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Knapsack problem

The knapsack problem or rucksack problem is a problem in combinatorial optimization : Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. 0/1 Knapsack Problem: Dynamic Programming Approach: Knapsack Problem: Knapsack is basically means bag. A bag of given capacity. We want to pack n items in your luggage. The ith item is worth v i dollars and weight w i pounds. Take as valuable a load as possible, but cannot exceed W pounds. v i w i W are integers. 0/1 Knapsack Problem: Dynamic Programming Approach: Knapsack Problem: Knapsack is basically means bag. A bag of given capacity. We want to pack n items in your luggage. The ith item is worth v

Eight queens puzzle

Eight queens puzzle Eight Queens Puzzle The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other. Thus, a solution requires that no two queens share the same row, column, or diagonal. The eight queens puzzle is an example of the more general n queens problem of placing n non-attacking queens on an n×n chessboard, for which solutions exist for all natural numbers n with the exception of n=2 and n=3. The eight queens puzzle has 92 distinct solutions. If solutions that differ only by the symmetry operations of rotation and reflection of the board are counted as one, the puzzle has 12 solutions. These are called fundamental solutions; representatives of each are shown below. A fundamental solution usually has eight variants (including its original form) obtained by rotating 90, 180, or 270° and then reflecting each of the four rotational variants in a mirror in a fixed position. However, should a soluti

Sorting Operations in Design Analysis and Algorithm

/* Implementing sorting in a C Program * Written by: Riddhi Lalakiya. */ Sorting Algorithms in C 1.BubbleSort : 1. Algorithm : begin BubbleSort(list) for all elements of list if list[i] > list[i+1] swap(list[i], list[i+1]) end if end for return list end BubbleSort 2. Pseudocode : procedure bubbleSort( list : array of items ) loop = list.count; for i = 0 to loop-1 do: swapped = false for j = 0 to loop-1 do: /* compare the adjacent elements */ if list[j] > list[j+1] then /* swap them */ swap( list[j], list[j+1] ) swapped = true end if end for /*if no number was swapped that means array is sorted now, break the loop.*/ if(not swapped) then break end if end for

Riddhi Lalakiya

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