Add software complexity and put all in metrics directory

Author: mjdecker

_notes/software-testing/metrics/software-complexity.md

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+---
+title: "Software Complexity"
+layout: notes
+---
+
+# Complexity Measures/Metrics
+* LOC - a function of complexity
+* Halstead Complexity Measures
+* McCabe’s Complexity Measures
+* McClure's Complexity Metric
+
+# Halstead’s Software Science (entropy measures)
+* Computer program in software science is considered a series of operator/operator tokens
+	- n<sub>1<sub> - number of distinct operators
+	- n<sub>2</sub> - number of distinct operands
+	- N<sub>1</sub> - total number of operators
+	- N<sub>2</sub> - total number of operands
+* All software Sicence measures built off of these
+
+# Example Halstead Complexity Measures
+		if (k < 2) {
+  			if (k > 3)
+    			x = x * k;
+		}
+
+* Distinct operators: if ( ) { } > < = * ;
+* Distinct operands: k 2 3 x
+
+* n<sub>1</sub> = 10 <br/>
+   n<sub>2</sub> = 4<br/>
+   N<sub>1</sub> = 13<br/>
+   N<sub>2</sub> = 7
+
+* Different sources compute differently
+
+# Halstead Metrics
+
+
+* Length (Size):  N = N<sub>1</sub> + N<sub>2</sub>
+* Vocabulary:  n = n<sub>1</sub> + n<sub>2</sub>
+* Estimated length: N̂ = n<sub>1</sub> log<sub>2</sub> n<sub>1</sub> + n<sub>2</sub> log<sub>2</sub> n<sub>2</sub>
+
+	- Close estimate of length for well structured programs
+
+* Purity ratio: PR =  N̂ / N
+
+# Program Complexity
+
+* Volume: V = N log<sub>2</sub> n
+
+	- Number of bits to provide a unique designator for each of the n items in the program vocabulary.
+
+* Program effort: E = V / L
+
+	- where, L = V<sup>*</sup> / V, and 
+	- V<sup>*</sup> is the volume of most compact design implementation
+	- This is a good measure of program understandability
+	- L can be estimated with: (2 / n<sub>1</sub>) (n<sub>2</sub> / N<sub>2</sub>)
+
+# McCabe’s Complexity Measures
+* McCabe’s metrics are based on a control flow representation of the program.
+* A program graph is used to depict control flow.
+* Nodes represent processing tasks (one or more code statements)
+* Edges represent control flow between nodes
+
+# Cyclomatic Complexity
+* Set of independent paths through the graph (basis set)
+
+* V(G) = E – N + 2
+	- E is the number of flow graph edges
+	- N is the number of nodes
+
+* V(G) = P + 1
+	- P is the number of predicate nodes
+
+# Cyclomatic Complexity Meaning
+* V(G) is the number of (enclosed) regions/areas of the planar graph
+* Number of regions increases with the number of decision paths and loops.
+* A quantitative measure of testing difficulty and an indication of ultimate reliability
+* Experimental data shows value of V(G) should be no more then 10.  Testing is very difficulty above this value.
+
+# McClure's Complexity Metric
+
+* Complexity = C + V
+
+	- C is the number of comparisons in a module
+	- V is the number of control variables referenced in the module
+* Similar to McCabe’s but with regard to control variables.