# Questions tagged [greedy-algorithms]

Questions about algorithms that make at each step the locally optimal choice.

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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 ...
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### Maximum number of similar groups of a given size that can be made from a given array

I am given an array of numbers, not necessarily unique, and the size of a group. Let the array be denoted by $B$ and the size of the group be $A$. I need to find the maximum number of groups with the ...
274 views

### Job Scheduling with deadline with $nlogn$ algorithm

We know that there is a Greedy algorithm for scheduling of $n$ jobs which each job has its own deadline and profit. In greedy algorithm, we sort the set by their profit descendant, And if a job can ...
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### Why this greedy algorithm fails in rod cutting problem?

Recall the rod cutting problem. Given a rod of length $n$ inches and a table of prices $p_{i}$ for $i=1,2,3,4,\,.\,.\,.$ determine the maximum revenue $r_n$ obtainable by cutting up the rod and ...
748 views

### Knapsack with a fixed number of weights

Consider a special case of the knapsack problem in which all weights are integers, and the number of different weights is fixed. For example, the weight of every item is either 1k or 2k or 4k. There ...
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### Selecting elements from two arrays to get a target sum

Let $A$ and $B$ be two arrays of size $n$ with positive integer values. Let $k$ be a given positive integer. Design an algorithm to solve the following problem. For each index $i$ ($1\leq i \leq n$)...
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### Determine aproximation factor in a greedy algorithm

Suppose we have n food dishes associated to a cost c, and we have i guests such that each one of them has a certain number of preferences. We want to choose a menu such that we minimize the cost and ...
101 views

### Tight analysis for the ration of $1-\frac{1}{e}$ in the unweighted maximum coverage problem

The unweighted maximum coverage problem is defined as follows: Instance: A set $E = \{e_1,...,e_n\}$ and $m$ subsets of $E$, $S = \{S_1,...,S_m\}$. Objective: find a subset $S' \subseteq S$ such ...
48 views

### Weighted Activity Selection Problem with allowing shifting starting time

I have some activities with weights, and I would like to select non overlapping activities by maximizing the total weight. This is known problem and solution exists. In my case, I am allowed to ...
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### You have K amoebas and one amoeba can divide into A,B,C amoebas after one instruction then find the minimum no. of instruction to have N amoebas

. You have developed an artificial amoeba, and you can control exactly how it divides. Each individual amoeba can be instructed to divide into A, B, or C amoebas. That is, if you instruct an amoeba to ...
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### Schedule each entree so that all entrees are completed in the shortest amount of time

Lets say we have plenty people to dress up entrees, but only one chef to cook them. Each entree $E_i$, takes $c_i$ time to cook and $d_i$ time to "dress up". The dressing up of entrees can occur while ...
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### Hitting Set Problem with non-minimal Greedy Algorithm

The Hitting Set Problem is defined as having a universal set $\mathfrak{U}$, and nonempty sets $S_i \subseteq \mathfrak{U}$ for $1 \leq i \leq n$, and finding a set $\mathcal{H} \subset \mathfrak{U}$ ...
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### Converting a greedy algorithm to a dynamic programming algorithm

Suppose I have a greedy approach to solve a certain problem. Say, I wish to solve the problem of coloring a particular graph. Now, my naive approach would be: First, find a maximum indpendent set of ...
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### Carpet into Box

Given a carpet of size a * b [length * breadth] and a box of size c * d, one has to fit the carpet in the box in the minimum number of moves. A move is to fold the carpet in half, either by length or ...
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### Length of shortest codeword in Huffman encoding

Under Huffman Encoding, if one character occurs more than 1/3rd of the time, is it guaranteed that there will be at least one character whose codeword is of length 1? I thought of 2 cases where this ...
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### Minimum Spanning Tree with one particular edge minimised(continued)

I have recently encountered a coding problem, specifically, the CCC problem S4. In the problem, it states that you are given a spanning tree, or otherwise a "valid plan of pipes", that connect each ...
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### Minimum spanning tree such that one edge can be minimised

During a computer coding exam, I have encountered such a problem. Given a list of vertexes and edges between the vertexes,and a positive number, D, what is the minimum spanning tree between the ...
581 views

### Merging balls interview problem

Here is an interview problem about balls rolling towards buckets from Sprinklr Interview Experience at GeekforGeeks. You are given $n$ balls on the table and all the balls are rolling towards the ...