3694 - Distinct Points Reachable After Substring Removal.

Medium

You are given a string s consisting of characters 'U', 'D', 'L', and 'R', representing moves on an infinite 2D Cartesian grid.

• 'U': Move from (x, y) to (x, y + 1).

• 'D': Move from (x, y) to (x, y - 1).

• 'L': Move from (x, y) to (x - 1, y).

• 'R': Move from (x, y) to (x + 1, y).

You are also given a positive integer k.

You must choose and remove exactly one contiguous substring of length k from s. Then, start from coordinate (0, 0) and perform the remaining moves in order.

Return an integer denoting the number of distinct final coordinates reachable.

Example 1:

Input: s = "LUL", k = 1

Output: 2

Explanation:

After removing a substring of length 1, s can be "UL", "LL" or "LU". Following these moves, the final coordinates will be (-1, 1), (-2, 0) and (-1, 1) respectively. There are two distinct points (-1, 1) and (-2, 0) so the answer is 2.

Example 2:

Input: s = "UDLR", k = 4

Output: 1

Explanation:

After removing a substring of length 4, s can only be the empty string. The final coordinates will be (0, 0). There is only one distinct point (0, 0) so the answer is 1.

Example 3:

Input: s = "UU", k = 1

Output: 1

Explanation:

After removing a substring of length 1, s becomes "U", which always ends at (0, 1), so there is only one distinct final coordinate.

Constraints:

• <code>1 <= s.length <= 10⁵</code>

• s consists of only 'U', 'D', 'L', and 'R'.

• 1 <= k <= s.length