The Pointer Arithmetic of Constant Time: Why Arrays Scale O(1)

TL;DR: Array indexing is O(1) because it relies on a single pointer calculation: base_address + (index * element_size) . Since arrays use contiguous memory allocation, the CPU uses the base register and an offset to resolve any memory address in a fixed number of cycles, regardless of the array's total length. We treat array indexing as a fundamental constant in software engineering. Whether you are pulling an item from a list of ten or ten million, the performance remains the same. This isn't a result of clever searching algorithms; it is a side effect of how memory is physically structured and addressed at the hardware level. When you access arr[i] , you aren't searching; you are calculating a physical location on the memory bus. How does a computer find an element in an array? The CPU resolves an index by adding a calculated offset to the array's base memory address. This is a single-step arithmetic operation: BaseAddress + (Index * ElementSize) . At the machine level, when you decl