Task 01: You are given a weighted, directed graph with N nodes and M edges. Each edge is represented as a triple (u, v, w), where u and v are the nodes connected by the edge and w is the weight of the edge. Your task is to find the shortest path from a source node S to all other nodes in the graph using Dijkstra's algorithm. You should output the shortest distance from the source node to each of the other nodes in the graph. If a node is not reachable from the source node, its distance should be represented as -1. Input The first line of the input contains two integers, N and M (1 <= N<= 1000, 1 <= M <= 100000) denoting the number of nodes and edges in the graph, respectively. The next M lines each contain three integers, u, v (1 <= u, v <= N), and w (1 <= w <= 100) denoting an edge from node u to node v with weight w. The last line of the input contains an integer S (1 <= S <= N) denoting the source node. Output Output N space-separated integers, where the i-th integer represents the shortest distance from the source node to node i. If a node is not reachable from the source node, output -1 instead.
Task 01: You are given a weighted, directed graph with N nodes and M edges. Each edge is represented as a triple (u, v, w), where u and v are the nodes connected by the edge and w is the weight of the edge. Your task is to find the shortest path from a source node S to all other nodes in the graph using Dijkstra's algorithm. You should output the shortest distance from the source node to each of the other nodes in the graph. If a node is not reachable from the source node, its distance should be represented as -1. Input The first line of the input contains two integers, N and M (1 <= N<= 1000, 1 <= M <= 100000) denoting the number of nodes and edges in the graph, respectively. The next M lines each contain three integers, u, v (1 <= u, v <= N), and w (1 <= w <= 100) denoting an edge from node u to node v with weight w. The last line of the input contains an integer S (1 <= S <= N) denoting the source node. Output Output N space-separated integers, where the i-th integer represents the shortest distance from the source node to node i. If a node is not reachable from the source node, output -1 instead.
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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Question
Please use python and python file i/o to solve the problem. Create an input file input1_1.txt take input from sample input as shown below, solve the problem and print the output to output1_1.txt file as shown in the question.
Transcribed Image Text:Task 01:
You are given a weighted, directed graph with N nodes and M
edges. Each edge is represented as a triple (u, v, w), where u
and v are the nodes connected by the edge and w is the weight of
the edge.
Your task is to find the shortest path from a source node S to
all other nodes in the graph using Dijkstra's algorithm. You
should output the shortest distance from the source node to each
of the other nodes in the graph. If a node is not reachable from
the source node, its distance should be represented as -1.
Input
The first line of the input contains two integers, N and M (1 <=
N <= 1000, 1 <= M <= 100000) denoting the number of nodes and
edges in the graph, respectively.
The next M lines each contain three integers, u, v (1 <= u, v <=
N), and w (1 <= w <= 100) denoting an edge from node u to node v
with weight w.
The last line of the input contains an integer S (1 <= S <= N)
denoting the source node.
Output
Output N space-separated integers, where the i-th integer
represents the shortest distance from the source node to node i.
If a node is not reachable from the source node, output -1
instead.
Transcribed Image Text:58
125
1 3 7
14 2
24 3
254
358
4 3 2
5 4 10
1
Sample Input 2
68
1 2 3
1 3 6
3 42
452
5 2 10
5 1 1
622
6 3 10
3
05429
Sample Output 2
5 80 24-1
Explanation of Sample Input 1
5
Distance from node 1 to node 1 is 0.
Distance from node 1 to node 2 is 5.
Distance from node 1 to node 3 is 4.
Distance from node 1 to node 4 is 2.
Distance from node 1 to node 5 is 9.
Sample Graph 2
N
6
2
10
3
7
10
3
2
10
2
Using Dijkstra's algorithm, the shortest path from node 1 to all
other nodes in the given graph is:
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