Question

GIVEN A SEQUENTIAL LIST WITH N NUMBERS, REPRESENTED IN A ONE-DIMENSIONAL ARRAY. WRITE AN ALGORITHM TO CHECK IF THE LIST HAS ANY DUPLICATES, SHOW HOW YOUR ALGORITHM WORKS. EXPLAIN THE TIME COMPLEXITY OF YOUR ALGORITHM. CAN YOU THINK OF A BETTER ALGORITHM TO DO THE JOB? IF SO, EXPLAIN.

Answer 1

Algorithm to check for duplicates in an array:

• Traverse the array and try to input each element in a hashtable/set with the number as the hash key.
• If you cannot enter the element, then it is a duplicate.

Here's how the algorithm works:

• Create an empty set.
• Traverse the array.
• For each element in the array, check if it is in the set.
• If the element is in the set, then it is a duplicate.
• If the element is not in the set, add it to the set.
• If the end of the array is reached, then there are no duplicates.

The time complexity of this algorithm is O(n) because it only requires one pass through the array to check for duplicates. The space complexity is also O(n) because the set can potentially hold all n elements of the array.

A better algorithm to do the job is to sort the array and then check for adjacent elements that are the same. This algorithm has a time complexity of O(n log n) due to the sorting step, but it has a space complexity of O(1) because it does not require any additional data structures. However, this algorithm modifies the original array, which may not be desirable in some situations.