Greedy vs Brute Force

Brute force tries every possible solution and picks the best. For $n$ items, this often means $O(2^n)$ or $O(n!)$ time. It may also use $O(n)$ to $O(2^n)$ space to store candidates. Unusable for large inputs.

Greedy makes one choice per step without looking back. It gives $O(n)$ or $O(n \log n)$ time, depending on whether sorting is needed. Space is usually $O(1)$ extra beyond the input.

The tradeoff: brute force always finds the optimum, greedy only works when the greedy choice property holds. But when greedy works, it is dramatically faster.