Minimize steps defined by a string required to reach the destination from a given source

Given a string str and four integers X₁, Y₁, X₂ and Y₂, where (X₁, Y₁) denotes the source coordinates and (X₂, Y₂) denotes the coordinates of the destination. Given a string str, the task is to find the minimum number of steps of the following four types required to reach destination from the source:  

• If str[i] = ‘E’: Convert (X₁, Y₁) to (X₁ + 1, Y₁).
• If str[i] = ‘W’: Convert (X₁, Y₁) to (X₁ – 1, Y₁).
• If str[i] = ‘N’: Convert (X₁, Y₁) to (X₁, Y₁ + 1).
• If str[i] = ‘S’: Convert (X₁, Ysub>1) to (X₁, Y₁ – 1).

If the destination cannot be reached, print -1. 
Note: It is not necessary to use str[i] always and can be skipped. But skipped characters will add to the steps used. 

Examples

Input: str = “SESNW”, x1 = 0, y1 = 0, x2 = 1, y2 = 1 
Output: 4 
Explanation:
To move from (0, 0) to (1, 1), it requires one ‘E’ and one ‘N’. 
Therefore, the path defined by the substring “SESN” ensures that the destination is reached {(0, 0) -> skip S -> E(1, 0) -> skip S -> (1, 1)}. 
Therefore, the minimum length of the string traversed is 4. 

Input: str = “NNNNNNNN”, x1 = 1, y1 = 1, x2 = 1, y2 = 2 
Output: 1 
Explanation:
From current position (1, 1) it can move to co-ordinate (1, 2) using first ‘N’ direction. 
Therefore, the minimum length of the string traverse is 1. 

Approach: The idea is to iterate through the string and perform the moves until the destination is reached. Below are the steps:

1. Initialize four variable pos1, pos2, pos3 and pos4 to store the positions of E, W, N, S respectively.
2. Now, check if (x1, y1) is equal to (x2, y2) then the current position is already the destination so print 0.
3. Otherwise, iterate over the string and check the following four conditions: 
   • If x2 > x1 then iterate until a ‘E’ comes and update that index in pos1.
   • If x2 < x1 then iterate until a ‘W’ comes and update that index in pos2.
   • If y2 > y1 then iterate until a ‘N’ comes and update that index in pos3.
   • If y2 < y1 then iterate until a ‘S’ comes and update that index in pos4.
4. After performing above operations check if x1 != x2 and y1 != y2 then print “-1” that means it is impossible to reach the destination.
5. Otherwise, find the max of pos1, pos2, pos3 and pos4 and print it.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the minimum length
// of string required to reach from
// source to destination
void minimum_length(int x1, int y1,
                    int x2, int y2,
                    string str)
{
    // Size of the string
    int n = str.size();

    // Stores the index of the four
    // directions E, W, N, S
    int pos1, pos2, pos3, pos4;
    pos1 = -1;
    pos2 = -1;
    pos3 = -1;
    pos4 = -1;

    // If destination reached
    if (x1 == x2 && y1 == y2) {
        cout << 0 << endl;
    }

    // Iterate over the string
    else {
        for (int i = 0; i < n; i++) {

            // Move east
            if (x2 > x1) {

                // Change x1 according
                // to direction E
                if (str[i] == 'E') {
                    x1 = x1 + 1;
                    if (x1 == x2) {
                        pos1 = i;
                    }
                }
            }

            // Move west
            if (x2 < x1) {

                // Change x1 according
                // to direction W
                if (str[i] == 'W') {
                    x1 = x1 - 1;
                    if (x1 == x2) {
                        pos2 = i;
                    }
                }
            }

            // Move north
            if (y2 > y1) {

                // Change y1 according
                // to direction N
                if (str[i] == 'N') {
                    y1 = y1 + 1;
                    if (y1 == y2) {
                        pos3 = i;
                    }
                }
            }

            // Move south
            if (y2 < y1) {

                // Change y1 according
                // to direction S
                if (str[i] == 'S') {
                    y1 = y1 - 1;
                    if (y1 == y2) {
                        pos4 = i;
                    }
                }
            }
        }

        int z;
        // Store the max of all positions
        z = max(max(max(pos1, pos2),
                    pos3),
                pos4);

        // Print the minimum length of
        // string required
        if (x1 == x2 && y1 == y2) {
            cout << z + 1 << endl;
        }

        // Otherwise, it is impossible
        else {
            cout << "-1" << endl;
        }
    }
}

// Driver Code
int main()
{
    // Given string
    string str = "SESNW";

    // Given source and destination
    int x1 = 0, x2 = 1, y1 = 0, y2 = 1;

    // Function Call
    minimum_length(x1, y1, x2, y2, str);
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
import java.lang.*;
import java.io.*;

class GFG{

// Function to find the minimum length
// of string required to reach from
// source to destination
static void minimum_length(int x1, int y1,
                           int x2, int y2,
                           String str)
{

    // Size of the string
    int n = str.length();

    // Stores the index of the four
    // directions E, W, N, S
    int pos1, pos2, pos3, pos4;
    pos1 = -1;
    pos2 = -1;
    pos3 = -1;
    pos4 = -1;

    // If destination reached
    if (x1 == x2 && y1 == y2)
    {
        System.out.println("0");
    }

    // Iterate over the string
    else
    {
        for(int i = 0; i < n; i++)
        {

            // Move east
            if (x2 > x1)
            {

                // Change x1 according
                // to direction E
                if (str.charAt(i) == 'E')
                {
                    x1 = x1 + 1;

                    if (x1 == x2)
                    {
                        pos1 = i;
                    }
                }
            }

            // Move west
            if (x2 < x1)
            {

                // Change x1 according
                // to direction W
                if (str.charAt(i) == 'W')
                {
                    x1 = x1 - 1;

                    if (x1 == x2)
                    {
                        pos2 = i;
                    }
                }
            }

            // Move north
            if (y2 > y1)
            {

                // Change y1 according
                // to direction N
                if (str.charAt(i) == 'N')
                {
                    y1 = y1 + 1;

                    if (y1 == y2)
                    {
                        pos3 = i;
                    }
                }
            }

            // Move south
            if (y2 < y1)
            {

                // Change y1 according
                // to direction S
                if (str.charAt(i) == 'S')
                {
                    y1 = y1 - 1;

                    if (y1 == y2)
                    {
                        pos4 = i;
                    }
                }
            }
        }
        int z;

        // Store the max of all positions
        z = Math.max(pos1,
            Math.max(Math.max(pos2, pos3),
                              pos4));

        // Print the minimum length of
        // string required
        if (x1 == x2 && y1 == y2)
        {
             System.out.println(z + 1);
        }

        // Otherwise, it is impossible
        else
        {
             System.out.println("-1");
        }
    }
}

// Driver Code
public static void main (String[] args)
throws java.lang.Exception
{

    // Given string
    String str = "SESNW";

    // Given source and destination
    int x1 = 0, x2 = 1, y1 = 0, y2 = 1;

    // Function call
    minimum_length(x1, y1, x2, y2, str);
}
}

// This code is contributed by bikram2001jha

Python3

# Python3 program for the above approach

# Function to find the minimum length
# of string required to reach from
# source to destination
def minimum_length(x1, y1, x2, y2, str):

    # Size of the string
    n = len(str)

    # Stores the index of the four
    # directions E, W, N, S
    pos1 = -1
    pos2 = -1
    pos3 = -1
    pos4 = -1

    # If destination reached
    if (x1 == x2 and y1 == y2):
        print("0")

    # Iterate over the string
    else:
        for i in range(n):

            # Move east
            if (x2 > x1):

                # Change x1 according
                # to direction E
                if (str[i] == 'E'):
                    x1 = x1 + 1

                    if (x1 == x2):
                        pos1 = i

            # Move west
            if (x2 < x1):

                # Change x1 according
                # to direction W
                if (str[i] == 'W'):
                    x1 = x1 - 1

                    if (x1 == x2):
                        pos2 = i

            # Move north
            if (y2 > y1):

                # Change y1 according
                # to direction N
                if (str[i] == 'N'):
                    y1 = y1 + 1

                    if (y1 == y2):
                        pos3 = i

            # Move south
            if (y2 < y1):

                # Change y1 according
                # to direction S
                if (str[i] == 'S'):
                    y1 = y1 - 1

                    if (y1 == y2):
                        pos4 = i

        z = 0

        # Store the max of all positions
        z = max(pos1, max(max(pos2, pos3), pos4))

        # Print the minimum length of
        # string required
        if (x1 == x2 and y1 == y2):
            print(z + 1)

        # Otherwise, it is impossible
        else:
            print("-1")

# Driver Code

# Given string
str = "SESNW"

# Given source and destination
x1 = 0
x2 = 1
y1 = 0
y2 = 1

# Function call
minimum_length(x1, y1, x2, y2, str)

# This code is contributed by Amit Katiyar

C#

// C# program for the above approach
using System;

class GFG{

// Function to find the minimum length
// of string required to reach from
// source to destination
static void minimum_length(int x1, int y1,
                           int x2, int y2,
                           string str)
{

    // Size of the string
    int n = str.Length;

    // Stores the index of the four
    // directions E, W, N, S
    int pos1, pos2, pos3, pos4;
    pos1 = -1;
    pos2 = -1;
    pos3 = -1;
    pos4 = -1;

    // If destination reached
    if (x1 == x2 && y1 == y2)
    {
        Console.WriteLine("0");
    }

    // Iterate over the string
    else
    {
        for(int i = 0; i < n; i++)
        {

            // Move east
            if (x2 > x1)
            {

                // Change x1 according
                // to direction E
                if (str[i] == 'E')
                {
                    x1 = x1 + 1;

                    if (x1 == x2)
                    {
                        pos1 = i;
                    }
                }
            }

            // Move west
            if (x2 < x1)
            {

                // Change x1 according
                // to direction W
                if (str[i] == 'W')
                {
                    x1 = x1 - 1;

                    if (x1 == x2)
                    {
                        pos2 = i;
                    }
                }
            }

            // Move north
            if (y2 > y1)
            {

                // Change y1 according
                // to direction N
                if (str[i] == 'N')
                {
                    y1 = y1 + 1;

                    if (y1 == y2)
                    {
                        pos3 = i;
                    }
                }
            }

            // Move south
            if (y2 < y1)
            {

                // Change y1 according
                // to direction S
                if (str[i] == 'S')
                {
                    y1 = y1 - 1;

                    if (y1 == y2)
                    {
                        pos4 = i;
                    }
                }
            }
        }
        int z;

        // Store the max of all positions
        z = Math.Max(pos1,
            Math.Max(Math.Max(pos2, pos3),
                              pos4));

        // Print the minimum length of
        // string required
        if (x1 == x2 && y1 == y2)
        {
             Console.WriteLine(z + 1);
        }

        // Otherwise, it is impossible
        else
        {
             Console.WriteLine("-1");
        }
    }
}

// Driver Code
public static void Main ()
{

    // Given string
    string str = "SESNW";

    // Given source and destination
    int x1 = 0, x2 = 1, y1 = 0, y2 = 1;

    // Function call
    minimum_length(x1, y1, x2, y2, str);
}
}

// This code is contributed by sanjoy_62

Javascript

<script>

// Javascript program for the above approach

// Function to find the minimum length
// of string required to reach from
// source to destination
function minimum_length(x1, y1,
                    x2,  y2,
                     str)
{

    // Size of the string
    var n = str.length;

    // Stores the index of the four
    // directions E, W, N, S
    var pos1, pos2, pos3, pos4;
    pos1 = -1;
    pos2 = -1;
    pos3 = -1;
    pos4 = -1;

    // If destination reached
    if (x1 == x2 && y1 == y2) {
        document.write(0+"<br>");
    }

    // Iterate over the string
    else {
        for (var i = 0; i < n; i++) {

            // Move east
            if (x2 > x1) {

                // Change x1 according
                // to direction E
                if (str[i] == 'E') {
                    x1 = x1 + 1;
                    if (x1 == x2) {
                        pos1 = i;
                    }
                }
            }

            // Move west
            if (x2 < x1) {

                // Change x1 according
                // to direction W
                if (str[i] == 'W') {
                    x1 = x1 - 1;
                    if (x1 == x2) {
                        pos2 = i;
                    }
                }
            }

            // Move north
            if (y2 > y1) {

                // Change y1 according
                // to direction N
                if (str[i] == 'N')
                {
                    y1 = y1 + 1;
                    if (y1 == y2)
                    {
                        pos3 = i;
                    }
                }
            }

            // Move south
            if (y2 < y1) {

                // Change y1 according
                // to direction S
                if (str[i] == 'S') {
                    y1 = y1 - 1;
                    if (y1 == y2) {
                        pos4 = i;
                    }
                }
            }
        }
        var z;

        // Store the max of all positions
        z = Math.max(Math.max(Math.max(pos1, pos2),
                    pos3),
                pos4);

        // Print the minimum length of
        // string required
        if (x1 == x2 && y1 == y2) {
            document.write(z + 1 + "<br>" );
        }

        // Otherwise, it is impossible
        else {
            document.write("-1<br>");;
        }
    }
}

// Driver Code

// Given string
var str = "SESNW";

// Given source and destination
var x1 = 0, x2 = 1, y1 = 0, y2 = 1;

// Function Call
minimum_length(x1, y1, x2, y2, str);

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

Output:

4

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