increase the counter of coll
            if (str[i] == 'L') {
                coll++;
                if (colr > 0) {
                    colr--;
                }
  
                // If value of coll is equal to
                // column then break
                if (coll == M) {
                    break;
                }
            }
  
            // If current move is "R" then
            // increase the counter of colr
            else if (str[i] == 'R') {
                colr++;
                if (coll > 0) {
                    coll--;
                }
  
                // If value of colr is equal to
                // column then break
                if (colr == M) {
                    break;
                }
            }
  
            // If current move is "U" then
            // increase the counter of rowu
            else if (str[i] == 'U') {
                rowu++;
                if (rowd > 0) {
                    rowd--;
                }
  
                // If value of rowu is equal to
                // row then break
                if (rowu == N) {
                    break;
                }
            }
  
            // If current move is "D" then
            // increase the counter of rowd
            else if (str[i] == 'D') {
                rowd++;
                if (rowu > 0) {
                    rowu--;
                }
  
                // If value of rowd is equal to
                // row then break
                if (rowd == N) {
                    break;
                }
            }
        }
  
        // If robot is within the bounds of the grid
        if (Math.Abs(rowd) < N && Math.Abs(rowu) < N
            && Math.Abs(coll) < M && Math.Abs(colr) < M) {
            return true;
        }
  
        // Unsafe
        return false;
    }
  
    // Driver code
    public static void Main(String[] args)
    {
        int N = 1, M = 1;
        String str = "R";
  
        if (isSafe(N, M, str.ToCharArray()))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}
  
// This code has been contributed by 29AjayKumar

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Output:

No


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