What are greedy algorithms, and how are they useful in competitive programming?
Greedy algorithms make locally optimal choices at each step, aiming to find a globally optimal solution, which works well in certain types of problems.
Greedy algorithms are a problem-solving approach in which the algorithm makes the best choice at each step, hoping to reach the overall optimal solution. In competitive programming, greedy algorithms are useful because they are often simpler and faster than dynamic programming or brute-force methods. They work best in problems where a local optimum at each step leads to a global optimum, such as in activity selection, coin change, and certain scheduling problems. For a greedy algorithm to be correct, the problem must have the 'greedy-choice property' and 'optimal substructure.' Practicing greedy algorithm problems helps programmers recognize patterns and limitations of this approach, making it easier to apply in contests. Although not universally applicable, greedy methods are powerful tools for competitive programmers when used correctly.