Arrays and Matrices
Arrays and Matrices
1
Sieve of Eratosthenes
counting primes
arrays in Python
2
Matrices
matrices as lists of arrays
finding the minimum
finding saddle points
MCS 275 Lecture 3
Programming Tools and File Management
Jan Verschelde, 13 January 2017
Programming Tools (MCS 275)
Arrays and Matrices
L-3
15 January 2016
1 / 38
Arrays and Matrices
1
Sieve of Eratosthenes
counting primes
arrays in Python
2
Matrices
matrices as lists of arrays
finding the minimum
finding saddle points
Programming Tools (MCS 275)
Arrays and Matrices
L-3
15 January 2016
2 / 38
the Sieve of Eratosthenes
Input/Output specification:
input : a natural number n
output : all prime numbers n
Running factorization in primes for all numbers n
is too expensive.
Sieve of Eratosthenes:
1
Boolean table isprime[i] records prime numbers:
if i is prime, then isprime[i] == True,
otherwise isprime[i] == False.
2
All multiples of prime numbers are not prime:
for all isprime[i]: isprime[i*k] = False.
Programming Tools (MCS 275)
Arrays and Matrices
L-3
15 January 2016
3 / 38
all primes less than 10
T = True, F = False
i
0
2
3
2
T
T
T
3
T
T
T
4
T
F
F
5
T
T
T
6
T
F
F
7
T
T
T
8
T
F
F
9
T
T
F
10
T
F
F
Initially, all entries in the table are True.
The algorithm uses a double loop:
1
2
the first loop runs for i from 2 to n;
the second loop runs only if i is prime,
setting to False all multiples of i.
Be more efficient, first loop: while (i < n//i).
Programming Tools (MCS 275)
Arrays and Matrices
L-3
15 January 2016
4 / 38
Arrays and Matrices
1
Sieve of Eratosthenes
counting primes
arrays in Python
2
Matrices
matrices as lists of arrays
finding the minimum
finding saddle points
Programming Tools (MCS 275)
Arrays and Matrices
L-3
15 January 2016
5 / 38
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