What approaches and techniques are used to handle collisions in the Dictionary data structure to ensure correct program operation?

In the data structure Dictionary in C#, the following approaches are usually used to handle collisions:

1. Chaining method — when a collision occurs, all elements with the same hash are stored in a linked list (or another collection) in one array cell. Searching involves traversing this list.

2. Open addressing — when a collision occurs, the next free cell is searched according to a certain sequence (linear probing, quadratic probing, double hashing).

The standard C# Dictionary uses the chaining method, where each array cell contains the index of the first element in a linked list of entries with the same hash. This ensures efficient addition, search, and deletion of elements.

A simplified example:

class DictionaryEntry {
    public int HashCode;
    public string Key;
    public string Value;
    public DictionaryEntry Next; // reference to the next element in case of collision
}

Thus, when adding a new element with a collision, it is added to the linked list of the corresponding cell, and during search, this list is traversed to find the desired key.