**Topological Sort Algorithm Explanation and Redesign**This image contains a Python function `topsort(G)` that performs a topological sort on a directed acyclic graph (DAG) represented as a dictionary `G`. The algorithm uses an in-degree method to determine a valid sort order. Here's a detailed breakdown:### Original Algorithm:1. **Calculate In-degrees:** - The `count` dictionary stores the in-degree (number of incoming edges) for each node. It is initialized by setting each node's count to 0 and then incremented for every incoming edge to that node.2. **Initialize Queue:** - The list `Q` collects nodes with an in-degree of 0. These nodes have no dependencies and can be processed initially.3. **Process Nodes:** - An empty list `S` is initialized to hold the sorted order of nodes. - Using a while loop, the algorithm continues while there are nodes in `Q`. - Pop a node `u` from `Q`, append it to `S`, and decrement the in-degree of all its neighbors. - If any neighbor’s in-degree becomes 0, it is added to `Q` for future processing.### Requested Modification:- The task is to redesign the algorithm to select and process the last node in the queue `Q` at each iteration rather than the first.### Redesigned Algorithm:To adjust the implementation so that it selects the last node in each iteration:```pythondef topsort(G): count = dict((u, 0) for u in G) # The in-degree for each node for u in G: for v in G[u]: count[v] += 1 # Count every in-edge Q = [u for u in G if count[u] == 0] # Valid initial nodes S = [] # The result while Q: # While we have start nodes... u = Q.pop() # Pick the last one S.append(u) # Use it as first of the rest for v in G[u]: count[v] -= 1 # "Uncount" its out-edges if count[v] == 0: # New valid start nodes? Q.append(v) # Deal with them next return S```### Explanation of Changes:- **

EXPLANATION: Define function “topsort” with graph, start and path array as the parameters. Define…

Redesign the topsort algorithm below so that it selects the last node in each iteration rather than the first. Please use python ad show all work so I can better understand the problem. def topsort(G): count = dict((u, 0) for u in G) for u in G: # The in-degree for each node for v in G[u]: count[v] += 1 Q = [u for u in G if count[u] == 0] S - () while Q: # Count every in-edge # Valid initial nodes # The result # while we have start nodes... # Pick one # Use it as first of the rest u - Q. pop() S. append (u) for v in G[u]: count[v] -- 1 if count[v] == 0: Q.append(v) # "Uncount" its out-edges # New valid start nodes? # Deal with them next return S

Redesign the topsort algorithm below so that it selects the last node in each iteration rather than the first. Please use python ad show all work so I can better understand the problem. def topsort(G): count = dict((u, 0) for u in G) for u in G: # The in-degree for each node for v in G[u]: count[v] += 1 Q = [u for u in G if count[u] == 0] S - () while Q: # Count every in-edge # Valid initial nodes # The result # while we have start nodes... # Pick one # Use it as first of the rest u - Q. pop() S. append (u) for v in G[u]: count[v] -- 1 if count[v] == 0: Q.append(v) # "Uncount" its out-edges # New valid start nodes? # Deal with them next return S

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Randomized Select Algorithm

A randomized algorithm is defined as one that uses a certain amount of randomization in its logic or operation. It is said to be an algorithm that depends on the random number to perform its operation. It is used for reducing the overall time complexity, space complexity in the standard algorithm. The randomized algorithm uses the concept of random numbers to find the solutions to the different kinds of problems and also to improve the problem solutions.

Question

**Topological Sort Algorithm Explanation and Redesign**

This image contains a Python function `topsort(G)` that performs a topological sort on a directed acyclic graph (DAG) represented as a dictionary `G`. The algorithm uses an in-degree method to determine a valid sort order. Here's a detailed breakdown:

### Original Algorithm:

1. **Calculate In-degrees:**
- The `count` dictionary stores the in-degree (number of incoming edges) for each node. It is initialized by setting each node's count to 0 and then incremented for every incoming edge to that node.

2. **Initialize Queue:**
- The list `Q` collects nodes with an in-degree of 0. These nodes have no dependencies and can be processed initially.

3. **Process Nodes:**
- An empty list `S` is initialized to hold the sorted order of nodes.
- Using a while loop, the algorithm continues while there are nodes in `Q`.
- Pop a node `u` from `Q`, append it to `S`, and decrement the in-degree of all its neighbors.
- If any neighbor’s in-degree becomes 0, it is added to `Q` for future processing.

### Requested Modification:

- The task is to redesign the algorithm to select and process the last node in the queue `Q` at each iteration rather than the first.

### Redesigned Algorithm:

To adjust the implementation so that it selects the last node in each iteration:

```python
def topsort(G):
count = dict((u, 0) for u in G) # The in-degree for each node
for u in G:
for v in G[u]:
count[v] += 1 # Count every in-edge

Q = [u for u in G if count[u] == 0] # Valid initial nodes
S = [] # The result

while Q: # While we have start nodes...
u = Q.pop() # Pick the last one
S.append(u) # Use it as first of the rest
for v in G[u]:
count[v] -= 1 # "Uncount" its out-edges
if count[v] == 0: # New valid start nodes?
Q.append(v) # Deal with them next

return S
```

### Explanation of Changes:

- **

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