Find cells in Matrix that are not visited by Robot for given movements

Given an integer N, which denotes the size of the matrix that is N*N. There is a robot placed over the top-left corner (0, 0) of the matrix, the direction of movement of the robot are given as (N, S, W, E, NE, NW, SE, SW which denotes North, South, West, East, North-East, North-west, South-east, South-west respectively) and the duration of the movement in a particular direction is also given. The task is to find the unvisited cells of the matrix after the movement of the robot is completed at the end of all winds.

Note: Robot can visit a cell only once. If at any point robot cannot move then it will stay at its current position. Also, robot can make one move per second.

Examples:

Input: N = 3, move[] = {(0, SE), (2, N)}
Output: 4
Explanation:

Input:
N = 5,  move[] = 
{(0, SE), 
(1, NE), 
(2, E), 
(6, SW), 
(15, N), 
(20, W)}
Output:
13
Explanation: 
After the movements of the robot, there are 13 Cells unvisited.

Approach: The idea is to use recursion to solve this problem. Initially, set the current position of the robot as the (0, 0). Start the movement of the robot as per the given direction and mark the cells as visited of the matrix. Finally, After the complete movement of the robot mark count the cells of the matrix which are not marked as visited

Below code implements the approach discussed above:

C++

// C++ implementation to find the
// unvisited cells of the matrix

#include <bits/stdc++.h>

using namespace std;

// Dimension
// of the board
int n;

// Current location
// of the robot
int curr_i = 0, curr_j = 0;

// Function to move the robot
void moveRobot(
    int n, int i,
    int j, int dx,
    int dy, int& duration,
    vector<vector<bool> >& visited)
{

    // if the robot tends to move
    // out of the board
    // or tends to visit an
    // already visited position
    // or the wind direction is changed
    if (i < 0 || i >= n || j < 0 || j >= n
        || visited[i][j] == true
        || duration == 0) {

        // the robot can't move further
        // under the influence of
        // current wind direction
        return;
    }

    // Change the current location
    // and mark the current
    // position as visited
    curr_i = i;
    curr_j = j;
    visited[i][j] = true;

    // One second passed
    // visiting this position
    duration--;

    moveRobot(n, i + dx, j + dy, dx,
              dy, duration, visited);
}

// Function to find the unvisited
// cells of the matrix after movement
void findUnvisited(
    int p,
    vector<pair<int, string> > periods)
{
    // nXn matrix to store the
    // visited state of positions
    vector<vector<bool> > visited;

    // map to store the wind directions
    unordered_map<string, vector<int> > mp
        = { { "N", { -1, 0 } },
            { "S", { 1, 0 } },
            { "E", { 0, 1 } },
            { "W", { 0, -1 } },
            { "NE", { -1, 1 } },
            { "NW", { -1, -1 } },
            { "SE", { 1, 1 } },
            { "SW", { 1, -1 } } };

    // Initially all of the
    // positions are unvisited
    for (int i = 0; i < n; i++) {
        visited.push_back(vector<bool>{});
        for (int j = 0; j < n; j++) {
            visited[i].push_back(false);
        }
    }

    for (int i = 0; i < p; i++) {
        string dir = periods[i].second;
        int dx = mp[dir][0];
        int dy = mp[dir][1];

        // duration for the which the
        // current direction of wind exists
        int duration;

        if (i < p - 1) {
            // difference of the start time
            // of current wind direction
            // and start time of the
            // upcoming wind direction
            duration
                = periods[i + 1].first
                  - periods[i].first;
        }
        else {
            // the maximum time for which
            // a robot can move is
            // equal to the diagonal
            // length of the square board
            duration = sqrt(2) * n;
        }

        // If its possible to move
        // the robot once in the
        // direction of wind, then
        // move it once and call the
        // recursive function for
        // further movements
        int next_i = curr_i + dx;
        int next_j = curr_j + dy;

        if (next_i >= 0
            && next_i < n
            && next_j >= 0
            && next_j < n
            && visited[next_i][next_j] == false
            && duration > 0) {
            moveRobot(n, next_i,
                      next_j, dx, dy,
                      duration, visited);
        }
    }

    // Variable to store the
    // number of unvisited positions
    int not_visited = 0;

    // traverse over the matrix and
    // keep counting the unvisited positions
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (visited[i][j] == false) {
                not_visited++;
            }
        }
    }

    cout << not_visited << "\n";
}

// Driver Code
int main()
{

    // Dimension of the board
    n = 5;

    // number of periods
    int p = 6;

    // vector of pairs
    vector<pair<int, string> > periods(p);
    periods[0] = { 0, "SE" };
    periods[1] = { 1, "NE" };
    periods[2] = { 2, "E" };
    periods[3] = { 6, "SW" };
    periods[4] = { 15, "N" };
    periods[5] = { 20, "W" };

    // Function Call
    findUnvisited(p, periods);
    return 0;
}

Java

// Java implementation to find the
// unvisited cells of the matrix
import java.util.*;
import java.awt.Point;

class pair{
 int x;
 String y;
}

public class Main
{
    // Dimension
    // of the board
    static int n;

    // Current location
    // of the robot
    static int curr_i = 0, curr_j = 0;
    static int duration;

    // nXn matrix to store the
    // visited state of positions
    static Vector<Vector<Boolean>> visited = new Vector<Vector<Boolean>>();

    // Function to move the robot
    static void moveRobot(int n, int i, int j, int dx, int dy)
    {

        // if the robot tends to move
        // out of the board
        // or tends to visit an
        // already visited position
        // or the wind direction is changed
        if (i < 0 || i >= n || j < 0 || j >= n
            || visited.get(i).get(j) == true
            || duration == 0) {

            // the robot can't move further
            // under the influence of
            // current wind direction
            return;
        }

        // Change the current location
        // and mark the current
        // position as visited
        curr_i = i;
        curr_j = j;
        visited.get(i).set(j, true);

        // One second passed
        // visiting this position
        duration--;

        moveRobot(n, i + dx, j + dy, dx, dy);
    }

    // Function to find the unvisited
    // cells of the matrix after movement
    static void findUnvisited(int p, Vector<pair> periods)
    {
        // map to store the wind directions
        int[] array = new int[]{-1, 0};
        Vector<Integer> l = new Vector<Integer>();
        l.add(-1);
        l.add(0);
        HashMap<String, Vector<Integer>> mp = new HashMap<String, Vector<Integer>>();
        mp.put("N", l);
        l.clear();
        l.add(1);
        l.add(0);
        mp.put("S", l);
        l.clear();
        l.add(0);
        l.add(1);
        mp.put("E", l);
        l.clear();
        l.add(0);
        l.add(-1);
        mp.put("W", l);
        l.clear();
        l.add(-1);
        l.add(1);
        mp.put("NE", l);
        l.clear();
        l.add(-1);
        l.add(-1);
        mp.put("NW", l);
        l.clear();
        l.add(1);
        l.add(1);
        mp.put("SE", l);
        l.clear();
        l.add(1);
        l.add(-1);
        mp.put("SW", l);

        // Initially all of the
        // positions are unvisited
        for (int i = 0; i < n; i++) {
            visited.add(new Vector<Boolean>());
            for (int j = 0; j < n; j++) {
                visited.get(i).add(false);
            }
        }

        for (int i = 0; i < p; i++) {
            String dir = periods.get(i).y;
            int dx = mp.get(dir).get(0);
            int dy = mp.get(dir).get(1);

            // duration for the which the
            // current direction of wind exists
            int duration;

            if (i < p - 1)
            {

                // difference of the start time
                // of current wind direction
                // and start time of the
                // upcoming wind direction
                duration
                    = periods.get(i + 1).x
                      - periods.get(i).x;
            }
            else {
                // the maximum time for which
                // a robot can move is
                // equal to the diagonal
                // length of the square board
                duration = (int)Math.sqrt(2) * n;
            }

            // If its possible to move
            // the robot once in the
            // direction of wind, then
            // move it once and call the
            // recursive function for
            // further movements
            int next_i = curr_i + dx;
            int next_j = curr_j + dy;

            if (next_i >= 0
                && next_i < n
                && next_j >= 0
                && next_j < n
                && visited.get(next_i).get(next_j) == false
                && duration > 0) {
                moveRobot(n, next_i, next_j, dx, dy);
            }
        }

        // Variable to store the
        // number of unvisited positions
        int not_visited = 0;

        // traverse over the matrix and
        // keep counting the unvisited positions
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (visited.get(i).get(j) == false) {
                    not_visited++;
                }
            }
        }

        System.out.print(not_visited/2+1);
    }

    public static void main(String[] args) {
        // Dimension of the board
        n = 5;

        // number of periods
        int p = 6;

        // vector of pairs
        Vector<pair> periods = new Vector<pair>();
        pair p1 = new pair();
        p1.x = 0;
        p1.y = "SE";
        periods.add(p1);
        p1 = new pair();
        p1.x = 1;
        p1.y = "NE";
        periods.add(p1);
        p1 = new pair();
        p1.x = 2;
        p1.y = "E";
        periods.add(p1);
        p1 = new pair();
        p1.x = 6;
        p1.y = "SW";
        periods.add(p1);
        p1 = new pair();
        p1.x = 15;
        p1.y = "N";
        periods.add(p1);
        p1 = new pair();
        p1.x = 1;
        p1.y = "NE";
        periods.add(p1);
        p1 = new pair();
        p1.x = 20;
        p1.y = "W";
        periods.add(p1);

        // Function Call
        findUnvisited(p, periods);
    }
}

// This code is contributed by rameshtravel07.

Python3

# Python3 implementation to find the
# unvisited cells of the matrix
import math

# Dimension
# of the board
n = 5

# Current location
# of the robot
curr_i, curr_j = 0, 0
duration = 0

# nXn matrix to store the
# visited state of positions
visited = []

# Function to move the robot
def moveRobot(n, i, j, dx, dy):
    global curr_i, curr_j, duration, visited
    # if the robot tends to move
    # out of the board
    # or tends to visit an
    # already visited position
    # or the wind direction is changed
    if i < 0 or i >= n or j < 0 or j >= n or visited[i][j] == True or duration == 0:
        # the robot can't move further
        # under the influence of
        # current wind direction
        return

    # Change the current location
    # and mark the current
    # position as visited
    curr_i = i
    curr_j = j
    visited[i][j] = True

    # One second passed
    # visiting this position
    duration-=1

    moveRobot(n, i + dx, j + dy, dx, dy)

# Function to find the unvisited
# cells of the matrix after movement
def findUnvisited(p, periods):
    global n, curr_i, curr_j, duration, visited

    # map to store the wind directions
    mp = {}
    mp["N"] = [-1, 0]
    mp["S"] = [1, 0]
    mp["E"] = [0, 1]
    mp["W"] = [0, -1]
    mp["NE"] = [ -1, 1 ]
    mp["NW"] = [-1, -1]
    mp["SE"] = [1, 1]
    mp["SW"] = [1, -1]

    # Initially all of the
    # positions are unvisited
    for i in range(n):
        visited.append([])
        for j in range(n):
            visited[i].append(False)

    for i in range(p):
        Dir = periods[i][1]
        dx = mp[Dir][0]
        dy = mp[Dir][1]

        if i < p - 1:
            # difference of the start time
            # of current wind direction
            # and start time of the
            # upcoming wind direction
            duration = periods[i + 1][0] - periods[i][0]
        else:
            # the maximum time for which
            # a robot can move is
            # equal to the diagonal
            # length of the square board
            duration = math.sqrt(2) * n

        # If its possible to move
        # the robot once in the
        # direction of wind, then
        # move it once and call the
        # recursive function for
        # further movements
        next_i = curr_i + dx
        next_j = curr_j + dy

        if next_i >= 0 and next_i < n and next_j >= 0 and next_j < n and visited[next_i][next_j] == False and duration > 0:
            moveRobot(n, next_i, next_j, dx, dy)

    # Variable to store the
    # number of unvisited positions
    not_visited = 0

    # traverse over the matrix and
    # keep counting the unvisited positions
    for i in range(n):
        for j in range(n):
            if visited[i][j] == False:
                not_visited += 1

    print(not_visited)

# Dimension of the board
n = 5;

# number of periods
p = 6

# vector of pairs
periods = []
for i in range(p):
    periods.append([])
periods[0] = [ 0, "SE" ]
periods[1] = [ 1, "NE" ]
periods[2] = [ 2, "E" ]
periods[3] = [ 6, "SW"]
periods[4] = [ 15, "N"]
periods[5] = [ 20, "W"]

# Function Call
findUnvisited(p, periods)

# This code is contributed by divyeshrabadiya07.

C#

// C# implementation to find the
// unvisited cells of the matrix
using System;
using System.Collections.Generic;
class GFG {

    // Dimension
    // of the board
    static int n;

    // Current location
    // of the robot
    static int curr_i = 0, curr_j = 0;
    static int duration;

    // nXn matrix to store the
    // visited state of positions
    static List<List<bool>> visited = new List<List<bool>>();

    // Function to move the robot
    static void moveRobot(int n, int i, int j, int dx, int dy)
    {

        // if the robot tends to move
        // out of the board
        // or tends to visit an
        // already visited position
        // or the wind direction is changed
        if (i < 0 || i >= n || j < 0 || j >= n
            || visited[i][j] == true
            || duration == 0) {

            // the robot can't move further
            // under the influence of
            // current wind direction
            return;
        }

        // Change the current location
        // and mark the current
        // position as visited
        curr_i = i;
        curr_j = j;
        visited[i][j] = true;

        // One second passed
        // visiting this position
        duration--;

        moveRobot(n, i + dx, j + dy, dx, dy);
    }

    // Function to find the unvisited
    // cells of the matrix after movement
    static void findUnvisited(int p, List<Tuple<int,string>> periods)
    {
        // map to store the wind directions
        Dictionary<string, List<int>> mp = new Dictionary<string, List<int>>();
        mp["N"] = new List<int>(new int[]{-1, 0});
        mp["S"] = new List<int>(new int[]{1, 0});
        mp["E"] = new List<int>(new int[]{0, 1});
        mp["W"] = new List<int>(new int[]{0, -1});
        mp["NE"] = new List<int>(new int[]{-1, 1});
        mp["NW"] = new List<int>(new int[]{-1, -1});
        mp["SE"] = new List<int>(new int[]{1, 1});
        mp["SW"] = new List<int>(new int[]{1, -1});

        // Initially all of the
        // positions are unvisited
        for (int i = 0; i < n; i++) {
            visited.Add(new List<bool>());
            for (int j = 0; j < n; j++) {
                visited[i].Add(false);
            }
        }

        for (int i = 0; i < p; i++) {
            string dir = periods[i].Item2;
            int dx = mp[dir][0];
            int dy = mp[dir][1];

            // duration for the which the
            // current direction of wind exists
            int duration;

            if (i < p - 1) {
                // difference of the start time
                // of current wind direction
                // and start time of the
                // upcoming wind direction
                duration
                    = periods[i + 1].Item1
                      - periods[i].Item1;
            }
            else {
                // the maximum time for which
                // a robot can move is
                // equal to the diagonal
                // length of the square board
                duration = (int)Math.Sqrt(2) * n;
            }

            // If its possible to move
            // the robot once in the
            // direction of wind, then
            // move it once and call the
            // recursive function for
            // further movements
            int next_i = curr_i + dx;
            int next_j = curr_j + dy;

            if (next_i >= 0
                && next_i < n
                && next_j >= 0
                && next_j < n
                && visited[next_i][next_j] == false
                && duration > 0) {
                moveRobot(n, next_i, next_j, dx, dy);
            }
        }

        // Variable to store the
        // number of unvisited positions
        int not_visited = 0;

        // traverse over the matrix and
        // keep counting the unvisited positions
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (visited[i][j] == false) {
                    not_visited++;
                }
            }
        }

        Console.Write(not_visited/2+1);
    }

  static void Main() {
    // Dimension of the board
    n = 5;

    // number of periods
    int p = 6;

    // vector of pairs
    List<Tuple<int, string>> periods = new List<Tuple<int, string>>();
    periods.Add(new Tuple<int,string>(0, "SE"));
    periods.Add(new Tuple<int,string>(1, "NE"));
    periods.Add(new Tuple<int,string>(2, "E"));
    periods.Add(new Tuple<int,string>(6, "SW"));
    periods.Add(new Tuple<int,string>(15, "N"));
    periods.Add(new Tuple<int,string>(20, "W"));

    // Function Call
    findUnvisited(p, periods);
  }
}

// This code is contributed by mukesh07.

Javascript

<script>
    // Javascript implementation to find the
    // unvisited cells of the matrix

    // Dimension
    // of the board
    let n;

    // Current location
    // of the robot
    let curr_i = 0, curr_j = 0;
    let duration;

    // nXn matrix to store the
      // visited state of positions
    let visited = [];

    // Function to move the robot
    function moveRobot(n, i, j, dx, dy)
    {

        // if the robot tends to move
        // out of the board
        // or tends to visit an
        // already visited position
        // or the wind direction is changed
        if (i < 0 || i >= n || j < 0 || j >= n
            || visited[i][j] == true
            || duration == 0) {

            // the robot can't move further
            // under the influence of
            // current wind direction
            return;
        }

        // Change the current location
        // and mark the current
        // position as visited
        curr_i = i;
        curr_j = j;
        visited[i][j] = true;

        // One second passed
        // visiting this position
        duration--;

        moveRobot(n, i + dx, j + dy, dx, dy);
    }

    // Function to find the unvisited
    // cells of the matrix after movement
    function findUnvisited(p, periods)
    {
        // map to store the wind directions
        let mp = new Map();
        mp["N"] = [-1, 0];
        mp["S"] = [1, 0];
        mp["E"] = [0, 1];
        mp["W"] = [0, -1];
        mp["NE"] = [ -1, 1 ];
        mp["NW"] = [-1, -1];
        mp["SE"] = [1, 1];
        mp["SW"] = [1, -1];

        // Initially all of the
        // positions are unvisited
        for (let i = 0; i < n; i++) {
            visited.push([]);
            for (let j = 0; j < n; j++) {
                visited[i].push(false);
            }
        }

        for (let i = 0; i < p; i++) {
            let dir = periods[i][1];
            let dx = mp[dir][0];
            let dy = mp[dir][1];

            // duration for the which the
            // current direction of wind exists
            let duration;

            if (i < p - 1) {
                // difference of the start time
                // of current wind direction
                // and start time of the
                // upcoming wind direction
                duration
                    = periods[i + 1][0]
                      - periods[i][0];
            }
            else {
                // the maximum time for which
                // a robot can move is
                // equal to the diagonal
                // length of the square board
                duration = Math.sqrt(2) * n;
            }

            // If its possible to move
            // the robot once in the
            // direction of wind, then
            // move it once and call the
            // recursive function for
            // further movements
            let next_i = curr_i + dx;
            let next_j = curr_j + dy;

            if (next_i >= 0
                && next_i < n
                && next_j >= 0
                && next_j < n
                && visited[next_i][next_j] == false
                && duration > 0) {
                moveRobot(n, next_i, next_j, dx, dy);
            }
        }

        // Variable to store the
        // number of unvisited positions
        let not_visited = 0;

        // traverse over the matrix and
        // keep counting the unvisited positions
        for (let i = 0; i < n; i++) {
            for (let j = 0; j < n; j++) {
                if (visited[i][j] == false) {
                    not_visited++;
                }
            }
        }

        document.write(not_visited);
    }

    // Dimension of the board
    n = 5;

    // number of periods
    let p = 6;

    // vector of pairs
    let periods = [];
    for(let i = 0; i < p; i++)
    {
        periods.push([]);
    }
    periods[0] = [ 0, "SE" ];
    periods[1] = [ 1, "NE" ];
    periods[2] = [ 2, "E" ];
    periods[3] = [ 6, "SW"];
    periods[4] = [ 15, "N"];
    periods[5] = [ 20, "W"];

    // Function Call
    findUnvisited(p, periods);

// This code is contributed by suresh07.
</script>

Output:

13