added examples and README

README.md

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+# Max Flow using Dinic's Algorithm
+
+## Installation
+
+This project does not have any specific requirements other than a cpp compiler. The installations process follows the CMake procedure:
+
+```
+git clone https://git.pranger.xyz/sp/MaxFlowDinic
+cd MaxFlowDinic
+mkdir build
+cd build
+cmake .. && make
+```
+
+## Usage
+
+To display the help message:
+
+```
+> ./build/maxFlow -h
+
+You need to pass either and input graph file or an input graph string.
+Allowed options:
+  -h, --help              Print this help message.
+  -f, --input-file arg    Filename of input graph file.
+  -s, --input-string arg  Input graph string.
+  -o, --stdout            Output to stdout.
+  -p, --output-file arg   Filename for output.
+  -a, --max-flow          Include verbose information about the max flow to the output.
+  -m, --minimum-cut       Include the minimum cut set to the output.
+  -v, --verbose           Output verbose algorithmic information and runtime. Pass twice to get information about all augmenting paths computed.
+```
+
+The examples folder features a few toy examples. Using the `-f` option to pass the path to an input file and `-mavv` gives a verbose output.
+
+For example:
+```
+>./build/maxFlow -f examples/1.txt -mavv
+#Vertices: 10
+#Arc: 14
+Source: 1, Sink: 10
+Vertices: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
+  1 -> 2 capacity = 5
+  2 -> 10 capacity = 4
+  1 -> 10 capacity = 7
+  1 -> 3 capacity = 8
+  3 -> 10 capacity = 9
+  1 -> 4 capacity = 3
+  4 -> 7 capacity = 1
+  7 -> 10 capacity = 1
+  1 -> 5 capacity = 3
+  5 -> 8 capacity = 4
+  8 -> 10 capacity = 6
+  1 -> 6 capacity = 7
+  6 -> 9 capacity = 6
+  9 -> 10 capacity = 5
+Found max flow |x| = 28
+Max Flow per arc:
+  1 -> 2 flow = 4/5
+  2 -> 10 flow = 4/4
+  1 -> 10 flow = 7/7
+  1 -> 3 flow = 8/8
+  3 -> 10 flow = 8/9
+  1 -> 4 flow = 1/3
+  4 -> 7 flow = 1/1
+  7 -> 10 flow = 1/1
+  1 -> 5 flow = 3/3
+  5 -> 8 flow = 3/4
+  8 -> 10 flow = 3/6
+  1 -> 6 flow = 5/7
+  6 -> 9 flow = 5/6
+  9 -> 10 flow = 5/5
+Min Cut X: {1, 2, 4, 6, 9}
+Complement(X): {3, 5, 7, 8, 10}
+Elapsed time: 1ms (1046µs).
+Computation Statistics:
+  #level graphs built: 4
+  #augmenting paths computed: 6
+    1 > 10 | flow = 7
+    1 > 2 > 10 | flow = 4
+    1 > 3 > 10 | flow = 8
+    1 > 4 > 7 > 10 | flow = 1
+    1 > 5 > 8 > 10 | flow = 3
+    1 > 6 > 9 > 10 | flow = 5
+  #recursive buildPath calls: 32
+```

examples/1.txt

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+10 14 1 10
+1 2 5
+2 10 4
+1 10 7
+1 3 8
+3 10 9
+1 4 3
+4 7 1
+7 10 1
+1 5 3
+5 8 4
+8 10 6
+1 6 7
+6 9 6
+9 10 5

examples/2.txt

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+4 5 1 4
+1 2 4
+1 3 8
+2 3 1
+3 2 1
+3 4 3
+2 4 8

examples/3.txt

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+5 7 1 5
+1 3 5
+1 4 3
+3 4 3
+4 2 5
+3 2 3
+2 5 7
+3 5 3

examples/FF_killer.txt

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+4 5 1 4
+1 2 99
+1 3 99
+2 3 1
+2 4 99
+3 4 99