Dynamic programming builds solutions from solutions to simpler subproblems. It's closely allied to recursion, but dynamic programming algorithms are formulated as iteration usually over a very regular datastructure.
0
votes
0answers
39 views
Dynamic programming vs branch-and-bound for the knapsack problem
I have to implement a program that solves the 0-1 knapsack problem, where the weights and values of all items are nonnegative integers.
We went over two methods in class: dynamic algorithms ...
5
votes
5answers
269 views
My brute force solution is too slow, needed DP solution [closed]
Concise problem definition:
given n and {a,b,c};
(1 ≤ n, a, b, c ≤ 4000);
Constraint -> a*i + b*j + c*k==n (i,j,k>=0);
Objective-> maximize(i,j,k)
Examples:
n=47 and a=7,b=5,c=8 -> ...
-2
votes
1answer
89 views
Unable to Solve Dynamic Programming
I had an assignment on dynamic programming due last night, but I had to turn it in unfinished because i could not understand how to solve the last problem:
The state wants to monitor traffic on a ...
2
votes
2answers
68 views
How to retrieve policy after Dynamic Programming?
I'm working on a simple resource allocation problem, that I'm solving using backward DP. The full code is at: http://codereview.stackexchange.com/questions/123641/allocating-a-resource
It works fine, ...
1
vote
1answer
51 views
Dynamic Programming: Shortest path with exactly k edges in a directed and weighted graph
I came across this problem of finding the shortest path with exactly k edges. After some searching, I found the code below. It uses a 3D DP. States are there for number of edges used, source vertex ...
3
votes
1answer
156 views
Dynamic Programming - Largest arrangement of bookcases
I'm trying to solve a problem, so I'm not looking for code, but for similar algorithms so I can solve it myself.
I am given n bookcases each with a size amount of books inside. I am to move some of ...
8
votes
1answer
157 views
Finding all possible ways of inserting a pattern into a string
I've been thinking about this problem for a while, and I can only find a recursive solution but I'm feeling that there is a dynamic programming way to do it, I just can't figure it out. Is this a ...
5
votes
2answers
142 views
Find path of steepest descent along with path length in a matrix
Came across this problem --
You are given a grid with numbers that represent the elevation at a particular point. From each box in the grid you can go north, south, east, west - but only if the ...
2
votes
1answer
134 views
Maximizing Value and Volume, minimizing weight - Knapsack
Trying out a Knapsack variant where the rules are
Any item you take must fit completely in the bag
Usable metrics of the bag are length(l),width(w),height(h) and you can assume that if the products ...
0
votes
1answer
125 views
How to find a subset of size k such that the minimum distance between values is maximum
Suppose I have a sorted array which contains n integers.
How do I find subset of size k such that the minimum distance between all pairs of integers in the subset is maximized, I mean they are at ...
1
vote
0answers
50 views
Select the sequence to minimize the cost
Lets say there is a delivery-boy who wants to distribute some food packets over N cities (1..N).
We know the number Pi of packages that are to be delivered at city i.
We know the distance between ...
-1
votes
1answer
504 views
Grid walking explanation [closed]
There's a problem on hackerrank.com called Grid Walking.
Here is its description:
You are situated in an N dimensional grid at position (x1,x2,...,xN). The dimensions of the grid are ...
2
votes
5answers
404 views
Are mocks in unit tests dangerous in dynamic languages?
I've started relying heavily on a mocking framework in php for my unit tests.
My concern is that with a dynamic language, there is no way of enforcing a return type. When mocking, you have to ensure ...
6
votes
3answers
414 views
Picking m number in the best possible time
Imagine we want to pick m numbers from n numbers so that the difference of the maximum and minimum of the m numbers be minimum, for example if
m = 4
n =6
numbers: 10 12 10 7 5 22
The ...
0
votes
0answers
144 views
scrabble solving with maximum score
I was asked a question
You are given a list of characters, a score associated with each character and a dictionary of valid words ( say normal English dictionary ). you have to form a word ...
3
votes
4answers
2k views
Robot in a grid
This was recently asked to someone I know.
A robot has to move in a grid which is in the form of a matrix. It can go to
A(i,j)--> A(i+j,j) (Down)
A(i,j)--> A(i,i+j) (Right)
...
0
votes
1answer
172 views
dynamic programming with memoization
I’ve a problem with a programming exercise. I hope you can help me. In this exercise I need to find out what the maximum profit is of taking pictures from several items in a park. For taking pictures ...
4
votes
2answers
897 views
Number of strings containing a specific substring
I've seen numerous questions (and answers) concerning the number of binary strings (e.g "10010" containing some binary substring (e.g "00"). I'd like to know if there is a way to generalize this:
...
9
votes
3answers
239 views
number of strings, when each character must occur even times
I've been bashing my skull at this problem for some time now, and its really starting to frustrate me. The problem is:
I have a set of characters, A, B, C, and D. I have to tell in how many ways a ...
2
votes
2answers
394 views
Dynamic Programming Problem - To find smallest integer number 'x' which contains only digits 1's and 0's such that x mod n = 0
To design an algorithm that will output the smallest integer number 'x' which contains only digits 1's and 0's such that x mod n = 0 and x > 0.....
For example:
2 divides 10
3 divides 111
4 ...
3
votes
2answers
593 views
Looking for a DP algorithm for a specific packing problem
I have the following problem to solve:
Given a ferry with length d and a list of n cars conataining their length we must load the cars on the ferry in an order in which they appear in the list on 2 ...
1
vote
1answer
102 views
find the minimum number of sets
Let's explain my question with example I have some integer sets for example
S1 = {2,3}
S2 = {2, 5}
S3 = {4, 5}
S4 = {4}
S5 = {5}
And I have sample set Ssample with 4 elements {2, 3, 4, 5}.
So ...
2
votes
3answers
5k views
Efficient algorithm to count number of substrings divisible by 3
Given a string of decimal digits, I have to find the number of all substrings divisible by 3 in the range L to R [both inclusive], where L & R are index[1-based] of the specified string
string ...
2
votes
2answers
522 views
Finding common prefixes for a set of strings
I am trying to find common prefixes for a sorted set of strings. i.e. if the following strings are given:
AB123456
AB123457
ABCDEFGH
ABCDEFGX1
ABCDEFGY
XXXX
then my function should return three ...
0
votes
1answer
366 views
Number of sequences when no adjacent items can be the same
I came across this one problem,
There is a particular sequence only uses the numbers 1, 2, 3, 4 and no two adjacent numbers are the same.
Write a program that given n1 1s, n2 2s, n3 3s, n4 4s ...
4
votes
1answer
62 views
How to diversify an optimal solution set?
If given a list of players, their salaries, and their projections, one can easily find the top 'n' projected teams (where a team is a combination of players), such that every team is under the salary ...
-1
votes
1answer
280 views
optimise my solution
I just solve this but want know more efficient way to do matrix multiplication
M :
------
1 1 0
0 0 5
3 2 0
f[n] = M^n
I have implemented using Exponentiation_by_squaring
Is there more ...
1
vote
2answers
107 views
Need to organize words based on their components, any other way aside from brute force?
I'm not sure if this process has a name.
I have some words (about 9,000). They are in Japanese, but I'll try to explain this using English words. I want to categorize the words by the components (in ...
4
votes
0answers
520 views
Dynamic programming in Bin packing
Problem: Given a list L of objects of possible sizes from set S={1,2,4,8} and unlimited supply of bins of sizes 16 each and we have to use minimum possible numbers of bins to pack all objects of L.
I ...
-1
votes
1answer
220 views
How to solve linear recurrences involving two functions?
Actually I came across a question in Dynamic Programming where we need to find the number of ways to tile a 2 X N area with tiles of given dimensions..
Here is the problem statement
Now after a bit ...
5
votes
4answers
704 views
The optimal recipe problem
Suppose I have a list of Ingredients In My Fridge which are going off soon, and a list of Recipes which use up various Ingredients. (Some of which I don't currently have.)
Is there an algorithm which ...
0
votes
2answers
453 views
Finding lowest cost path - dynamic
I have to write a dynamic algorithm for finding lowest cost path. So I have a point that I have to visit. I can jump only between points by distance - 5 I have an array of distance from 0-point for ...
1
vote
1answer
199 views
Memoization Memory
Memoization is definitely a powerful technique.
But Dynamic Programming is slightly better IMO, since it does not involve the memory strain (in a recursive program, the parameters occupy memory and ...
0
votes
2answers
57 views
Is array dependence on previous terms considered recursive?
For example, take the case of Fibonacci number to calculate nth number you require n-1 and n-2 term.
If I do it with bottom up approach, is it recursion as f(n) depends on f(n-1)?
13
votes
4answers
3k views
How do you identify a problem as being suitable for dynamic programming?
I have been reading up on dynamic programming lately. Would like to hear from someone who started from scratch and now is pretty good at identifying and solving DP problems. I am struggling in ...
4
votes
0answers
289 views
Help/suggestions for Parallel assembly line scheduling (Dynamic programming)
I am working on a problem similar to the assembly line scheduling by dynamic programming.The issue is that unlike the classic problem where we have predefined stations now I only have information ...
1
vote
1answer
370 views
Can someone help me in creating a dynamic programming solution to this problem?
I have some function names which are assigned to some nodes. I have to decide which functions to move to other nodes to increase speed.
Why do I have to move the functions to other nodes? If ...
2
votes
1answer
321 views
Programming puzzle with constant selection
THE QUESTION:
There is an event where there are N contestants. There are three tasks in the event: A,B,C (say). Each participant takes part in the events in the listed order: i.e a contestant must ...
7
votes
3answers
651 views
Longest subsequence without string
Does there exist a dynamic programming algorithm to find the longest subsequence in a string X that does not contain Y as substring? Just that this problem seems so similar to other DP string ...
5
votes
2answers
601 views
Training Camp Algorithm
Problem Statement -
The task is to find the most profitable contiguous segment of tests, given a sequence of test scores, with being allowed to drop any k tests from a chosen range.
The problem ...
2
votes
3answers
1k views
Domino Solitaire Algorithm
Problem Statement -
Given a 2xN grid of numbers, the task is to find the most profitable tiling combination (each tile covers 2x1 cells; vertically or horizontally) covering all tiles.
I thought ...
-2
votes
4answers
1k views
C simple arrays and pointers question
So here's the confusion, let's say I declare an array of characters
char name[3] = "Sam";
and then I declare another array but this time using pointers
char * name = "Sam";
What's the ...
4
votes
3answers
1k views
Round Table - Minimum Cost Algorithm
Problem Link - http://www.iarcs.org.in/zco2013/index.php/problems/ROUNDTABLE
It's dinner time in Castle Camelot, and the fearsome Knights of the Round Table are clamouring for dessert. You, the ...
-2
votes
1answer
782 views
Grid Game Algorithm
Problem Link - http://www.iarcs.org.in/inoi/2009/zco2009/zco2009-1a.php
You have to find the path with the maximum weight, from the top-left cell to the bottom-right cell. It could've been solved ...
4
votes
2answers
260 views
Looking for a dynamic programming solution
Given a sequence of integers in range 1 to n. Each number can appear at most once. Let there be a symbol X in the sequence which means remove the minimum element from the list. There can be an ...
3
votes
2answers
4k views
Separating words in a string
How do I separate words in a string?
In the following I have a random sample of words in a string extracted from text file with over a million words.
Here's the string:
"intervene Pockets ...
1
vote
1answer
387 views
Minimizing use of paper
I've recently faced this problem in a dynamic programming curriculum, and I honestly have no idea about how to determine the appropriate state.
You're given N (1 <= N <= 70) paragraphs and M (1 ...
8
votes
2answers
3k views
How to get better at solving Dynamic programming problems
I recently came across this question: "You are given a boolean expression consisting of a string of the symbols 'true', 'false', 'and', 'or', and 'xor'. Count the number of ways to parenthesize the ...
3
votes
2answers
2k views
How to prove a Dynamic programming strategy will work for an algorithm?
How can I prove that a dynamic programming (dp) strategy for a problem will work or not? For greedy algorithms, we can prove by showing the sub problems exhibits matroid property.
Is there any such ...
3
votes
2answers
403 views
Help on a Dynamic Programming definition in Cormen
I am reading about Dynamic Programming from Cormen.
In the beginning of the chapter it says (relating to the term Dynamic Programming):
"Programming” in this context refers to a tabular method, ...
