Ways to Solve DP 2

This is in continuation of our previous post in the series .If you have not seen that please have a look to my earlier post in the series

So in previous post we have seen the Top down approach to solve the DP problem . Now we will see the other approach to solve the problem

Bottom Up Approach

Lets understand this by taking the same fibonacci problem again . So here we first focus on the base cases ie we know for fibonacci problem

fib(0) =0 , fib(1) =1 ,fib(2)=1 and so on …

So we iteratively start from the base case and use the already calculated result to calculate the further result . Lets look at the solution to this problem using bottom up approach.

Since we are iterating here from 0 -n once, our time complexity will be O(n) and our space will also be O(n), as we have created a 1D array from 0 to n. This makes our current solution comparable to the top-down solution, although without recursion. This code is likely easier to understand.

I hope now identifying the DP problem and two approaches to solve the DP problem is clear .Lets look up Knapsack problems in our next post .

Till then Stay Tuned !

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