CS1112 Lecture 27 2008/12/4
Lecture slides 1
Previous Lecture:
Insertion sort vs. merge sort
Timing with tic toc
Time efficiency vs. memory efficiency
Today’s Lecture:
Models and data
Congressional apportionment
Sensitivity analysis
Simulation—Google “page rank”
December 4, 2008 Lecture 27 6
What are the “errors” in calculating the surface area of
the Earth?
myPi= 3.14;
r= 3961.11345;
earthArea= 4*myPi*r*r;
A. Math error in myPi
B. Measurement error in r
C. Rounding error in arithmetic
D. All of the above
December 4, 2008 Lecture 27 11
The apportionment problem
Number of states: n
State populations: p(1),…,p(n)
Total population: P
State delegation size: d(1),…,d(n)
Number of seats: D
Distribute 435 Congressional seats among the 50 states
so that the ratio of population to delegation size is
roughly the same from state to state.
December 4, 2008 Lecture 27 16
An Apportionment Method determines
delegation sizes d(1),…,d(n) that are whole
numbers so that representation is approximately
equal:
)(
)(
...
)1( )1(
nd
np
d
p≈≈
Definition
December 4, 2008 Lecture 27 29
% Every state gets a district
d= ones(50,1);
% “Deal out” remaining districts
for k= 51:435
% Let i be the index of the state that
% most deserves an additional district
d(i)= d(i) + 1;
end
December 4, 2008 Lecture 27 34
% Every state gets a district
d= ones(50,1);
% “Deal out” remaining districts
for k= 51:435
[z,i]= max((p./d).*(p./(d+1)))
d(i)= d(i) + 1;
end
Allocate using the method of equal proportions
See posted version for detail
