Hash collisions explained with a parking lot analogy

Picture a parking lot with numbered spots. Your hash function looks at your license plate and tells you which spot to park in. A collision is when your assigned spot is already taken. The strategies are just different parking policies: - External chaining: every spot has a little lane behind it, and cars line up in that lane. Nobody moves; lanes just get longer. - Linear probing: spot taken? Try the next one, then the next. Easy, but cars bunch up into long clusters. - Quadratic probing: jump 1, then 4, then 9 spots away. Breaks up clusters, but you might never try some spots. - Double hashing: a second function on your plate decides how far you jump each time. Resizing is building a bigger lot and re-parking every car, because each car's spot depends on the lot size. That's why load factor matters: once the lot is mostly full, finding a spot gets slow for everyone.