problemeasyalgorithmsleetcode-1496leetcode 1496leetcode1496

Path Crossing

EasyUpdated: Aug 2, 2025
Practice on:
LeetCode

Problem

Given a string path, where path[i] = 'N', 'S', 'E' or 'W', each representing moving one unit north, south, east, or west, respectively. You start at the origin (0, 0) on a 2D plane and walk on the path specified by path.

Return true if the path crosses itself at any point, that is, if at any time you are on a location you have previously visited. Return false otherwise.

Examples

Example 1


![](https://assets.leetcode.com/uploads/2020/06/10/screen-
shot-2020-06-10-at-123929-pm.png)

Input: path = "NES"
Output: false 
Explanation: Notice that the path doesn't cross any point more than once.

Example 2


![](https://assets.leetcode.com/uploads/2020/06/10/screen-
shot-2020-06-10-at-123843-pm.png)

Input: path = "NESWW"
Output: true
Explanation: Notice that the path visits the origin twice.

Constraints

  • 1 <= path.length <= 10^4
  • path[i] is either 'N', 'S', 'E', or 'W'.

Solution

Method 1 - Hash Set for Visited Positions

Intuition

We simulate the walk on the 2D grid, keeping track of all visited positions in a set. If we ever visit a position we've already seen, the path crosses itself.

Approach

  1. Start at (0, 0) and add it to a set.
  2. For each character in path, move in the corresponding direction and check if the new position is already in the set.
  3. If yes, return true. If we finish the path without revisiting any position, return false.

Code

C++
#include <unordered_set>
#include <string>
using namespace std;
bool isPathCrossing(string path) {
    unordered_set<long long> seen;
    int x = 0, y = 0;
    seen.insert(0);
    for (char c : path) {
        if (c == 'N') ++y;
        else if (c == 'S') --y;
        else if (c == 'E') ++x;
        else if (c == 'W') --x;
        long long key = ((long long)x << 32) | (y & 0xffffffffLL);
        if (seen.count(key)) return true;
        seen.insert(key);
    }
    return false;
}
Go
func isPathCrossing(path string) bool {
    seen := map[[2]int]bool{}
    x, y := 0, 0
    seen[[2]int{x, y}] = true
    for _, c := range path {
        switch c {
        case 'N': y++
        case 'S': y--
        case 'E': x++
        case 'W': x--
        }
        pos := [2]int{x, y}
        if seen[pos] { return true }
        seen[pos] = true
    }
    return false
}
Java
import java.util.*;
class Solution {
    public boolean isPathCrossing(String path) {
        Set<String> seen = new HashSet<>();
        int x = 0, y = 0;
        seen.add("0,0");
        for (char c : path.toCharArray()) {
            if (c == 'N') y++;
            else if (c == 'S') y--;
            else if (c == 'E') x++;
            else if (c == 'W') x--;
            String key = x + "," + y;
            if (seen.contains(key)) return true;
            seen.add(key);
        }
        return false;
    }
}
Kotlin
fun isPathCrossing(path: String): Boolean {
    val seen = mutableSetOf<Pair<Int, Int>>()
    var x = 0; var y = 0
    seen.add(0 to 0)
    for (c in path) {
        when (c) {
            'N' -> y++
            'S' -> y--
            'E' -> x++
            'W' -> x--
        }
        val pos = x to y
        if (!seen.add(pos)) return true
    }
    return false
}
Python
def isPathCrossing(path: str) -> bool:
    seen = set()
    x = y = 0
    seen.add((0, 0))
    for c in path:
        if c == 'N': y += 1
        elif c == 'S': y -= 1
        elif c == 'E': x += 1
        elif c == 'W': x -= 1
        if (x, y) in seen:
            return True
        seen.add((x, y))
    return False
Rust
use std::collections::HashSet;
pub fn is_path_crossing(path: String) -> bool {
    let mut seen = HashSet::new();
    let (mut x, mut y) = (0, 0);
    seen.insert((x, y));
    for c in path.chars() {
        match c {
            'N' => y += 1,
            'S' => y -= 1,
            'E' => x += 1,
            'W' => x -= 1,
            _ => {}
        }
        if !seen.insert((x, y)) { return true; }
    }
    false
}
TypeScript
function isPathCrossing(path: string): boolean {
    const seen = new Set<string>();
    let x = 0, y = 0;
    seen.add('0,0');
    for (const c of path) {
        if (c === 'N') y++;
        else if (c === 'S') y--;
        else if (c === 'E') x++;
        else if (c === 'W') x--;
        const key = `${x},${y}`;
        if (seen.has(key)) return true;
        seen.add(key);
    }
    return false;
}

Complexity

  • ⏰ Time complexity: O(n), where n is the length of the path.
  • 🧺 Space complexity: O(n) for the set of visited positions.

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