dynamic-programming

I am trying to solve the following question : A sequence in which the value of elements first decrease and then increase is called V- Sequence. In a valid V-Sequence there should be at least one element in the decreasing and at least one element in the increasing arm. For example, "5 3 1 9 17 23" is a valid V-Sequence having two elements in the decreasing arm namely 5 and 3, and 3 elements in the increasing arm namely 9, 17 and 23 . But none of the sequence "6 4 2" or "8 10 15" are V-Sequence since "6 4 2" has no element in the increasing part while "8 10 15" has no element in the decreasing

The Problem is making n cents change with quarters, dimes, nickels, and pennies, and using the least total number of coins. In the particular case where the four denominations are quarters,dimes, nickels, and pennies, we have c1 = 25, c2 = 10, c3 = 5, and c4 = 1. If we have only quarters, dimes, and pennies (and no nickels) to use, the greedy algorithm would make change for 30 cents using six coins —a quarter and five pennies—whereas we could have used three coins , namely, three dimes. Given a set of denominations, how can we say whether greedy approach creates an optimal solution? What you

I need a clarification of the answer of this question but I can not comment (not enough rep) so I ask a new question. Hope it is ok. The problem is this: Given an array, you have to find the max possible two equal sum, you can exclude elements. i.e 1,2,3,4,6 is given array we can have max two equal sum as 6+2 = 4+3+1 i.e 4,10,18, 22, we can get two equal sum as 18+4 = 22 what would be your approach to solve this problem apart from brute force to find all computation and checking two possible equal sum? edit 1: max no of array elements are N <= 50 and each element can be up to 1<= K <=1000 edit

I was wondering how to solve such a problem using DP. Given n balls and m bins, each bin having max. capacity c1, c2,...cm. What is the total number of ways of distributing these n balls into these m bins. The problem I face is How to find a recurrence relation (I could when the capacities were all a single constant c). There will be several test cases, each having its own set of c1,c2....cm. So how would the DP actually apply for all these test cases because the answer explicitly depends on present c1,c2....cm, and I can't store (or pre-compute) the answer for all combinations of c1,c2....cm.

Everyday I struggle with algorithm questions and try to ask here which I can't answer. Excuse me, if I cause any headache. Anyway, Here is the problem from the University of Waterloo ACM Programming Contest. In how many ways can you tile a 3xn rectangle with 2x1 dominoes? Nirvana : smells like recursion spirit You can solve this by using dynamic programming. Check this for a possible solution. Just an explicit solution to the equations given implicitly in taskinoor's answer: Or f[n]=((1 + (-1)^n)*((2 - Sqrt[3])^(n/2)*(-1 + Sqrt[3]) + (1 + Sqrt[3])* (2 + Sqrt[3])^(n/2)))/(4*Sqrt[3]) if anyone

I have this problem in my textbook: Given a group of n items, each with a distinct value V(i), what is the best way to divide the items into 3 groups so the group with the highest value is minimIzed? Give the value of this largest group. I know how to do the 2 pile variant of this problem: it just requires running the knapsack algorithm backwards on the problem. However, I am pretty puzzled as how to solve this problem. Could anyone give me any pointers? Answer: Pretty much the same thing as the 0-1 knapsack, although 2D Tough homework problem. This is essentially the optimization version of