dynamic-programming

I was asked this question while interviewing for a startup and saw this again in the recent contest at Code Sprint:systems **The question : You are given the stock prices for a set of days . Each day, you can either buy one unit of stock, sell any number of stock units you have already bought, or do nothing. What is the maximum profit you can obtain by planning your trading strategy optimally?** Examples ( The input i.e the no of days can vary ) 5 3 2 => profit = 0 // since the price decreases each day ,the max profit we can make = 0 1 2 100 => profit = 197 1 3 1 2 =>profit = 3 // we buy at 1

I am looking for a manageably understandable example for someone who wants to learn Dynamic Programming. There are nice answers here about what is dynamic programming . The fibonacci sequence is a great example, but it is too small to scratch the surface. It looks a great subject to learn about although I haven't taken the algorithms class yet, hopefully it is on my list for the spring. Check out this site: Dynamic Programming Practice Problems Here is a good tutorial comprising 29 solved DP problem with great explanation. The idea behind dynamic programming is that you're caching (memoizing)

I'm having trouble figuring out my last section of code for a Dynamic Coin Changing Problem. I have included the code below. I can't figure out the last else . Should I just use the greedy algorithm at that point or can I calculate the answer from values already in the table? I've worked hard on trying to understand this problem and I think I'm pretty close. The method finds the minimum amount of coins needed to make a certain amout of change by creating a table and using the results that are stored in the table to solve the larger problem without using recursion. public static int minCoins

Just looking for a bit of direction, I realise that the example given is possible to solve using brute force iteration, but I am looking for a more elegant (ie. mathematical?) solution which could potentially solve significantly larger examples (say 20x20 or 30x30). It is entirely possible that this cannot be done, and I have had very little success in coming up with an approach which does not rely on brute force... I have a matrix (call it A) which is nxn. I wish to select a subset (call it B) of points from matrix A. The subset will consist of n elements, where one and only one element is

Here is a problem from Algorithms book by Vazirani The input to this problem is a tree T with integer weights on the edges. The weights may be negative, zero, or positive. Give a linear time algorithm to find the shortest simple path in T. The length of a path is the sum of the weights of the edges in the path. A path is simple if no vertex is repeated. Note that the endpoints of the path are unconstrained. HINT: This is very similar to the problem of finding the largest independent set in a tree. How can I solve this problem in linear time? Here is my algorithm but I'm wonder if it is linear

Say S = 5 and N = 3 the solutions would look like - <0,0,5> <0,1,4> <0,2,3> <0,3,2> <5,0,0> <2,3,0> <3,2,0> <1,2,2> etc etc. In the general case, N nested loops can be used to solve the problem. Run N nested loop, inside them check if the loop variables add upto S. If we do not know N ahead of time, we can use a recursive solution. In each level, run a loop starting from 0 to N, and then call the function itself again. When we reach a depth of N, see if the numbers obtained add up to S. Any other dynamic programming solution? Try this recursive function: f(s, n) = 1 if s = 0 = 0 if s != 0 and

I am trying to find the best way to solve the following problem. By best way I mean less complex. As an input a list of tuples (start,length) such: [(0,5),(0,1),(1,9),(5,5),(5,7),(10,1)] Each element represets a sequence by its start and length , for example (5,7) is equivalent to the sequence (5,6,7,8,9,10,11) - a list of 7 elements starting with 5. One can assume that the tuples are sorted by the start element. The output should return a non-overlapping combination of tuples that represent the longest continuous sequences(s). This means that, a solution is a subset of ranges with no overlaps

here is another dynamic programming question ( Vazirani ch6 ) Consider the following 3-PARTITION problem. Given integers a1...an, we want to determine whether it is possible to partition of {1...n} into three disjoint subsets I, J, K such that sum(I) = sum(J) = sum(K) = 1/3*sum(ALL) For example, for input (1; 2; 3; 4; 4; 5; 8) the answer is yes, because there is the partition (1; 8), (4; 5), (2; 3; 4). On the other hand, for input (2; 2; 3; 5) the answer is no. Devise and analyze a dynamic programming algorithm for 3-PARTITION that runs in time poly- nomial in n and (Sum a_i) How can I solve