Add example of finding MST using Kruskal's algorithm

+ Using example graph and pseudocode from MIT Algorithms
This commit is contained in:
2021-07-16 18:16:04 -04:00
parent 835dbc7f7d
commit 23c4f0e491
4 changed files with 176 additions and 58 deletions

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@@ -1,7 +1,7 @@
/*##############################################################################
## Author: Shaun Reed ##
## Legal: All Content (c) 2021 Shaun Reed, all rights reserved ##
## About: An example of an object graph implementation ##
## About: An example of a weighted graph implementation ##
## Algorithms in this example are found in MIT Intro to Algorithms ##
## ##
## Contact: shaunrd0@gmail.com | URL: www.shaunreed.com | GitHub: shaunrd0 ##
@@ -15,14 +15,14 @@ int main (const int argc, const char * argv[])
{
// We could initialize the graph with some localNodes...
std::vector<Node> localNodes{
{1, {2, 5}}, // Node 1
{2, {1, 6}}, // Node 2
{3, {4, 6, 7}},
{4, {3, 7, 8}},
{5, {1}},
{6, {2, 3, 7}},
{7, {3, 4, 6, 8}},
{8, {4, 6}},
{1, {{2, 0}, {5, 0}}}, // Node 1
{2, {{1, 0}, {6, 0}}}, // Node 2
{3, {{4, 0}, {6, 0}, {7, 0}}},
{4, {{3, 0}, {7, 0}, {8, 0}}},
{5, {{1, 0}}},
{6, {{2, 0}, {3, 0}, {7, 0}}},
{7, {{3, 0}, {4, 0}, {6, 0}, {8, 0}}},
{8, {{4, 0}, {6, 0}}},
};
Graph bfsGraphInit(localNodes);
@@ -32,14 +32,14 @@ int main (const int argc, const char * argv[])
// Initialize a example graph for Breadth First Search
Graph bfsGraph(
{
{1, {2, 5}}, // Node 1
{2, {1, 6}}, // Node 2...
{3, {4, 6, 7}},
{4, {3, 7, 8}},
{5, {1}},
{6, {2, 3, 7}},
{7, {3, 4, 6, 8}},
{8, {4, 6}},
{1, {{2, 0}, {5, 0}}}, // Node 1
{2, {{1, 0}, {6, 0}}}, // Node 2...
{3, {{4, 0}, {6, 0}, {7, 0}}},
{4, {{3, 0}, {7, 0}, {8, 0}}},
{5, {{1, 0}}},
{6, {{2, 0}, {3, 0}, {7, 0}}},
{7, {{3, 0}, {4, 0}, {6, 0}, {8, 0}}},
{8, {{4, 0}, {6, 0}}},
}
);
// The graph traversed in this example is seen in MIT Intro to Algorithms
@@ -68,12 +68,12 @@ int main (const int argc, const char * argv[])
// Initialize an example graph for Depth First Search
Graph dfsGraph(
{
{1, {2, 4}},
{2, {5}},
{3, {5, 6}},
{4, {2}},
{5, {4}},
{6, {6}},
{1, {{2, 0}, {4, 0}}},
{2, {{5, 0}}},
{3, {{5, 0}, {6, 0}}},
{4, {{2, 0}}},
{5, {{4, 0}}},
{6, {{6, 0}}},
}
);
// The graph traversed in this example is seen in MIT Intro to Algorithms
@@ -89,15 +89,15 @@ int main (const int argc, const char * argv[])
// The book starts on the 'shirt' node (with the number 6, in this example)
Graph topologicalGraph (
{
{1, {4, 5}}, // undershorts
{2, {5}}, // socks
{3, {}}, // watch
{4, {5, 7}}, // pants
{5, {}}, // shoes
{6, {8, 7}}, // shirt
{7, {9}}, // belt
{8, {9}}, // tie
{9, {}}, // jacket
{1, {{4, 0}, {5, 0}}}, // undershorts
{2, {{5, 0}}}, // socks
{3, {}}, // watch
{4, {{5, 0}, {7, 0}}}, // pants
{5, {}}, // shoes
{6, {{8, 0}, {7, 0}}}, // shirt
{7, {{9, 0}}}, // belt
{8, {{9, 0}}}, // tie
{9, {}}, // jacket
}
);
@@ -119,15 +119,15 @@ int main (const int argc, const char * argv[])
// + We have to initialize the graph carefully to get this result -
Graph topologicalGraph2 (
{
{6, {8, 7}}, // shirt
{8, {9}}, // tie
{7, {9}}, // belt
{9, {}}, // jacket
{3, {}}, // watch
{1, {4, 5}}, // undershorts
{4, {5, 7}}, // pants
{5, {}}, // shoes
{2, {5}}, // socks
{6, {{8, 0}, {7, 0}}}, // shirt
{8, {{9, 0}}}, // tie
{7, {{9, 0}}}, // belt
{9, {}}, // jacket
{3, {}}, // watch
{1, {{4, 0}, {5, 0}}}, // undershorts
{4, {{5, 0}, {7, 0}}}, // pants
{5, {}}, // shoes
{2, {{5, 0}}}, // socks
}
);
auto order2 = topologicalGraph2.TopologicalSort(*topologicalGraph2.NodeBegin());
@@ -137,4 +137,31 @@ int main (const int argc, const char * argv[])
order2.pop_back();
}
std::cout << std::endl;
std::cout << "\n\n##### Minimum Spanning Trees #####\n";
// This example graph is seen in MIT Algorithms chapter 23, figure 23.4
// + The result we produce is the same in total weight
// + Differs only in the connection of nodes (2->3) *instead of* (8->1)
// ++ Both of these edges have the same weight, and we do not create a cycle
Graph graphMST(
{
{1, {{2, 4}}},
{2, {{3, 8}}},
{3, {{4, 7}}},
{4, {{5, 9}}},
{5, {{6, 10}}},
{6, {{3, 4}, {4, 14}, {7, 2}}},
{7, {{8, 1}}},
{8, {{1, 8}, {2, 11}, {9, 7}}},
{9, {{3, 2}, {7, 6}}}
}
);
InfoMST resultMST = graphMST.KruskalMST();
std::cout << "Finding MST using Kruskal's...\n\nMST result: \n";
for (const auto &edge : resultMST.edgesMST) {
std::cout << "Connected nodes: " << edge.second.first << "->"
<< edge.second.second << " with weight of " << edge.first << "\n";
}
std::cout << "Total MST weight: " << resultMST.weightMST << std::endl;
}