Rust solution
Intuition

The problem requires calculating the maximum possible distance based on movements represented by a string of directions. We are allowed to make up to
# Intuition
<!-- Describe your first thoughts on how to solve this problem. -->
*   The problem requires calculating the maximum possible distance based on movements represented by a string of directions. We are allowed to make up to k changes to the directions in order to maximize the distance. The challenge is to track the effects of each direction and compute the maximum distance efficiently.

*   We need to handle directions ('N', 'S', 'E', 'W') and determine how we can strategically modify them (if needed) within the constraint of k changes to maximize the distance.

# Approach
<!-- Describe your approach to solving the problem. -->
*   Initial Setup: Track counts of each direction: North (n), South (s_count), East (e), and West (w).
*   Iterate Through Directions: Traverse through each character in the string and update the corresponding direction count.
*   Calculate Maximum Distance: For each new direction, compute the potential maximum distance by applying the current direction counts and modifying some of the directions if k changes are allowed. The formula used checks different combinations of directions with adjustments allowed by k.
*   Track the Maximum Distance: After each character update, update the maximum possible distance using the formula.
*   Final Result: The final max will contain the maximum distance that can be achieved by making the allowed changes.

# Complexity
- Time complexity: O(n)
<!-- Add your time complexity here, e.g. $$O(n)$$ -->

- Space complexity: O(1)
<!-- Add your space complexity here, e.g. $$O(n)$$ -->

# Code
```rust []
impl Solution {
    pub fn max_distance(s: String, k: i32) -> i32 {
        let mut n = 0;
        let mut s_count = 0;
        let mut e = 0;
        let mut w = 0;
        let mut max = 0;

        for c in s.chars() {
            match c {
                'N' => n += 1,
                'S' => s_count += 1,
                'E' => e += 1,
                'W' => w += 1,
                _ => (),
            }

            max = max.max(n + e - w - s_count + 2 * std::cmp::min(s_count + w, k));
            max = max.max(n + w - s_count - e + 2 * std::cmp::min(s_count + e, k));
            max = max.max(s_count + e - n - w + 2 * std::cmp::min(n + w, k));
            max = max.max(s_count + w - n - e + 2 * std::cmp::min(n + e, k));
        }

        max
    }
}

```
['Hash Table', 'Math', 'String', 'Counting', 'Rust']