4.3 Dynamic Programming Algorithms
Dynamic Programming (DP) is an algorithmic technique that breaks down an optimization problem into simpler subproblems. The solution to the overall problem depends on the optimal solution to its subproblems.
The advantage of DP over divide-and-conquer algorithms is that DP is applicable to dependent subproblems. In other words, when subproblems share sub-subproblems, DP will work while divide-and-conquer algorithms will not.
DP algorithms solve subproblems just once and then save the answer in a table. This avoids the need to re-compute the answer every time the subproblem is encountered. This saves time and frees up computing power to solve other problems.
DP is a powerful technique that has many applications in areas such as computer science, economics, and engineering. By breaking down complex problems into smaller, more manageable subproblems, DP enables us to solve problems that would otherwise be too difficult to tackle.
Consider the problem...