Dynamic Programming Questions Medium
The optimal substructure property in Dynamic Programming 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 can break down a problem into smaller subproblems, and the optimal solution to the larger problem can be obtained by combining the optimal solutions to the subproblems, then the problem exhibits the optimal substructure property.
This property is crucial in Dynamic Programming as it allows us to solve a problem efficiently by breaking it down into smaller, overlapping subproblems and storing the solutions to these subproblems in a table or memoization array. By solving the subproblems only once and reusing their solutions, we can avoid redundant computations and significantly improve the efficiency of our algorithm.
The optimal substructure property is a key characteristic of many problems that can be solved using Dynamic Programming, such as the famous Fibonacci sequence, shortest path problems, and the knapsack problem. By identifying and utilizing the optimal substructure property, we can design efficient algorithms that solve these problems optimally.