diff --git a/dynamic-programming.html.markdown b/dynamic-programming.html.markdown index 95f774bf..94be22e9 100644 --- a/dynamic-programming.html.markdown +++ b/dynamic-programming.html.markdown @@ -11,39 +11,40 @@ contributors: Dynamic Programming is a powerful technique used for solving a particular class of problems as we will see.The idea is very simple, If you have solved a problem with the given input, then save the result for future reference, so as to avoid solving the same problem again. -Always remember!! +Always remember! "Those who can't remember the past are condemned to repeat it" ## Ways of solving such Problems -1.) Top-Down : Start solving the given problem by breaking it down. If you see that the problem has been solved already, then just return the saved answer. If it has not been solved, solve it and save the answer. This is usually easy to think of and very intuitive. This is referred to as Memoization. +1. *Top-Down* : Start solving the given problem by breaking it down. If you see that the problem has been solved already, then just return the saved answer. If it has not been solved, solve it and save the answer. This is usually easy to think of and very intuitive. This is referred to as Memoization. -2.) Bottom-Up : Analyze the problem and see the order in which the sub-problems are solved and start solving from the trivial subproblem, up towards the given problem. In this process, it is guaranteed that the subproblems are solved before solving the problem. This is referred to as Dynamic Programming. +2. *Bottom-Up* : Analyze the problem and see the order in which the sub-problems are solved and start solving from the trivial subproblem, up towards the given problem. In this process, it is guaranteed that the subproblems are solved before solving the problem. This is referred to as Dynamic Programming. ## Example of Dynamic Programming -The Longest Increasing Subsequence problem is to find the longest increasing subsequence of a given sequence. Given a sequence S= {a1 , a2 , a3, a4, ............., an-1, an } we have to find a longest subset such that for all j and i, j a[j] and LS[i] a[j] and LS[i]