Given an array of 10⁶ integers, design and analyze a radix sort algorithm that…

Radix sort processes integers digit by digit from least significant to most significant position. For base-16, each digit represents 4 bits. We utilize a stable counting sort subroutine for each of the 4-bit chunks sequentially. Assuming standard 32-bit integers, there are exactly 8 digits (32/4). The theoretical time complexity is O(d * (n + k)), where d is the number of digits, n is the array size, and k is the base. Here d=8, n=10^6, k=16. Thus, the complexity simplifies to linear time O(n). For time estimation, a 2 GHz CPU executes 2 * 10^9 cycles per second. Total operations roughly equal d * n = 8 * 10^6 passes. Assuming an average of 10 cycles per operation for memory access and logic, total cycles are approximately 8 * 10^7. Dividing by frequency gives roughly 0.04 seconds. This assumes efficient memory access and minimal cache misses. In practice, overhead might increase this slightly, but it remains sub-second. The algorithm is significantly efficient for large datasets with fixed integer sizes compared to comparison sorts like QuickSort which are O(n log n).