Homework Answers
Bin Packing Problem:
- Actually.. Bin Packing Problem is a Mathematical Problem Which is a combinatorial of NP-hard Problem.
- Bin Packing Problem is The problem Various Objects of certain sizes into a minimum numbers of bin with a fixed size.
Applications:
- Loading of containers like trucks.
- Placing data on multiple disks.
- Job scheduling.
- Packing a Advertisement in fixed length radio/TV station breaks.
Different Type Algorithm solve the Bin Packing Problem:
- Next Fit
- Best Fit
- First Fit
- First Fit Decreasing
Add Answer to:
This is all I have
2. Consider the following approximation algorithm for the bin packing problem....
In the bin packing problem, items of different weights (or sizes) must be packed into a...
In the bin packing problem, items of different weights (or sizes) must be packed into a finite number of bins each with the capacity C in a way that minimizes the number of bins used. The decision version of the bin packing problem (deciding if objects will fit into <= k bins) is NP-complete. There is no known polynomial time algorithm to solve the optimization version of the bin packing problem. In this practice problem you will be examining three...
Give an algorithm that minimizes the maximum load of bins for the following description: We are given a list of n items with sizes s1, 82,. . , Sn A sequential bin packing of these at in sad ins (Tha...
Give an algorithm that minimizes the maximum load of bins for
the following description:
We are given a list of n items with sizes s1, 82,. . , Sn A sequential bin packing of these at in sad ins (That is, each bin has items si, si+1,. , s, for some indices i < j.) Bins have unbounded capacities. The load of a bin is the sum of the elements in it. Give an algorithm that determines a sequential packing...
Consider the following two problems: Bin Packing: Given n items with positive integer sizes s1, s2,...
Consider the following two problems: Bin Packing: Given n items with positive integer sizes s1, s2, . . . , sn, a capacity C for bins and a positive integer k, is it possible to pack the n items using at most k bins? Partition: Given a set S of n integers, is it possible to partition S into two subsets S1 and S2 so that the sum of the integers in S1 is equal to the sum of the...
Consider the following four problems: Bin Packing: Given n items with positive integer sizes s1,s2,...,sn, a...
Consider the following four problems: Bin Packing: Given n items with positive integer sizes s1,s2,...,sn, a capacity C for bins and a positive integer k, is it possible to pack the n items using at most k bins? Partition: Given a set S of n integers, is it possible to partition S into two subsets S1 and S2 so that the sum of the integers in S1 is equal to the sum of the integers in S2? Longest Path: Given...
[Recursive Cost] [ALGORITHM] Improving Efficiency PLEASE explain in DETAIL the following question in detail. The algorithm...
[Recursive Cost] [ALGORITHM] Improving
Efficiency
PLEASE explain in DETAIL the following question in detail. The
algorithm is also given below. Thank You!
1.a) Define recursively the worst case cost Kn of the Knapsack
function for n items. Remember that you need to provide both the
base case and the recurrence relation. Also do not forget to
include the cost of the function Worth in your cost. Justify your
answer (i.e. explain what each component of the formula
represents). [5points]
1.b) Use...
Suppose you have a minimization problem and an algorithm A, that has an approximation ratio of...
Suppose you have a minimization problem and an algorithm A, that has an approximation ratio of 4. When run on some input I, A produced a solution with cost 20. What can you say about the optimal answer (let's call it OPT)? Mark “true" or "false" for inequalities below and briefly explain your answer(s). • OP T5 • OP T < 5 • OP T >80 • OP T < 80
#3. Suppose you have a minimization problem and an algorithm A, that has an approximation ratio...
#3. Suppose you have a minimization problem and an algorithm A, that has an approximation ratio of 4. When run on some input I, A produced a solution with cost 20. What can you say about the optimal answer (let's call it OPT)? Mark "true" or "false" for inequalities below and briefly explain your answer(s). • OPT 25 • OPT<5 • OPT> 80 • OP T S 80
Q4) [5 points] Consider the following two algorithms: ALGORITHM 1 Bin Rec(n) //Input: A positive decimal...
Q4) [5 points] Consider the following two algorithms: ALGORITHM 1 Bin Rec(n) //Input: A positive decimal integer n llOutput: The number of binary digits in "'s binary representation if n1 return 1 else return BinRec(ln/2)) +1 ALGORITHM 2 Binary(n) tive decimal integer nt io 's binary representation //Output: The number of binary digits in i's binary representation count ←1 while n >1 do count ← count + 1 return count a. Analyze the two algorithms and find the efficiency for...
Consider the following greedy algorithm for the knapsack problem: each time we pick the item with...
Consider the following greedy algorithm for the knapsack problem: each time we pick the item with the highest value to weight ratio to the bag. Skip items that will make the total weight exceeded the capacity of the bag. Find a counterexample to show that this approach will not work, and the result could be 100 times worse than the optimal solution. That is, construct a table of set of items with weight and values and find a bag capacity...
Can I get some help with this question for c++ if you can add some comments...
Can I get some help with this question for c++ if you can add
some comments too to help understand that will be much
appreciated.
Code:
#include <cstdlib>
#include <getopt.h>
#include <iostream>
#include <string>
using namespace std;
static long comparisons = 0;
static long swaps = 0;
void swap(int *a, int *b)
{
// add code here
}
void selectionSort(int *first, int *last)
{
// add code here
}
void insertionSort(int *first, int *last)
{
// add code here
}...
Give an algorithm that minimizes the maximum load of bins for
the following description:
We are given a list of n items with sizes s1, 82,. . , Sn A sequential bin packing of these at in sad ins (That is, each bin has items si, si+1,. , s, for some indices i < j.) Bins have unbounded capacities. The load of a bin is the sum of the elements in it. Give an algorithm that determines a sequential packing...
[Recursive Cost] [ALGORITHM] Improving
Efficiency
PLEASE explain in DETAIL the following question in detail. The
algorithm is also given below. Thank You!
1.a) Define recursively the worst case cost Kn of the Knapsack
function for n items. Remember that you need to provide both the
base case and the recurrence relation. Also do not forget to
include the cost of the function Worth in your cost. Justify your
answer (i.e. explain what each component of the formula
represents). [5points]
1.b) Use...
Suppose you have a minimization problem and an algorithm A, that has an approximation ratio of 4. When run on some input I, A produced a solution with cost 20. What can you say about the optimal answer (let's call it OPT)? Mark “true" or "false" for inequalities below and briefly explain your answer(s). • OP T5 • OP T < 5 • OP T >80 • OP T < 80
#3. Suppose you have a minimization problem and an algorithm A, that has an approximation ratio of 4. When run on some input I, A produced a solution with cost 20. What can you say about the optimal answer (let's call it OPT)? Mark "true" or "false" for inequalities below and briefly explain your answer(s). • OPT 25 • OPT<5 • OPT> 80 • OP T S 80
Q4) [5 points] Consider the following two algorithms: ALGORITHM 1 Bin Rec(n) //Input: A positive decimal integer n llOutput: The number of binary digits in "'s binary representation if n1 return 1 else return BinRec(ln/2)) +1 ALGORITHM 2 Binary(n) tive decimal integer nt io 's binary representation //Output: The number of binary digits in i's binary representation count ←1 while n >1 do count ← count + 1 return count a. Analyze the two algorithms and find the efficiency for...
Can I get some help with this question for c++ if you can add
some comments too to help understand that will be much
appreciated.
Code:
#include <cstdlib>
#include <getopt.h>
#include <iostream>
#include <string>
using namespace std;
static long comparisons = 0;
static long swaps = 0;
void swap(int *a, int *b)
{
// add code here
}
void selectionSort(int *first, int *last)
{
// add code here
}
void insertionSort(int *first, int *last)
{
// add code here
}...
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