Somewhere in between → tutorial and quiz (post dinner some day, Wed/Friday)
Many important stuff happen in text.
WhatsApp, reviews of restaurants, et cetera
Given a passage, tell the theme of the passage.
Passage → Important words (using some frequency analysis probably) → Top ten words → give a title
(Definition should be independent of programming language)
Alphabet \(\Sigma\) → (finite) set of symbols
String over \(\Sigma\):
Empty string \(\epsilon\) → length 0
\(\Sigma^* = \Sigma \cup \Sigma^1 \cup \Sigma^2 \cup ...\)
Assume \(|\Sigma| = 100\).
Then, the set of words of length \(\le 100\) has cardinality \(1 + 100 + \cdots + 100^{100} = (100^{101} - 1)/99\)
Q. What is the largest string length in (standard) C++? Experiment.
include <string>
using namespace std;
string s1, s2;
s1, s2 → empty strings, can check it using:
s1.length() returns length of the string
In general, we can do stringboject.method().
Can use == and !=; e.g., s1 == s2 will return true if they’re both empty. (Like at the time of initialisation.)
Can make arrays also. string name[100], thus it’s a proper data type.
Can use + for concatenation.
Search or find → strings can be accessed as if an array of characters.
Given a path, how many directories? Count the number of non-contiguous colons.
Can also ask what the deepest directory is.
$ cat $PATH displays the content on the screen. Example - cat randinp
Question: Take last 100 emails.
How many people have written to you?
The dates and times.
Binary search: \(T(n) = T(n/2) + 3\)
In general, we may divide the problem into \(a\) parts, each of size \(n/b\). (\(b = a\) is not necessary, maybe not disjoint.)
Then, \(T(n) = aT(n/b) + g(n).\)
(In the case of binary sort, we didn’t have to analyse both parts.)
If \(g(n)\) is polynomial, say \(n^d\), then we know the complexity \(T(n)\) as a function of \(n\). (Master’s Theorem)