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# DSA

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# DSA

Knapsack Problem, traveling sales Problem

Knapsack Problem, traveling sales Problem

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### DSA

1. 1. NADAR SARASWATHI COLLEGE OF ARTS AND SCIENCE DEPARTMENT OF COMPUTER SCIENCE KNAPSACK PROBLEMS NAME : P.ANUSUYA CLASS : I-M.SC(CS)
2. 2. KNAPSACK PROBLEM : • Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack. In other words, given two integer arrays val[0..n-1] and wt[0..n-1] which represent values and weights associated with n items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of val[] such that sum of the weights of this subset is smaller than or equal to W. • You cannot break an item, either pick the complete item or don’t pick it (0-1 property).
3. 3. KNAPSACK PROBLEM EXAMPLE : You are given weights and values of N items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack. Note that we have only one quantity of each item. In other words, given two integer arrays val[0..N-1] and wt[0..N-1] which represent values and weights associated with N items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of val[] such that sum of the weights of this subset is smaller than or equal to W. You cannot break an item, either pick the complete item or don’t pick it (0-1 property).Complete the function knapSack() which takes maximum capacity W, weight array wt[], value array val[], and the number of items n as a parameter and returns the maximum possible value you can get.
4. 4. EXAMPLE 1&2 :
5. 5. TRAVELING SALES PROBLEM : • Given a set of cities and distances between every pair of cities, the problem is to find the shortest possible route that visits every city exactly once and returns to the starting point. • Note the difference between Hamiltonian Cycle and TSP. The Hamiltonian cycle problem is to find if there exists a tour that visits every city exactly once. Here we know that Hamiltonian Tour exists (because the graph is complete) and in fact, many such tours exist, the problem is to find a minimum weight Hamiltonian Cycle. • For example, consider the graph shown in the figure on the right side. A TSP tour in the graph is 1-2-4-3-1. The cost of the tour is 10+25+30+15 which is 80. • The problem is a famous NP-hard problem. There is no polynomial-time known solution for this problem.
6. 6. EFFICIENCY CONSIDERATION : • The efficiency of an algorithm defines the number of computational resources used by an algorithm and time taken by an algorithm to produce the desired result. • An algorithm which takes fewer resources and computes results in a minimum time for a problem then that algorithm is known as efficient. • The efficiency of an algorithm defines the number of computational resources used by an algorithm and time taken by an algorithm to produce the desired result. • The efficiency of the algorithm is measured based on the usage of different resources and minimum running time. • Since every algorithm uses computer resources to run, But to analyze an algorithm, execution time and internal memory are essential to consider.
7. 7. •THANK YOU ☺️