# Questions tagged [dynamic-programming]

Questions about problems that can be solved by combining recursively obtained solutions of subproblems.

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### Finding optimal separating value

Problem description We are given two sorted arrays of even numbers: A and B. Values of A are generally supposed to be smaller than values of B. So we are asked to find a value X where X is an odd ...
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### Question on an Algorithm for Longest Increasing Subsequence

I have been reading this paper: https://arxiv.org/abs/2011.10874 This paper presented an exact randomized algorithm with update time $\tilde{O}(n^{0.8})$. I will quickly talk about the overall idea of ...
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### the number of arrangements of N players around a round table, where each player can sit on one of 3 contiguous chairs

Consider the fact that each player can either sit on their desired chair or on the neighbouring chair. Two configurations are distinct if at least one person is sitting in another chair. My attempt ...
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### Minimum number of swaps to make two arrays strictly increasing

I'm trying to understand the solution of the following problem (LC 801): Given two arrays, A and B, of the same nonzero length, find the minimum number of swaps (A[i] <--> B[i]) to make A and B ...
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### Longest path on a full tree

Given a full tree $\ T = (V, E, w)$ I need to find the path with maximum length from root $\\ s$ to any of the leaves. I was thinking I could use some sort of BFS. Because I'm looking for maximum ...
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### Find the minimum subset of a set of numbers with product divisible by a given integer

The following problem was part of a local programming contest I attended..(I solved it via the obvious Brute Force solution) I was wondering whether there was a cleaner Dynamic Programming solution. ...
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### Why is backtracking a necessary step in the Maze problem?

The problem I am working on is specifically this: A Maze is given as N*N binary matrix of blocks where source block is the upper left most block i.e., maze and destination block is lower ...
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### Dynamic programming algorithm to find largest triangle in binary square matrix where elements equal “1”

I'm struck how to find DP recurrence for: You are given a binary square matrix M of size nxn. We define a (p,q, l)-triangle of M, where p >= 1, q >= 1, L >= 1, p+L >= n+1, and q+L >= n+...
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### Dynamic programming substring problem with 4 characters

You start with a string made up of 4 characters: A, B, C, and D. The string can be at most 10^5 characters long. You edit the string in this manner: Split the string between two consecutive ...
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### Calculate the sum of all sub-arrays with given indices

I am new to Algorithms and Competitive Coding. I have a problem as follow: For this problem, the time limit is 1 second so brute force is not a good way to solve. The only way I think must be Dynamic ...
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### how does the shap algorithm work in polynomial time?

I'm trying to understand how the shap algorithm calculates in polynomial time an estimation to the feature attribution function that satisfies the shapely value attributes (specifically for tree based ...
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### Matrix chain multiplication recurrence and its solution

We want to calculate $A_1 \times A_2 \times \cdots \times A_n$, where $A_i$ has dimensions $d_{i-1} \times d_i$. In the classical matrix chain multiplication problem, we wish to minimize the total ...
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### 0/1 Knapsack problem. How does the total weight does not exceed the limit?

I am trying to wrap my head around the knapsack problem algorithm. I understood the most of it except one tiny thing. On the left is the [val,weight] and on the ...
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### Count the possible plans for nurses

I am new to Algorithms and Competitive Coding. I read an exercise paper given by my teacher as below: The director of a hospital want to schedule a working plan for a nurse in a given period of N ...
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### Write recurrence for cost minimization

So I am trying to find the recurrence for this problem but I feel like it is missing something. An ice cream shop is looking to minimize their operation costs, under the given constraints: They are ...
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### Two-Sum - Range Allowance Algorithm Design

🧩 What is the best way to find if there are two individual capacities that sum to a total capacity within a range of plus and minus the total capacity? Optimize for runtime over memory complexity. ...
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### What is the best algorithm to find the optimal path in reducing company's real-estate footprint?

I was hoping someone could point me in the right direction in terms of what type of problem I am describing and what type of algorithm I should use to answer it. Here is the problem: A company is in ...
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### Relationship between dynamic programming and reinforcement learning

I wasn't sure whether to post this here or in the ai stack exchange - please let me know if i need to move my post elsewhere) I have been learning about how dynamic programming can be used as a tool ...
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### Find exact sum in path

So the question is Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path. You can only move down and to ...
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### Two-Sum - Pre-sort Optimization Algorithm Design

🧩 Is it possible to optimize the runtime of a two-sum solution by receiving a pre-sorted input either in ascending or descending order? 🚀 Original Two-Sum Determine whether there are two items whose ...
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### Minimum sum of squared Euclidean distance between two arrays

Question: Given two sorted sequences in increasing order, $X$ and $Y$. $Y$ is of size $k$ and $X$ is of size $m$. I would like to find a subset of $X$, $i.e$, $X'$ of size $k$, and considering the ...