There are n nodes and m bridges in between these nodes. Print the possible path through each node using each edges (if possible), traveling through each edges only once.
Input : [[0, 1, 0, 0, 1], [1, 0, 1, 1, 0], [0, 1, 0, 1, 0], [0, 1, 1, 0, 0], [1, 0, 0, 0, 0]] Output : 5 -> 1 -> 2 -> 4 -> 3 -> 2 Input : [[0, 1, 0, 1, 1], [1, 0, 1, 0, 1], [0, 1, 0, 1, 1], [1, 1, 1, 0, 0], [1, 0, 1, 0, 0]] Output : "No Solution"
It is one of the famous problems in Graph Theory and known as problem of “Seven Bridges of Königsberg”. This problem was solved by famous mathematician Leonhard Euler in 1735. This problem is also considered as the beginning of Graph Theory.
The problem back then was that: There was 7 bridges connecting 4 lands around the city of Königsberg in Prussia. Was there any way to start from any of the land and go trough each of the bridges once and only once? Please see these wikipedia images for more clarity.
Euler first introduced graph theory to solve this problem. He considered each of the lands as a node of a graph and each bridge in between as an edge in between. Now he calculated if there is any Eulerian Path in that graph. If there is an Eulerian path then there is a solution otherwise not.
Problem here, is a generalized version of the problem in 1735.
Below is the implementation :
2-0 0-1 1-2 2-3 1-0 0-2 2-3 3-1 1-0 0-2
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