Table of Contents

## How do you find the optimal solution for a knapsack problem?

Weight = {2, 3, 5, 7, 1, 4, 1}

- To prove: Optimal solution that gives maximum profit.
- Proof:
- Step 1: (To find profit/ weight ratio)
- Step 2: (Arrange this profit/weight ratio in non-increasing order as n values) Since the highest profit/weight ratio is 6.
- Order = (5, 1, 6, 3, 7, 2, 4)

**What is the formula for calculating optimal solution in 0-1 knapsack?**

Then S’ = S – {i} is an optimal solution for W – wi dollars and the value to the solution S is Vi plus the value of the sub-problem. We can express this fact in the following formula: define c[i, w] to be the solution for items 1,2, ¦ , i and the maximum weight w.

### Can a greedy algorithm produce an optimal solution?

A greedy algorithm is a simple, intuitive algorithm that is used in optimization problems. The algorithm makes the optimal choice at each step as it attempts to find the overall optimal way to solve the entire problem. However, in many problems, a greedy strategy does not produce an optimal solution.

**Why does greedy algorithm does not work for the 0-1 knapsack problem?**

Each item is taken or not taken. Cannot take a fractional amount of an item taken or take an item more than once. It cannot be solved by the Greedy Approach because it is enable to fill the knapsack to capacity. Greedy Approach doesn’t ensure an Optimal Solution.

#### What is a 0-1 knapsack problem?

Definition. The most common problem being solved is the 0-1 knapsack problem, which restricts the number of copies of each kind of item to zero or one. Given a set of items numbered from 1 up to , each with a weight and a value , along with a maximum weight capacity , maximize subject to and .

**What is the time complexity of 0-1 knapsack problem?**

The time complexity of this naive recursive solution is exponential (2^n). In the following recursion tree, K() refers to knapSack(). The two parameters indicated in the following recursion tree are n and W. The recursion tree is for following sample inputs.

## How do you solve 0 1 knapsack problem using backtracking?

For the given set of items and knapsack capacity = 5 kg, find the optimal solution for the 0/1 knapsack problem making use of dynamic programming approach….Problem-

Item | Weight | Value |
---|---|---|

1 | 2 | 3 |

2 | 3 | 4 |

3 | 4 | 5 |

4 | 5 | 6 |

**How many types of knapsack problems are there?**

There are different kind of knapsack problems: 0-1 Knapsack Problem †’ In this type of knapsack problem, there is only one item of each kind (or we can pick only one). So, we are available with only two options for each item, either pick it (1) or leave it (0) i.e., xiˆˆ{0,1} x i ˆˆ { 0 , 1 } .

### Which of the following methods can be used to solve the 0 1 knapsack problem?

Which of the following methods can be used to solve the Knapsack problem? Explanation: Brute force, Recursion and Dynamic Programming can be used to solve the knapsack problem.

**What is DP in Java?**

Dynamic Programming (DP) is an algorithmic technique for solving an optimization problem by breaking it down into simpler subproblems and utilizing the fact that the optimal solution to the overall problem depends upon the optimal solution to its subproblems.

#### What is greedy method in algorithm?

Greedy is an algorithmic paradigm that builds up a solution piece by piece, always choosing the next piece that offers the most obvious and immediate benefit. So the problems where choosing locally optimal also leads to global solution are best fit for Greedy. For example consider the Fractional Knapsack Problem.

**What is the time complexity of greedy knapsack problem?**

Explanation: As the main time taking a step is of sorting so it defines the time complexity of our code. So the time complexity will be O(n log n) if we use quick sort for sorting. 6. Fractional knapsack problem can be solved in time O(n).

## What is the difference between knapsack and 0 1 knapsack problem?

In the 0“1 Knapsack problem, we are not allowed to break items. We either take the whole item or don’t take it. In Fractional Knapsack, we can break items for maximizing the total value of knapsack. This problem in which we can break item also called fractional knapsack problem.

**Which of the following is not greedy algorithm?**

Computer Science Engineering (CSE) Question The Bellman-Ford algorithm is a graph search algorithm that finds the shortest path between a given source vertex and all other vertices in the graph. This algorithm can be used on both weighted and unweighted graphs.

### What is the solution to the fractional knapsack problem?

This problem in which we can break an item is also called the fractional knapsack problem. A brute-force solution would be to try all possible subset with all different fraction but that will be too much time taking. An efficient solution is to use Greedy approach.

**What is the use of knapsack problem?**

The branch and bound algorithm to solve the 0-1 knapsack problem, one of the most widely-used combinatorial optimization algorithms, is used to capture the customer values and the discrete characteristics of loads. The objective of the model is to maximize customer values within given supply capacity.

#### What is the other name of Dijkstra algorithm?

Dijkstra’s algorithm finds the shortest paths from a given node to all other nodes in a graph. Dijkstra’s algorithm (or Dijkstra’s Shortest Path First algorithm, SPF algorithm) is an algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks.

**Is selection sort greedy?**

A selection sort could indeed be described as a greedy algorithm, in the sense that it: tries to choose an output (a permutation of its inputs) that optimizes a certain measure (“sortedness”, which could be measured in various ways, e.g. by number of inversions), and.

## What is the time complexity of Dijkstra’s algorithm?

Time Complexity of Dijkstra’s Algorithm is O ( V 2 ) but with min-priority queue it drops down to O ( V + E l o g V ) .

**What is the best shortest path algorithm?**

What Is the Best Shortest Path Algorithm?

- Dijkstra’s Algorithm. Dijkstra’s Algorithm stands out from the rest due to its ability to find the shortest path from one node to every other node within the same graph data structure.
- Bellman-Ford Algorithm.
- Floyd-Warshall Algorithm.
- Johnson’s Algorithm.
- Final Note.

### How do you use Dijkstra’s algorithm?

We step through Dijkstra’s algorithm on the graph used in the algorithm above:

- Initialize distances according to the algorithm.
- Pick first node and calculate distances to adjacent nodes.
- Pick next node with minimal distance; repeat adjacent node distance calculations.
- Final result of shortest-path tree.

**What is Dijkstra’s shortest path algorithm?**

Dijkstra’s algorithm to find the shortest path between a and b. It picks the unvisited vertex with the lowest distance, calculates the distance through it to each unvisited neighbor, and updates the neighbor’s distance if smaller. Mark visited (set to red) when done with neighbors.

#### Is Dijkstra BFS or DFS?

According to this page, Dijkstra’s algorithm is just BFS with a priority queue.

**Is Dijkstra A greedy algorithm?**

It is a greedy algorithm that solves the single-source shortest path problem for a directed graph G = (V, E) with nonnegative edge weights, i.e., w (u, v) ‰¥ 0 for each edge (u, v) ˆˆ E.

## What is shortest path algorithm?

Shortest path algorithms are a family of algorithms designed to solve the shortest path problem. For simplicity and generality, shortest path algorithms typically operate on some input graph, G. This graph is made up of a set of vertices, V, and edges, E, that connect them.

**Why is the shortest path important?**

Finding the shortest path (SP) in a large-scale network analysis between any two nodes is a tough but very significant task. The SP can help us to analyze the information spreading performance and research the latent relationship in the weighted social network, and so on.

### How do you solve the shortest path problem?

The most important algorithms for solving this problem are:

- Dijkstra’s algorithm solves the single-source shortest path problem with non-negative edge weight.
- Bellman“Ford algorithm solves the single-source problem if edge weights may be negative.

**How do you find the shortest path?**

Dijkstra’s algorithm can be used to determine the shortest path from one node in a graph to every other node within the same graph data structure, provided that the nodes are reachable from the starting node. Dijkstra’s algorithm can be used to find the shortest path.

#### Can we use DFS to find shortest path?

DFS does not necessarily yield shortest paths in an undirected graph. If you try to find the shortest path from one node to another using DFS, then you will get the wrong answer unless you follow the edge directly connecting the start and destination nodes.

**What is single source shortest path algorithm?**

The single source shortest path algorithm (for arbitrary weight positive or negative) is also known Bellman-Ford algorithm is used to find minimum distance from source vertex to any other vertex. At first it finds those distances which have only one edge in the path.