Transcript Inclusion-Exclusion Principle 3 sets A,B,C C A*C A |A ˘ B ˘ C| = |A| + |B| + |C| -|A*B|-|A*C|-|B*C| +|A*B*C| *: intersection B*C A*B +2 -1 -1 |A ˘ B ˘ C| = |A|

Inclusion-Exclusion Principle
3 sets A,B,C
C
A*C
A
|A ˘ B ˘ C| =
|A| + |B| + |C|
-|A*B|-|A*C|-|B*C|
+|A*B*C|
*: intersection
B*C
A*B
+2
-1
-1
|A ˘ B ˘ C| =
|A| + |B| + |C|
-|A*B|-|A*C|-|B*C|
+|A*B*C|
B
+3
-3
+1
-1
|A ˘ B ˘ C| =
|A| + |B| + |C|
-|A*B|-|A*C|-|B*C|
+|A*B*C|
Your Programming Assignments
• Input f in F satisfying precondition
• Output g in G satisfying postcondition
• Claims about your program p: F -> G:
– Correctness
– Resource consumption
• Time: <= |F|*log(|F|) for |F|>100.
• Space: <= 10
• Energy
– Quality of G: 0.6
Programming Assignments
• Further claims about your program p: F -> G:
– Well designed
• Follows well accepted design guidelines
Evaluating Programming
Assignments
• Run them on a benchmark provided by the
teaching assistant / professor.
• Run them on all test cases provided by other
students. Reward students whose test cases
find bugs in programs of other students. Good
idea! Increases interaction.
• What about checking resource consumption
and quality claims? Require that they are
stated explicitly as part of the submission.
Claims
• I claim that my program p:F->G is correct for
all inputs satisfying the precondition and it
operates with resource consumption R and
achieves quality Q.
• I claim that my sorting program is correct for
all inputs of size n < 10^6 and it makes at most
n*log(log(n)) comparisons.