Find the memory locations which are assigned by the hashing function h(k)=k mod 101 to the records of students with the following Social Security numbers:
(Note enter the canonical representative for the answer modulo 101, thus your answer should be an integer between 0 and 100 inclusive for each part.)
241096275 (blank), 278648330 (blank),161509031 (blank), 467298263 (blank)

To find the memory locations assigned by the hashing function \( h(k) = k \mod 101 \) for the given Social Security numbers, we need to compute the remainder when each Social Security number is divided by 101. 

Here are the steps:

1. **For the Social Security number 241096275:**
   \[
   241096275 \mod 101 = 241096275 \div 101 = 2388120 \text{ remainder } 55
   \]
   Thus, \( h(241096275) = 55 \).

2. **For the Social Security number 278648330:**
   \[
   278648330 \mod 101 = 278648330 \div 101 = 2758922 \text{ remainder } 8
   \]
   Thus, \( h(278648330) = 8 \).

3. **For the Social Security number 161509031:**
   \[
   161509031 \mod 101 = 161509031 \div 101 = 1591138 \text{ remainder } 93
   \]
   Thus, \( h(161509031) = 93 \).

4. **For the Social Security number 467298263:**
   \[
   467298263 \mod 101 = 467298263 \div 101 = 4626712 \text{ remainder } 51
   \]
   Thus, \( h(467298263) = 51 \).

So, the memory locations assigned by the hashing function for the given Social Security numbers are:

1. \( 241096275 \) maps to memory location \( 55 \).
2. \( 278648330 \) maps to memory location \( 8 \).
3. \( 161509031 \) maps to memory location \( 93 \).
4. \( 467298263 \) maps to memory location \( 51 \).

Would you like any more details or have any questions?

Here are 8 related questions that might expand on this topic:

1. What is the purpose of a hashing function in computer science?
2. How does the modulo operation help in creating a hash function?
3. Can you give an example of a collision in a hash table?
4. What are some common methods for resolving collisions in hash tables?
5. How would the performance of a hash table be affected if many collisions occur?
6. What is the load factor in a hash table, and why is it important?
7. Can you explain the difference between a hash table and an array?
8. How does the choice of a hashing function affect the efficiency of a hash table?

**Tip:** When designing a hash function, it's important to ensure that it distributes keys uniformly across the hash table to minimize collisions and maintain efficient performance.

Explore how hashing functions assign memory locations based on the modulo operation. Calculate memory locations for specific Social Security numbers using the hash function h(k) = k mod 101. Suitable for advanced high school students learning about data structures and algorithms.

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