Explain the concept of hash collisions and their impact on performance.

Hash collisions occur when two different inputs produce the same hash value. In other words, it is a situation where two or more keys are mapped to the same location in a hash table. This can happen due to the limited range of hash values compared to the potentially infinite number of inputs.

The impact of hash collisions on performance depends on the specific hashing algorithm and the handling of collisions. In general, hash collisions can have the following effects:

1. Increased time complexity: When a collision occurs, the hash table needs to resolve it by either finding an alternative location to store the data or by using a collision resolution technique. This additional step increases the time complexity of operations like insertion, retrieval, and deletion. The more collisions there are, the longer it takes to perform these operations.

2. Degraded search efficiency: In a hash table, the primary advantage is the ability to quickly locate an element based on its key. However, when collisions occur, the search efficiency decreases as the hash table needs to search through multiple elements stored at the same location. This can lead to longer search times and reduced performance.

3. Increased memory usage: To handle collisions, additional memory may be required to store the collided elements. This can result in increased memory usage, especially if the number of collisions is high. In some cases, collision resolution techniques like chaining or open addressing may require additional memory overhead to maintain linked lists or probe sequences.

4. Uneven distribution of data: Hash collisions can cause an uneven distribution of data across the hash table. If certain hash values have a higher probability of collisions, it can lead to clustering, where multiple elements are stored in close proximity. This can result in inefficient use of memory and slower performance due to increased search times within clusters.

To mitigate the impact of hash collisions on performance, various collision resolution techniques can be employed. These include separate chaining, where collided elements are stored in linked lists, and open addressing, where alternative locations are searched to find an empty slot for the collided element. Additionally, choosing a good hashing algorithm and ensuring a proper balance between the number of elements and the size of the hash table can help minimize the occurrence of collisions and improve performance.