dynamic-programming

I am aware of solutions that uses the bottom up dynamic programing approach to solve this problem in O(n^2). I am specifically looking for a top down dp approach. Is it possible to achieve longest palindromic substring using a recursive solution? Here is what I have tried but it fails for certain cases, but I feel I am almost on the right track. #include <iostream> #include <string> using namespace std; string S; int dp[55][55]; int solve(int x,int y,int val) { if(x>y)return val; int &ret = dp[x][y]; if(ret!=0){ret = val + ret;return ret;} //cout<<"x: "<<x<<" y: "<<y<<" val: "<<val<<endl; if(S

I am trying to solve this Problem.The question is as follows Given an input string and a dictionary of words, find out if the input string can be segmented into a space-separated sequence of dictionary words. Dictionary is an array of strings. My Approach is the following recursive fn with storing of the results of recursive calls. The output is fine but I see that the stored result is never used. My solution is hopefully correct as it passed the test cases.But I would be great if I know whether DP is used. The code is: #include <iostream> #include <string.h> using namespace std; int r[100]

In 16.1 An activity-selection problem of Introduction to Algorithm , the dynamic programming solution for this problem was given as c[i, j] = 0 if S(i, j) is empty c[i, j] = max { c[i, k] + c[k, j] + 1 } if S(i, j) is not empty where S(i, j) denotes the set of activities that start after activity a(i) finishes and that finish before activity a(j) starts, and c[i, j] denotes the size of an optimal solution for the set S(i, j) However, I am thinking of another simpler solution c[i] = max { c[i - 1], c[f(i)] + 1 } where f(i) gives the activity that is compatible with a(i) and has the max finish

Let us call this problem the Slinger-Bird problem (actually the Slinger is analogous to a server and the bird to a request but I was having a nervous breakdown thinking about it so I changed them hoping to get a different perspective!). There are S stone throwers (slingers) and B birds. The slingers are not within the range of each other. Slinging once can kill all birds within the sight of a slinger and will consume one shot and one time unit I am trying to figure out the optimal solution that minimizes the time and the number of shots it takes to kill the birds given a particular arrival

I found this while looking up problems on dynamic programming. You are given an unparanthesized expression of the form V0 O0 V1 O1 .... Vn-1 We have to put brackets at places which maximizes the value of the entire expression. V's are the operands and O's are the operators. In the first version of problem operators can be * and + and operands are positive. Second version of problem is completely general. For the first version i came up with DP solution . Solution - A[] = operands array B[] - operators array T(A[i,j]) - max value of expression T(A[0,n-1]) = max over all i {(T(A[0,i]) Oi T(A[i+1