which of the following algorithims will run in constant time
accessing an element of an array
sorting an array
binary search on a sorted array
traversing an array
Accessing an element of an array and traversing an array will run in constant time.
Out of the given algorithms, accessing an element of an array will run in constant time.
Among the given algorithms, accessing an element of an array will run in constant time.
To understand why this is the case, we have to first understand what "constant time" means. In computer science, constant time refers to an algorithm or operation that takes the same amount of time, regardless of the input size. In other words, the execution time does not depend on the size of the problem.
In the case of accessing an element of an array, regardless of the size of the array, the time it takes to access a specific element will remain constant. This is because arrays are stored in memory as contiguous blocks, and accessing an element simply involves calculating its memory address using a simple mathematical formula. Therefore, the time complexity is O(1), which signifies constant time.
On the other hand, sorting an array, performing a binary search on a sorted array, and traversing an array will not run in constant time. These operations have time complexities that depend on the size of the array. Sorting an array typically has a time complexity of O(n log n) for most efficient sorting algorithms. Performing a binary search has a time complexity of O(log n) because it splits the search space in half at each step. Traversing an array has a time complexity of O(n) because it needs to visit each element in the array.
In summary, accessing an element of an array is the only operation among the given algorithms that runs in constant time.