What is the time complexity of the algorithm that iterates through an array once and performs a dictionary lookup in each iteration?

The algorithm described iterates over an array once, performing a dictionary lookup for each element. Because the loop runs exactly n times, where n is the number of elements in the array, the number of iterations grows linearly with the input size. Each dictionary lookup is an average‑case O(1) operation thanks to the underlying hash table implementation. Therefore, the total work done by the algorithm is n times a constant, which simplifies to O(n). There are no nested loops or recursive calls that would multiply the work by another factor, so the algorithm does not exhibit quadratic or higher‑order growth. In practice, this means that if you double the size of the input array, the runtime will roughly double as well, assuming the dictionary remains efficient. This linear time complexity is considered optimal for problems that require examining every element at least once, such as searching for a pair of numbers that satisfy a condition. Thus, the algorithm runs in linear time, O(n).