Even if thecontestants are divided into teams, they compete as individuals

typedef long long ll

Around the mid-19th century, Swiss astronomer Rudolf Wolf rolled a pair of dice 20000 times, recording each outcome.

It's like the firing of the neurons is going only in one direction.

can’t train for in advance

weird learning disability

And we can bring common tasks into distribution quite easily through RL and SFT.

Blind/deaf people

frontier models are terabytes sized

Many billions of years of evolution is our pre-training

unit

writing a dictionary of type (int × string) to a channel

Write a function which rotates a rect such that it is at least as tall as it is wide.

Rewrite the summary paragraph at the end of this chapter for the three argument function g a b c.

Why can we not write a function to halve all the elements of a list like this: map (( / ) 2) [10; 20; 30]? Write a suitable division function which can be partially applied in the manner we require.

member_all x ls

Write a function truncate which takes an integer and a list of lists, and returns a list of lists, each of which has been truncated to the given length. If a list is shorter than the given length, it is unchanged. Make use of partial application.

type of member x

What is its type?

Write the function union a b which forms the union of two dictionaries. The union of two dictionaries is the dictionary containing all the entries in one or other or both. In the case that a key is contained in both dictionaries, the value in the first should be preferred.

Write another function which uses the previous one, but handles the exception, and simply returns zero when a suitable integer cannot be found.

Write an exception definition and a function which calculates the largest integer smaller than or equal to the square root of a given integer. If the argument is negative, the exception should be raised.

Write another function smallest_or_zero which uses the smallest function but if Not_found is raised, returns zero.

exception.

Write the function for_all which, given a function of type α → bool and an argument list of type α list evaluates to true if and only if the function returns true for every element of the list. Give examples of its use.

Write a function filter which takes a function of type α → bool and an α list and returns a list of just those elements of the argument list for which the given function returns true.

Write a simple recursive function calm to replace exclamation marks in a char list with periods. For example calm [’H’; ’e’; ’l’; ’p’; ’!’; ’ ’; ’F’; ’i’; ’r’; ’e’; ’!’] should evaluate to [’H’; ’e’; ’l’; ’p’; ’.’; ’ ’; ’F’; ’i’; ’r’; ’e’; ’.’]. Now rewrite your function to use map instead of recursion. What are the types of your functions?

We mentioned that the comparison functions like  <  work for many OCaml types. Can you determine, by experimentation, how they work for lists? For example, what is the result of [1; 2] < [2; 3]? What happens when we sort the following list of type char list list? Why?

We know that take and drop can fail if called with incorrect arguments. Show that this is never the case in msort.

Combine the sort and insert functions into a single sort function.

Write a function to detect if a list is already in sorted order.

Can you explain why the rev function we defined is inefficient? How does the time it takes to run relate to the size of its argument? Can you write a more efficient version using an accumulating argument? What is its efficiency in terms of time taken and space used?

Use your member function to write a function make_set which, given a list, returns a list which contains all the elements of the original list, but has no duplicate elements. For example, make_set [1; 2; 3; 3; 1] might return [2; 3; 1]. What is the type of your function?

Write a function evens which does the opposite to odds, returning the even numbered elements in a list. For example, evens [2; 4; 2; 4; 2] should return [4; 4]. What is the type of your function?

Write a function which, given a list, builds a palindrome from it. A palindrome is a list which equals its own reverse. You can assume the existence of rev and @. Write another function which determines if a list is a palindrome.

Write a function drop_last which returns all but the last element of a list. If the list is empty, it should return the empty list. So, for example, drop_last [1; 2; 4; 8] should return [1; 2; 4]. What about a tail recursive version?

Write a function count_true which counts the number of true elements in a list. For example, count_true [true; false; true] should return 2. What is the type of your function? Can you write a tail recursive version?

h is not used in the expression 1 + length t

There is a special pattern x..y to denote continuous ranges of characters, for example ’a’..’z’ will match all lowercase letters. Write functions islower and isupper, each of type char → bool, to decide on the case of a given letter.

What does match 1 + 1 with 2 -> match 2 + 2 with 3 -> 4 | 4 -> 5 evaluate to?

For each of the previous three questions, comment on whether you think it is easier to read the function with or without pattern matching. How might you expect this to change if the functions were much larger?

Rewrite the not function from the previous chapter in pattern matching style. Use pattern matching to write a recursive function which, given a positive integer n, returns the sum of all the integers from 1 to n. Use pattern matching to write a function which, given two numbers x and n, computes xn.

f a matches the pattern 1. If it does, just return 1. If not,

Can you suggest a way of preventing the non-termination of the factorial function in the case of a zero or negative argument?

Write a function power x n which raises x to the power n. Give its type.

Write a function isconsonant which, given a lower-case character in the range ’a’…’z’, determines if it is a consonant.

Write a recursive function which, given a number n, calculates the sum 1 + 2 + 3 + … + n. What is its type?

Write a function which returns true if both of its arguments are non-zero, and false otherwise. What is the type of your function?

Write a function which multiplies a given number by ten. What is its type?

# let rec gcd a b = if b = 0 then a else gcd b (a mod b);; val gcd : int -> int -> int = <fun> # gcd 64000 3456;; - : int = 128 Here is the evaluation:

what if we try to evaluate factorial (-1)?

What is the effect of the comparison operators like < and > on alphabetic values of type char? For example, what does ’p’ < ’q’ evaluate to? What is the effect of the comparison operators on the booleans, true and false?

Why not just use, for example, the integer 0 to represent false and the integer 1 for true? Why have a separate bool type at all?

Can you discover what the mod operator does when one or both of the operands are negative? What about if the first operand is zero? What if the second is zero?

What happens when you try to evaluate the expression 1 / 0? Why?

The range of numbers available is limited. There are two special numbers: min_int and max_int. What are their values on your computer? What happens when you evaluate the expressions max_int + 1 and min_int - 1?

A programmer writes 1+2 * 3+4. What does this evaluate to? What advice would you give him?

Consider the evaluations of the expressions 1 + 2 mod 3, (1 + 2) mod 3, and 1 + (2 mod 3). What can you conclude about the + and mod operators?

’%’

if true then false else true

true && false

true || false

1 <> 1

400 > 200

800 / 80 / 8

if and then (in our example 100 > 99) must have type bool

Sometimes, those students with least prior programming experience perform the best.

some countries persistently have lower defect rates than others on a timescale of decades1,

But once that company is past the VC-funded hyper growth phase and wants to maximize its profits, it will end up with a multi-thousand person platforms org, just like Google's, unless the company wants to leave hundreds of millions or billions of dollars a year on the table due to hardware and software inefficiency.

inimical

nd how much that would then change our de­ci­sions or ac­tions