What is the Running Time of Insertion Sort if All Keys Are Equal?
Insertion sort is a simple sorting algorithm that works by iteratively inserting each unsorted element into its correct position in the sorted portion of the array. If the array is already sorted or if all keys are equal, the running time of insertion sort is approximately O(n).
In the case where all keys are equal, each element is trivially inserted into the sorted portion of the array. As each element is inserted, the number of sorted elements effectively increases by one. However, the number of elements remaining to be inserted, denoted by n - i, remains unchanged.
The insertion process takes constant time. Let's assume it takes c time units to insert an element into the sorted portion. Therefore, the total running time for insertion sort with all equal keys is O(cn). Since c is a constant, the running time is ultimately O(n).
Related Questions
- What is the best-case running time of insertion sort? O(n)
- What is the worst-case running time of insertion sort? O(n^2)
- Is insertion sort a stable sorting algorithm? Yes
- What is a common optimization for insertion sort? Binary search to find the insertion point
- What is the time complexity of insertion sort on nearly sorted arrays? O(n)
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