Dynamic programming is a group of computer algorithms that solve complex problems by breaking them down into smaller subproblems. It works with overlapping or optimal substructures and uses mathematical systems to find the best answer. The algorithm finds the shortest path to the solution using either a top-down or bottom-up approach.
Dynamic programming, when referring to the field of computer science, describes a group of similar computer algorithms intended to solve complex problems by breaking the problem into sets of smaller problems. First created by Richard Bellman in the 1950s, dynamic programming works with problems that are either overlapping subproblems or optimal substructures. To understand how dynamic programming works, it is better to understand the concept behind these two terms.
Stacked subproblems describe complicated equations that, when broken down into smaller sets of equations, reuse parts of the smaller equations more than once to get an answer. For example, a mathematical equation said to calculate all possible outcomes using a set of numbers may calculate the same result numerous times while calculating other outcomes only once. Dynamic programming would tell this problem that after calculating the result the first time it should save that result and plug the answer into the equation later instead of calculating it again. When dealing with long and complex processes and equations, this saves time and creates a faster solution using far fewer steps.
Optimal substructures create a solution by finding the best answer to all subproblems and then creating the best overall answer. After breaking down a complex problem into smaller problems, the computer uses a mathematical system to determine which is the best answer for each problem. Calculate the answer to the original problem from the smallest answers. Flaws exist with this process. While it provides the solution that works best mathematically, it may or may not be the best solution in real life, depending on the type of problem and how it relates to the real world.
During any of these operations, the dynamic programming algorithm tries to find the shortest path to the solution. It may require one of two approaches to do so. The top-down approach breaks the equation into smaller equations and reuses the answers for these equations as needed. The bottom-up approach tries to solve for the smallest mathematical value after factoring the equation and then works its way up to the largest from there. Both approaches save time, but dynamic programming only works when the original problem can be broken down into smaller equations that are reused at some point to solve the equation.
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