Open Addressing vs. Separate Chaining in Hashing

Open Addressing in Detail

How it Works

Open addressing keeps everything inside the hash table—no lists allowed! When a collision happens, it “probes” to find the next empty slot using a specific pattern. It’s like if your favorite seat at lunch is taken, so you move to the next free one nearby.

Say you’re adding “apple” to slot 2, but it’s full. Open addressing checks slot 3, then 4, until it finds an empty spot. To find “apple” later, it follows the same pattern until it hits the right item or an empty slot. There are a few ways to probe, which we’ll cover next.

Probing Methods

Linear Probing

Linear probing checks the very next slot if there’s a collision. If slot 2 is full, it tries 3, then 4, and so on.

• Good: It’s super easy to code up.
• Bad: It can cause “clustering,” where full slots bunch up and make collisions worse.

Quadratic Probing

Quadratic probing jumps farther each time—like 1 slot, then 4, then 9 (squares of 1, 2, 3). If slot 2 is taken, it tries 3, then 6, then 11.

• Good: Cuts down on clustering compared to linear probing.
• Bad: Might miss some slots and still clump a bit.

Double Hashing

Double hashing uses a second hash function to decide how far to jump. If slot 2 is full, and the second function says “jump 3,” it tries 5, then 8, and so on.

• Good: Spreads items out better, avoiding clumps.
• Bad: Trickier to set up because you need two good hash functions.

Advantages

• Faster with Cache: Since everything’s in one big array, computers can grab data quicker.
• Saves Space: No extra lists mean less memory used compared to chaining.

A study from Stanford showed open addressing can be 15% faster for lookups in small tables due to cache efficiency.

Disadvantages

• Picky About Hash Functions: Needs a really good hash function to spread things evenly, or it gets messy.
• Fills Up Fast: Once the table’s full, you’re stuck unless you make it bigger, which takes time.
• Clumping Problems: Probing can create clusters, slowing things down.

Comparison Between Open Addressing and Separate Chaining

Here’s a quick look at how these two stack up:

Separate chaining is like a stretchy backpack—it grows as you need it. Open addressing is more like a suitcase—great until it’s full, then you need a bigger one. Want to ace interviews with this stuff? Check out our top Amazon DSA questions.

Performance Analysis

Both methods aim to find stuff in O(1) time—that’s one quick step. But it depends on how full the table is, called the “load factor.”

Separate chaining stays fast if the hash function spreads items out. Average lookup is O(1), but if everything lands in one slot (worst case), it’s O(n). Open addressing is also O(1) on average, but as the table fills up—say, 80% full—probing takes longer, pushing it toward O(n) too.

Space-wise, separate chaining uses extra memory for lists, while open addressing just needs the table. Resizing a full open-addressed table can be slow, though. A 2020 study found double hashing cuts collision costs by 20% over linear probing, making it a solid choice.