# Check if a sequence of path visits any coordinate twice or not

Given string str of length N only consisting of characters ‘N’, ‘S’, ‘E’, or ‘W’, each representing moving one unit North, South, East, or West, respectively. A man starts at the origin (0, 0) on a 2D plane and walks according to the directions in the string. The task is to check whether the man crosses any coordinate in his walk, which he has already visited or not. If found to be true, then print “Crossed”. Otherwise, print “Not Crossed”.

Examples:

Input: str = “NESW”
Output: Crossed
Explanation:
The path for the man is given by:
(0, 0) -> (0, 1) -> (1, 1) -> (0, 1) -> (0, 0).
Since, the coordinate (0, 0) is visited again.
Therefore, print Crossed as he has crossed the path.

Input: str = “SESS”
Output: Not Crossed
Explanation:
The path for the man is given by:
(0, 0) -> (0, -1) -> (1, -1) -> (1, -2) -> (1, -3).
From the above path, the man never visited the same coordinate again.
Therefore, print Not Crossed.

Approach: The idea is to maintain a Set for the co-ordinates encountered to check whether already visited co-ordinates occurs or not. Below are the steps:

1. Initialize two variables X and Y and initiate the values as zero. These variables will represent x and y coordinates.
2. Insert X and Y in the set.
3. Iterate a loop over the range [0, N), and increment the X or Y coordinate as per the below condition:
• If the character is ‘N’, then increment Y by 1.
• If the character is ‘S’, then decrement Y by 1.
• If the character is ‘E’, then increment X by 1.
• If the character is ‘W’, then decrement X by 1.
4. Insert the updated X and Y coordinates in the above step for each character in the set.
5. While inserting the co-ordinates in the above step if any present co-ordinates are encountered then print Crossed.
6. Otherwise, print Not Crossed as all the points of co-ordinates are unique.

Below is the implementation of the above approach

## C++

 `// C++ program for the above appproach`   `#include ` `using` `namespace` `std;`   `// Function to check if the man crosses` `// previous visited coordinate or not` `bool` `isCrossed(string path)` `{` `    ``if` `(path.size() == 0)` `        ``return` `false``;`   `    ``// Stores the count of` `    ``// crossed vertex` `    ``bool` `ans = ``false``;`   `    ``// Stores (x, y) coordinates` `    ``set > set;`   `    ``// The coordinates for the origin` `    ``int` `x = 0, y = 0;` `    ``set.insert({ x, y });`   `    ``// Iterate over the string` `    ``for` `(``int` `i = 0; i < path.size(); i++) {`   `        ``// Condition to increment X or` `        ``// Y co-ordinates respectively` `        ``if` `(path[i] == ``'N'``)` `            ``set.insert({ x, y++ });`   `        ``if` `(path[i] == ``'S'``)` `            ``set.insert({ x, y-- });`   `        ``if` `(path[i] == ``'E'``)` `            ``set.insert({ x++, y });`   `        ``if` `(path[i] == ``'W'``)` `            ``set.insert({ x--, y });`   `        ``// Check if (x, y) is already` `        ``// visited` `        ``if` `(set.find({ x, y })` `            ``!= set.end()) {`   `            ``ans = ``true``;` `            ``break``;` `        ``}` `    ``}`   `    ``// Print the result` `    ``if` `(ans)` `        ``cout << ``"Crossed"``;` `    ``else` `        ``cout << ``"Not Crossed"``;` `}`   `// Driver Code` `int` `main()` `{` `    ``// Given string` `    ``string path = ``"NESW"``;`   `    ``// Function Call` `    ``isCrossed(path);`   `    ``return` `0;` `}`

## Java

 `// Java program for ` `// the above appproach` `import` `java.awt.Point;` `import` `java.util.HashSet;` `class` `GFG{`   `// Function to check if the man crosses` `// previous visited coordinate or not` `static` `void` `isCrossed(String path)` `{` `  ``if` `(path.length() == ``0``)` `    ``return``;`   `  ``// Stores the count of` `  ``// crossed vertex` `  ``boolean` `ans = ``false``;`   `  ``// Stores (x, y) coordinates` `  ``HashSet set = ` `          ``new` `HashSet();`   `  ``// The coordinates for the origin` `  ``int` `x = ``0``, y = ``0``;` `  ``set.add(``new` `Point(x, y));`   `  ``// Iterate over the String` `  ``for` `(``int` `i = ``0``; i < path.length(); i++) ` `  ``{` `    ``// Condition to increment X or` `    ``// Y co-ordinates respectively` `    ``if` `(path.charAt(i) == ``'N'``)` `      ``set.add(``new` `Point(x, y++));`   `    ``if` `(path.charAt(i) == ``'S'``)` `      ``set.add(``new` `Point(x, y--));`   `    ``if` `(path.charAt(i) == ``'E'``)` `      ``set.add(``new` `Point(x++, y));`   `    ``if` `(path.charAt(i) == ``'W'``)` `      ``set.add(``new` `Point(x--, y));`   `    ``// Check if (x, y) is already` `    ``// visited` `    ``if` `(set.contains(``new` `Point(x, y))) ` `    ``{` `      ``ans = ``true``;` `      ``break``;` `    ``}` `  ``}`   `  ``// Print the result` `  ``if` `(ans)` `    ``System.out.print(``"Crossed"``);` `  ``else` `    ``System.out.print(``"Not Crossed"``);` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `  ``// Given String` `  ``String path = ``"NESW"``;`   `  ``// Function Call` `  ``isCrossed(path);` `}` `}`   `// This code is contributed by Princi Singh`

## Python3

 `# Python3 program for the above appproach`   `# Function to check if the man crosses` `# previous visited coordinate or not` `def` `isCrossed(path):`   `    ``if` `(``len``(path) ``=``=` `0``):` `        ``return` `bool``(``False``)`   `    ``# Stores the count of` `    ``# crossed vertex` `    ``ans ``=` `bool``(``False``)`   `    ``# Stores (x, y) coordinates` `    ``Set` `=` `set``()`   `    ``# The coordinates for the origin` `    ``x, y ``=` `0``, ``0` `    ``Set``.add((x, y))`   `    ``# Iterate over the string` `    ``for` `i ``in` `range``(``len``(path)):`   `        ``# Condition to increment X or` `        ``# Y co-ordinates respectively` `        ``if` `(path[i] ``=``=` `'N'``):` `            ``Set``.add((x, y))` `            ``y ``=` `y ``+` `1`   `        ``if` `(path[i] ``=``=` `'S'``):` `            ``Set``.add((x, y))` `            ``y ``=` `y ``-` `1` `            `  `        ``if` `(path[i] ``=``=` `'E'``):` `            ``Set``.add((x, y))` `            ``x ``=` `x ``+` `1`   `        ``if` `(path[i] ``=``=` `'W'``):` `            ``Set``.add((x, y))` `            ``x ``=` `x ``-` `1` `            `  `        ``# Check if (x, y) is already visited` `        ``if` `(x, y) ``in` `Set``:` `            ``ans ``=` `bool``(``True``)` `            ``break`   `    ``# Print the result` `    ``if` `(ans):` `        ``print``(``"Crossed"``)` `    ``else``:` `        ``print``(``"Not Crossed"``)`   `# Driver code`   `# Given string` `path ``=` `"NESW"`   `# Function call` `isCrossed(path)`   `# This code is contributed by divyeshrabadiya07`

## C#

 `// C# program for the above appproach` `using` `System;` `using` `System.Collections.Generic;`   `class` `GFG{`   `// Function to check if the man crosses` `// previous visited coordinate or not` `static` `void` `isCrossed(String path)` `{` `    ``if` `(path.Length == 0)` `        ``return``;`   `    ``// Stores the count of` `    ``// crossed vertex` `    ``bool` `ans = ``false``;`   `    ``// Stores (x, y) coordinates` `    ``HashSet> mySet = ` `    ``new` `HashSet>();`   `    ``// The coordinates for the origin` `    ``int` `x = 0, y = 0;` `    ``mySet.Add(``new` `KeyValuePair<``int``, ``int``>(x, y));`   `    ``// Iterate over the String` `    ``for``(``int` `i = 0; i < path.Length; i++)` `    ``{` `        `  `        ``// Condition to increment X or` `        ``// Y co-ordinates respectively` `        ``if` `(path[i] == ``'N'``)` `            ``mySet.Add(` `                ``new` `KeyValuePair<``int``, ``int``>(x, y++));`   `        ``if` `(path[i] == ``'S'``)` `            ``mySet.Add(` `                ``new` `KeyValuePair<``int``, ``int``>(x, y--));`   `        ``if` `(path[i] == ``'E'``)` `            ``mySet.Add(` `                ``new` `KeyValuePair<``int``, ``int``>(x++, y));`   `        ``if` `(path[i] == ``'W'``)` `            ``mySet.Add(` `                ``new` `KeyValuePair<``int``, ``int``>(x--, y));`   `        ``// Check if (x, y) is already` `        ``// visited` `        ``if` `(mySet.Contains(` `                ``new` `KeyValuePair<``int``, ``int``>(x, y))) ` `        ``{` `            ``ans = ``true``;` `            ``break``;` `        ``}` `    ``}`   `    ``// Print the result` `    ``if` `(ans)` `        ``Console.Write(``"Crossed"``);` `    ``else` `        ``Console.Write(``"Not Crossed"``);` `}`   `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` `    `  `    ``// Given String` `    ``String path = ``"NESW"``;`   `    ``// Function call` `    ``isCrossed(path);` `}` `}`   `// This code is contributed by akhilsaini`

Output:

```Crossed

```

Time Complexity: O(N*log N)
Auxiliary Space: O(N)

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