Implement a Duplicate-Aware Layered Skip List

### Problem Implement Skiplist yourself without using built-in libraries. It maintains a sorted multiset through linked-list layers. search(target) reports membership; add(num) inserts one occurrence; erase(num) removes one occurrence and reports success, or returns false without a change if absent. Duplicate values are allowed. Preserve the source average O(log(n)) operation and O(n) space goals. ```cpp class Skiplist { public: Skiplist(); bool search(int target); void add(int num); bool erase(int num); }; ``` ### Examples **Example 1:** ```text Input: construct Skiplist(); add(5); add(5); erase(5); search(5); erase(5); search(5) Output: erase results true,true; search results true,false Explanation: Each successful erase removes only one of the two copies. ``` **Example 2:** ```text Input: construct Skiplist(); erase(0); add(0); search(0); erase(1) Output: false,true,false Explanation: Erasing an absent value leaves the structure unchanged, and0 is a permitted value. ``` ### Constraints - num and target are integers in `[0,20000]`. - At most 50000 total calls are made to search, add and erase. - Duplicates are allowed. - The source calls for a manually implemented skip list with average logarithmic operations and linear space; no unsupported execution or randomness guarantee is asserted here. ### Contract considerations Keep the constructor and search/add/erase methods. All nodes, links, predecessor searches and updates are hand-written. No map, set or library skip-list implementation substitutes for the required structure. ```hint Read the boundary condition If two equal values were added, should one successful erase necessarily make search return false? ``` ### Boundary reminders Keep the constructor and search/add/erase methods. All nodes, links, predecessor searches and updates are hand-written. No map, set or library skip-list implementation substitutes for the required structure.