tractable vs intractable problems

Tractable problems are those for which we have efficient methods to find a solution within a reasonable time, even if they are complex. In contrast, intractable problems are so difficult that solving them exactly can take an impractical amount of time, especially as problem size grows. Think of tractable problems as tasks you can complete with current tools fairly quickly, like sorting a list. Intractable problems resemble puzzles with an enormous number of possibilities, making exact solutions computationally unfeasible in practical time frames. These distinctions help determine how we approach problem-solving in computer science and algorithms.