Complexity analysis in competitive programming is essential for understanding the efficiency of your code in terms of time and space. Time complexity measures how processing time grows with input size, while space complexity assesses memory usage. Analyzing complexity guides your choice of algorithms, ensuring that your solution is efficient enough to handle maximum constraints without timing out or running out of memory. For instance, in problems with high input limits, O(n^2) algorithms are often impractical, and alternatives like O(n log n) or linear time solutions are needed. Regularly assessing the time and space complexity of your solutions allows you to make informed choices, optimizing code for speed and memory, which is crucial in a contest environment where every millisecond counts.