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Computer Science Stack Exchange

Questions tagged [optimal-strategy]

Finding an optimal strategy is common in games, where given a set of players the goal is to maximize the points of some fixed player. It is also common in resources allocation.

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Correctness of a greedy Algorithm on Knockout Tournaments

You are given a function $\operatorname{rk}:\{1\dots 2^k\}\rightarrow \mathbb{N^+}$ representing the ranks of the players $1\dots2^k$ in a participating in a tournament. The tournament evolves in a random way, so that when player $i$ faces player…
Guanaco96
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Is there a more efficient way to obtain the optimal input sequence in this finite-state system

Context: Consider $M$ finite state systems with evolution given by: $$ x^i_{k+1} = f(x_k^i,u_k) $$ where $x_k^i\in\{1,\dots,X\}$ is the state of system $i\in\{1,\dots,M\}$, $k\geq 0$, and $u_k\in\{1,\dots, U\}$ is some input which we can use at…
FeedbackLooper
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One-dimensional packing problem: Optimal decomposition of music structure

I am currently working on my Master thesis on the visualization of music structure and I'm looking to find an optimal description of repetitions found in a piece of music. Problem Description Given a section range in a song in seconds (or samples) ,…
Job Savelsberg
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Is there any way to program a chess bot which never loses?

Even if it may be complicated, is it possible with the present technology?
Ayush
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Best algorithm to evaluate a function that takes the elements of all possible combinations of N numbers

Consider a set $A$ containing $N$ real numbers. Let $f(X_{r,k})$ represent a function, where $X_{r,k}\subseteq A$ denotes the $k$th combination of $r$ elements from $A$, with $1 \leq k \leq \binom{N}{r}$ and $0 \leq r \leq N$. What is the most…
GeoArt
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Allocating m rooms of varying capacity to n booking requests of varying sizes

I am developing a system which performs automated room allotment. We have finite number of rooms, each with varying capacity. Each booking request is also of varying size. The goal here is to minimize number of rooms used and minimize room capacity…
Ravi M Patel
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Does the obvious way to seat the champion minimize the total number of times a player has to stand?

There is a chess tournament planned. It is a single-elimination tournament, and for spectacle purposes, only one match at a time will take place, on a table in the middle of the stage. The winner of a match will have to stand offstage if they don't…
Nathaniel
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Maximize the minimum gap while scheduling within intervals?

Problem There are N intervals in which a particular integer can be chosen. What is the maximum possible minimum gap between each integer if one integer is chosen for each of those intervals? For example: Input: [2,4], [0,8], [3,15], [10,20] We shall…
Shubhraneel Pal
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Responsive input sliders - is there a better way?

I am building an app where a user controls inputs via multiple sliders each with discrete steps. The app then uses the combination of slider values to run some calculations and returns back an output value. The sliders are meant to be highly…
Anubhav
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Allocation of many students to many schools based on capacity

Say I have a set of schools coordinates (S). I also have a set of neighborhoods centroid coordinates (N). I know how many kids are in each neighborhood, and they are categorized as either primary, middle or high school. So, in other words, N =…
William Abma
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Extract dominant value per column with single value per row in a matrix

Given a matrix $A \in \mathbb{R}_{+}^{n \times m}$ where $m \geq n$. I want to convert it into a form where there is a single $1$ per row yet no more than a single $1$ per column. The logic is convert the highest sum of values into 1. For instance,…
Avi T
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Efficient way to implement a bit-wise counter that becomes 1 every (k*n)+i times

My question is about LeetCode "137.Single Number II": 137.Single Number II Given an integer array nums where every element appears three times except for one, which appears exactly once. Find the single element and return it. You must implement a…
R. Javid
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Possible to solve a combinatorial game with integer programming?

I recently had the idea that it would be neat if it were possible to make a SAT solver play combinatorial games. To start, I'm trying a relatively simple case of solving single-stack Misère Nim through integer programming: there's a fixed limit $L$…
Exalted Toast
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How to find optimizers with computer in this kind of minimax problem

I have a minimax problem of the form $$\max_{\substack{u_1,\dots,u_n \ge 0 \\ u_1+\dots+u_n = 1}} \min_{\substack{v_1,\dots,v_m \ge 0 \\ v_1+\dots+v_m = 1 \\ v_{j_1} \le v_{j_2} \hspace{1mm} \forall (j_1,j_2) \in J}} \sum_{i=1}^n \sum_{j=1}^m…
mathworker21
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Variant of the Knapsack Problem 0-1 - One item from each set and zero-weighted items

I understand the basics of the 0-1 problem and its solution. I have a variant of it that I'm trying to solve in a decent way and I'm struggling on it, mostly because of the 0-weighted items. These are the rules: I have k finite sets of items. Each…
boulayo
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