Find the Fewest Grid Moves Needed to Collect Every Key

### Problem In `grid`, `@` is the single start, `.` is empty floor, and `#` is a wall. Lowercase letters are keys and their uppercase versions are locks. Move one cell north, south, east or west without crossing the boundary or a wall. Enter a lock only after obtaining its key; keys are retained. For some `1 <= k <= 6`, the grid contains exactly one key and one lock for each of the first k alphabet letters. Return the fewest moves needed to acquire every key, or `-1` when impossible. Opening every lock is not required. ```cpp class Solution { public: int shortestPathAllKeys(vector<string>& grid); }; ``` ### Examples **Example 1:** ```text Input: grid = ["@.aA"] Output: 2 Explanation: Two rightward moves acquire a; entering A is unnecessary. ``` **Example 2:** ```text Input: grid = ["@#a","A##","..."] Output: -1 Explanation: Both possible exits from the start are blocked, so the key cannot be reached. ``` ### Constraints - `m == grid.length`, `n == grid[i].length`, and `1 <= m,n <= 30`. - Cells contain English letters, `.`, `#`, or `@`, with exactly one `@`. - There are `1` to `6` unique keys, each with one matching lock, using the first k alphabet letters. ### Contract considerations Keys and locks use the contiguous letters a through the kth letter. Keys are not consumed by locks, and the starting cell counts as zero moves. ```hint Read the boundary condition Two visits to one cell can have different futures if their key sets differ. ``` ### Boundary reminders Keys and locks use the contiguous letters a through the kth letter. Keys are not consumed by locks, and the starting cell counts as zero moves.