Greedy Algorithms Questions Medium
The optimal substructure property in the context of greedy algorithms refers to the property that an optimal solution to a problem can be constructed from optimal solutions to its subproblems. In other words, if we have a problem that can be divided into smaller subproblems, and we can find the optimal solution for each subproblem, then we can combine these optimal solutions to obtain the optimal solution for the original problem.
This property is crucial for greedy algorithms because they make locally optimal choices at each step, hoping that these choices will lead to a globally optimal solution. By exploiting the optimal substructure property, greedy algorithms can iteratively build up the optimal solution by making the best choice at each step, without needing to reconsider previous choices.
In summary, the optimal substructure property allows greedy algorithms to solve complex problems by breaking them down into smaller subproblems and making locally optimal choices, ultimately leading to a globally optimal solution.