# 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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### Guessing number game "hot" or "cold"

I thought up this problem and am trying to come up with an optimal solution. I am thinking of a number uniformly randomly between 1-100, inclusive. If you guess the number, you "win". Else ...
• 11
1 vote
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1 vote
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### Best approach to resource allocation problem

Problem The enemy army has taken $n$ of our cities. In each city $i$ the enemy has placed $e_i$ soldiers. We have $n$ teams, each team $j$ with $d_j$ soldiers. If we place more soldiers in a city ...
• 163
136 views

### 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 ...
92 views

### 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 ...
59 views

### Can we get any subsequence of size $\ge \lfloor \frac{n}{2} \rfloor$ in a sorted order from a sequence in linear time?

Given a sequence $A$ of $N$ distinct integers, does there exist a strategy to get at least one subsequence with size $\geq \lfloor \frac{N}{2} \rfloor$ of the sequence in sorted order in $O(n)$ time? ...
31 views

### 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 ...
• 121
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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, ...
• 123
1 vote
676 views

### How can I prove that my greedy algorithm for least guards is optimal?

This is the problem: An art gallery hired you to put guards so they can monitor artworks in a hallway. The goal is to minimize the amount of guards needed in this hallway. Each guard has a range of ...
• 251
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 ...