yaworsw/euler-manager

---
:id: 107
:name: Minimal network
:url: https://projecteuler.net/problem=107
:content: "The following undirected network consists of seven vertices and twelve
  edges with a total weight of 243.\n\n ![]({{ images_dir }}/p107_1.gif)  \n\nThe
  same network can be represented by the matrix below.\n\n|     
  | **A** | **B** | **C** | **D** | **E** | **F** | **G** |\n| **A** | - | 16 | 12
  | 21 | - | - | - |\n| **B** | 16 | - | - | 17 | 20 | - | - |\n| **C** | 12 | - |
  - | 28 | - | 31 | - |\n| **D** | 21 | 17 | 28 | - | 18 | 19 | 23 |\n| **E** | -
  | 20 | - | 18 | - | - | 11 |\n| **F** | - | - | 31 | 19 | - | - | 27 |\n| **G**
  | - | - | - | 23 | 11 | 27 | - |\n\nHowever, it is possible to optimise the network
  by removing some edges and still ensure that all points on the network remain connected.
  The network which achieves the maximum saving is shown below. It has a weight of
  93, representing a saving of 243 − 93 = 150 from the original network.\n\n ![]({{
  images_dir }}/p107_2.gif)  \n\nUsing [network.txt](project/resources/p107_network.txt)
  (right click and 'Save Link/Target As...'), a 6K text file containing a network
  with forty vertices, and given in matrix form, find the maximum saving which can
  be achieved by removing redundant edges whilst ensuring that the network remains
  connected.\n\n"