# Displacement from origin after N moves of given distances in specified directions

• Last Updated : 14 Jun, 2021

Given an array A[] consisting of characters ‘U’, ‘D’, ‘L’, and ‘R’ representing directions up, down, left, and right, and another array B[] consisting of N positive integers, the task is to find the displacement of a robot, starting its journey from (0, 0) facing toward North, after N moves, where in the ith move, the robot moves a distance B[i] in the direction A[i].

Examples:

Input: A[] = {U, R, R, R, R}, B[] = {1, 1, 1, 1, 0}
Output: 0 North
Explanation:
Initially, the robot is at (0, 0) facing North.
After 1st move, the position is (0, 1) facing North.
After 2nd move, the position is (1, 1) facing East.
After 3rd move, the position is (1, 0) facing South.
After 4th move, the position is (0, 0) facing West.
After 5th move, the position is (0, 0) facing North.

Therefore, the displacement is 0 and the final direction is North.

Input: A[] = {U, L, R, D, R}, B[] = {5, 5, 5, 5, 5}
Output: 11 West

Approach: The given problem can be solved by traversing the given array and keep the track of the direction and the distance traveled in the direction North(N), South(S), East(E), and West(W). Follow the steps below to solve the problem:

• Initialize variables, say N, S, E, and W that stores the distances traversed in the directions North, South, East, and West respectively after given set of movements.
• Initialize a variable, say P as North, that stores the final direction after performing the given set of movements.
• Traverse the given arrays A[] and B[] simultaneously and update the value of distance traverse in all the directions with the current direction.
• Now, the vertical displacement is given by (N – S) and the horizontal displacement is given by (E – S).
• After completing the above steps, print the final displacement as and the final direction stored in P.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach #include using namespace std; // Function to find the displacement// from the origin and direction after// performing the given set of movesvoid finalPosition(char a[], int b[],                   int M){    // Stores the distances travelled    // in the directions North, South,    // East, and West respectively    int n = 0, s = 0, e = 0, w = 0;     // Store the initial    // position of robot    char p = 'N';     // Traverse the array B[]    for (int i = 0; i < M; i++) {         // If the current        // direction is North        if (p == 'N') {             if (a[i] == 'U') {                p = 'N';                n = n + b[i];            }            else if (a[i] == 'D') {                p = 'S';                s = s + b[i];            }            else if (a[i] == 'R') {                p = 'E';                e = e + b[i];            }            else if (a[i] == 'L') {                p = 'W';                w = w + b[i];            }        }         // If the current        // direction is South        else if (p == 'S') {            if (a[i] == 'U') {                p = 'S';                s = s + b[i];            }            else if (a[i] == 'D') {                p = 'N';                n = n + b[i];            }            else if (a[i] == 'R') {                p = 'W';                w = w + b[i];            }            else if (a[i] == 'L') {                p = 'E';                e = e + b[i];            }        }         // If the current        // direction is East        else if (p == 'E') {            if (a[i] == 'U') {                p = 'E';                e = e + b[i];            }            else if (a[i] == 'D') {                p = 'W';                w = w + b[i];            }            else if (a[i] == 'R') {                p = 'S';                s = s + b[i];            }            else if (a[i] == 'L') {                p = 'N';                n = n + b[i];            }        }         // If the current        // direction is West        else if (p == 'W') {            if (a[i] == 'U') {                p = 'W';                w = w + b[i];            }            else if (a[i] == 'D') {                p = 'E';                e = e + b[i];            }            else if (a[i] == 'R') {                p = 'N';                n = n + b[i];            }            else if (a[i] == 'L') {                p = 'S';                s = s + b[i];            }        }    }     // Stores the total    // vertical displacement    int ver_disp = n - s;     // Stores the total    // horizontal displacement    int hor_disp = e - w;     // Find the displacement    int displacement = floor(        sqrt((ver_disp * ver_disp)             + (hor_disp * hor_disp)));     // Print the displacement and    // direction after N moves    cout << displacement << " " << p;} // Driver Codeint main(){    char A[] = { 'U', 'R', 'R', 'R', 'R' };    int B[] = { 1, 1, 1, 1, 0 };      int N = sizeof(A) / sizeof(B);     finalPosition(A, B, N);     return 0;}

## Java

 // Java program for the above approachclass GFG{ // Function to find the displacement// from the origin and direction after// performing the given set of movesstatic void finalPosition(char[] a, int[] b, int M){         // Stores the distances travelled    // in the directions North, South,    // East, and West respectively    int n = 0, s = 0, e = 0, w = 0;     // Store the initial    // position of robot    char p = 'N';     // Traverse the array B[]    for(int i = 0; i < M; i++)    {                 // If the current        // direction is North        if (p == 'N')        {            if (a[i] == 'U')            {                p = 'N';                n = n + b[i];            }            else if (a[i] == 'D')            {                p = 'S';                s = s + b[i];            }            else if (a[i] == 'R')            {                p = 'E';                e = e + b[i];            }            else if (a[i] == 'L')            {                p = 'W';                w = w + b[i];            }        }         // If the current        // direction is South        else if (p == 'S')        {            if (a[i] == 'U')            {                p = 'S';                s = s + b[i];            }            else if (a[i] == 'D')            {                p = 'N';                n = n + b[i];            }            else if (a[i] == 'R')            {                p = 'W';                w = w + b[i];            }            else if (a[i] == 'L')            {                p = 'E';                e = e + b[i];            }        }         // If the current        // direction is East        else if (p == 'E')        {            if (a[i] == 'U')            {                p = 'E';                e = e + b[i];            }            else if (a[i] == 'D')            {                p = 'W';                w = w + b[i];            }            else if (a[i] == 'R')            {                p = 'S';                s = s + b[i];            }            else if (a[i] == 'L')            {                p = 'N';                n = n + b[i];            }        }         // If the current        // direction is West        else if (p == 'W')        {            if (a[i] == 'U')            {                p = 'W';                w = w + b[i];            }            else if (a[i] == 'D')            {                p = 'E';                e = e + b[i];            }            else if (a[i] == 'R')            {                p = 'N';                n = n + b[i];            }            else if (a[i] == 'L')            {                p = 'S';                s = s + b[i];            }        }    }     // Stores the total    // vertical displacement    int ver_disp = n - s;     // Stores the total    // horizontal displacement    int hor_disp = e - w;     // Find the displacement    int displacement = (int)Math.ceil(Math.sqrt(        (ver_disp * ver_disp) + (hor_disp * hor_disp)));     // Print the displacement and    // direction after N moves    System.out.print(displacement + " " + p);} // Driver Codepublic static void main(String args[]){    char[] A = { 'U', 'R', 'R', 'R', 'R' };    int[] B = { 1, 1, 1, 1, 0 };    int N = 1;         finalPosition(A, B, N);}} // This code is contributed by abhinavjain194

## Python3

 # Python3 program for the above approachfrom math import sqrt, floor # Function to find the displacement# from the origin and direction after# performing the given set of movesdef finalPosition(a, b, M):         # Stores the distances travelled    # in the directions North, South,    # East, and West respectively    n = 0    s = 0    e = 0    w = 0     # Store the initial    # position of robot    p = 'N'     # Traverse the array B[]    for i in range(M):                 # If the current        # direction is North        if (p == 'N'):            if (a[i] == 'U'):                p = 'N'                n = n + b[i]            elif (a[i] == 'D'):                p = 'S'                s = s + b[i]            elif (a[i] == 'R'):                p = 'E'                e = e + b[i]            elif (a[i] == 'L'):                p = 'W'                w = w + b[i]         # If the current        # direction is South        elif (p == 'S'):            if (a[i] == 'U'):                p = 'S'                s = s + b[i]            elif(a[i] == 'D'):                p = 'N'                n = n + b[i]            elif(a[i] == 'R'):                p = 'W'                w = w + b[i]            elif(a[i] == 'L'):                p = 'E'                e = e + b[i]         # If the current        # direction is East        elif(p == 'E'):            if (a[i] == 'U'):                p = 'E'                e = e + b[i]            elif (a[i] == 'D'):                p = 'W'                w = w + b[i]            elif (a[i] == 'R'):                p = 'S'                s = s + b[i]            elif (a[i] == 'L'):                p = 'N'                n = n + b[i]         # If the current        # direction is West        elif (p == 'W'):            if (a[i] == 'U'):                p = 'W'                w = w + b[i]            elif (a[i] == 'D'):                p = 'E'                e = e + b[i]            elif (a[i] == 'R'):                p = 'N'                n = n + b[i]            elif (a[i] == 'L'):                p = 'S'                s = s + b[i]     # Stores the total    # vertical displacement    ver_disp = n - s     # Stores the total    # horizontal displacement    hor_disp = e - w     # Find the displacement    displacement = floor(sqrt((ver_disp * ver_disp) +                              (hor_disp * hor_disp)) + 1)     # Print the displacement and    # direction after N moves    print(displacement,p) # Driver Codeif __name__ == '__main__':         A = [ 'U', 'R', 'R', 'R', 'R' ]    B = [ 1, 1, 1, 1, 0 ]    N = len(A)         finalPosition(A, B, N) # This code is contributed by ipg2016107

## C#

 // C# program for the above approachusing System; class GFG{ // Function to find the displacement// from the origin and direction after// performing the given set of movesstatic void finalPosition(char[] a, int[] b, int M){         // Stores the distances travelled    // in the directions North, South,    // East, and West respectively    int n = 0, s = 0, e = 0, w = 0;     // Store the initial    // position of robot    char p = 'N';     // Traverse the array B[]    for(int i = 0; i < M; i++)    {                 // If the current        // direction is North        if (p == 'N')        {            if (a[i] == 'U')            {                p = 'N';                n = n + b[i];            }            else if (a[i] == 'D')            {                p = 'S';                s = s + b[i];            }            else if (a[i] == 'R')            {                p = 'E';                e = e + b[i];            }            else if (a[i] == 'L')            {                p = 'W';                w = w + b[i];            }        }         // If the current        // direction is South        else if (p == 'S')        {            if (a[i] == 'U')            {                p = 'S';                s = s + b[i];            }            else if (a[i] == 'D')            {                p = 'N';                n = n + b[i];            }            else if (a[i] == 'R')            {                p = 'W';                w = w + b[i];            }            else if (a[i] == 'L')            {                p = 'E';                e = e + b[i];            }        }         // If the current        // direction is East        else if (p == 'E')        {            if (a[i] == 'U')            {                p = 'E';                e = e + b[i];            }            else if (a[i] == 'D')            {                p = 'W';                w = w + b[i];            }            else if (a[i] == 'R')            {                p = 'S';                s = s + b[i];            }            else if (a[i] == 'L')            {                p = 'N';                n = n + b[i];            }        }         // If the current        // direction is West        else if (p == 'W')        {            if (a[i] == 'U')            {                p = 'W';                w = w + b[i];            }            else if (a[i] == 'D')            {                p = 'E';                e = e + b[i];            }            else if (a[i] == 'R')            {                p = 'N';                n = n + b[i];            }            else if (a[i] == 'L')            {                p = 'S';                s = s + b[i];            }        }    }     // Stores the total    // vertical displacement    int ver_disp = n - s;     // Stores the total    // horizontal displacement    int hor_disp = e - w;     // Find the displacement    int displacement = (int)Math.Ceiling(Math.Sqrt(        (ver_disp * ver_disp) + (hor_disp * hor_disp)));     // Print the displacement and    // direction after N moves    Console.WriteLine(displacement + " " + p);} // Driver Codepublic static void Main(){    char[] A = { 'U', 'R', 'R', 'R', 'R' };    int[] B = { 1, 1, 1, 1, 0 };    int N = 1;         finalPosition(A, B, N);}} // This code is contributed by ukasp

## Javascript

 
Output:
1 N

Time Complexity: O(N)
Auxiliary Space: O(1)

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