title: Uniform hashing functions
body: <p>Hash table basics: - MAJOR TEST COMING UP. ALL HELP WOULD BE APPRECIATED.</p>
  
  <p>I am basically a bit confused on uniform hashing of keys.</p>
  
  <pre><code>----------------------
  | X X X                    &lt;=== Chains; X represents an item in there
  ----------------------
  | X X X                    &lt;=== Multiple X represents collisions
  ---------------------- 
  | 
  ----------------------
  | X X X
  ----------------------
  | X
  ----------------------
  </code></pre>
  
  <ol>
  <li><p>Consider the case of the above hash table where M = 5 (num of rows) and the total length to be 10. How would I know if this is hash table is uniformly hashed or not?</p></li>
  <li><p>If one makes a uniform hashing of a set of keys, does that mean the lists inside the chains in a hashtable aka the linked-lists due to collisions have the same length? Or does it mean the average?</p></li>
  <li><p>If one makes a uniform hashing of keys, does that mean the find and remove functions of this hashtable are O(1) (amortized) and a pure complexity of O(n/M) where M is the number of chains in total?</p></li>
  <li><p>Does the load factor or (N/#ofChains) identify the uniformity of the hashing?</p></li>
  </ol>
  
  <p>I hope you can help me with these questions. My professor had put a lot of concepts out in class and I am just basically bending them together here and I am getting confused when I put these concepts together. </p>
  
  <p>I was searching on the web for more to study about this concept and I saw a set of slides as shown below. I would be obliged if you <strong>can explain to me what the equation means in the second slide in relation to uniform hashing of keys</strong>.</p>
  
  <p><strong>Also, what does it mean when they say "the number of keys that map to each slot are equal." Does go to say that my hashtable that is shown above is NOT uniformily hashed?</strong></p>
  
  <p><img src="https://i.stack.imgur.com/V2ax0.png" alt="enter image description here"></p>
  
  <p>Thank you</p>