# Questions tagged [dynamic-programming]

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.

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### Leetcode: 2327. Number of People Aware of a Secret and Problem with programming skill in general

On day 1, one person discovers a secret. You are given an integer delay, which means that each person will share the secret with a new person every day, starting from delay days after discovering the ...
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1 vote
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### Ideal Profits in companies in Perfect Binary Search tree

I'm trying to solve the following problems here: In the X world, companies have a hierarchical structure to form a large binary tree network (can be assumed to be a perfect binary tree). Thus every ...
• 111
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### Given n points in Cartesian 2D coords and only able to move directly from point to point how can you reach any point while minimising the longest jump

Let's say you're given n points e.g. A(1,2) B(4,2) C(3,1) How could you reach any of the points from the orign while minimising the longest jump from point to point For example: A: OA, B: OACB, C: OAC ...
118 views

### What to memoize in Dynamic programming questions?

How do you know what to memoize in top-down Dynamic Programming problems? I understand it is to do with capturing the permutations of state. E.g. in the Fibonacci numbers question, it’s memoizing the ...
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### Optimal sequence of recipes

I assume the following is/reduces to a known problem, but I haven't been able to find it. I have a sequence of recipes with associated costs. Each recipe converts a set of resources to another set of ...
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### How should I apply dynamic programming on the following problem

I have an array of events where events[i] = [startDay_i, endDay_i, value_i]. The ith event starts at startDay_i and ends at endDay_i, Attending the ith event, I will receive value_i. Also given an ...
• 23
1 vote
393 views

### Algorithm – Number of strings containing every string of a given set a strings

I have a given set S of strings, and a length l, and I am looking for the number of strings of length l that contains every string of S. A naive approach would be to generate every string of length l (...
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1 vote
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### Calling recursive method in a loop - Backtracking

I'm confused about a matter that I've been unable to figure out. I'm doing some leetcode problems. In backtracking problems, sometimes we use loop within our recursive method to call the recursion but ...
• 127
1 vote
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### design problem handling a dynamic object

I am writing an application for different geometrical types of fuel tanks. I have a design problem that only at runtime I will receive the exact type of tank from the end user; and I don't know how ...
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### Maximize picks from a list when you can only choose 2 items from every 7 items [closed]

What would be an O(n) algorithm to maximize picks from a list when you can only choose 2 items from every 7 items. I've been thinking about this problem for a few days and I can't figure out an answer....
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### Is 'call site' compiler generated auto code?

Is 'call site' some auto code generated by compiler - I come across this term frequently and it sounds like calling method is simply referred as 'call site' - which literally sounds fine but I believe ...
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1 vote
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### Merging algorithm for overlapping intervals

I have been searching for an efficient algorithm to merge overlapping intervals on a dynamic array of intervals. For example, (start time, end time) wise, [(1, 2), (4, 8), (3, 10)] becomes [(1, 2)...
3k views

### find longest subsequence with sum less than or equal to k

I have a vector<int> num, I want to get the size of longest subarray with the sum less than or equal to k. My approach: O(n^2). Repeat for every element in the array. Can we do better?' ...
2k views

### Can the gold mine problem be solved using divide-and-conquer?

There's a well-known dynamic programming problem that goes by the name of the "gold mine." You have a n x n grid, each cell of which contains a certain value of coins. You begin at the bottom left ...
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### Overlapping subproblems in immutable languages

Whenever I solve a problem with overlapping subproblems, I reach for memoization because it's so simple to implement. However, memoizing in an immutable language that doesn't have built-in support for ...
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### Given an array of number, how to calculate to a target value

Chatting with a friend about a game we used to play, and thinking how to implement it in code. Here are the rules: Given a list of number e.g. {1,2,3,4} Try to use all the numbers from the list to ...
• 109
1 vote
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### Dynamic-programming matrix exercise [closed]

I'm practicing with dynamic programming and I'm trying to solve this exercise http://www.geeksforgeeks.org/collect-maximum-points-in-a-grid-using-two-traversals/ But I can't understand how to use ...
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### 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 -> ...
285 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 ...
400 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: https://codereview.stackexchange.com/questions/123641/allocating-a-resource It works fine,...
• 149
1 vote
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### 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 ...
822 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 ...
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### 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 ...
1k 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 ...
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### 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 ...
2k 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 ...
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### 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 (D1,D2,......
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### 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 ...
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### 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 ...
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### 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 out ...
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### 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) ...
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### 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 ...
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### 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: ...
453 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 ...
740 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 ...
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### 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 ...
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1 vote
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### 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 ...
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### 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 ...
• 49
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### 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 ...
• 141
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### 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 ...
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### 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 ...
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### 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 efficient ...
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1 vote
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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1 vote
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### 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 ...