Count Island Shapes up to Translation Only

### Problem Land cells equal one and connect only through shared edges. Two islands have the same shape exactly when translating one set of cells makes it equal the other; rotations and reflections do not count as equivalent. Return the number of distinct island shapes. ```cpp class Solution { public: int numDistinctIslands(vector<vector<int>>& grid); }; ``` ### Examples **Example 1:** ```text grid = [[1,1,0,1,1],[1,0,0,1,0]] Output: 1 Explanation: The two L shapes differ only by translation. ``` **Example 2:** ```text grid = [[1,1,0,0],[0,0,0,1],[0,0,0,1]] Output: 2 Explanation: Horizontal and vertical two-cell islands are rotations, not translations. ``` ### Constraints - The binary grid has m rows and n columns, each dimension in 1..50; every row contains n entries. ### Clarifying Questions Normalize translation without normalizing rotation or reflection, and keep four-direction connectivity. ```hint Read the boundary condition What coordinate offset cancels an island's absolute location while keeping its orientation? ``` ### Contract considerations Normalize translation without normalizing rotation or reflection, and keep four-direction connectivity.