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20 changed files with 56 additions and 364 deletions

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@ -1,2 +1,2 @@
# Ziglings # Ziglings
# ⚠️ My solutions, not the [original exercises](https://codeberg.org/ziglings/exercises) # ⚠️ (My solutions, not the [original exercises](https://codeberg.org/ziglings/exercises))

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@ -15,7 +15,7 @@ const print = std.debug.print;
// 1) Getting Started // 1) Getting Started
// 2) Version Changes // 2) Version Changes
comptime { comptime {
const required_zig = "0.12.0-dev.3397"; const required_zig = "0.12.0-dev.2618";
const current_zig = builtin.zig_version; const current_zig = builtin.zig_version;
const min_zig = std.SemanticVersion.parse(required_zig) catch unreachable; const min_zig = std.SemanticVersion.parse(required_zig) catch unreachable;
if (current_zig.order(min_zig) == .lt) { if (current_zig.order(min_zig) == .lt) {
@ -119,7 +119,7 @@ pub const logo =
; ;
pub fn build(b: *Build) !void { pub fn build(b: *Build) !void {
if (!validate_exercises()) std.process.exit(2); if (!validate_exercises()) std.os.exit(2);
use_color_escapes = false; use_color_escapes = false;
if (std.io.getStdErr().supportsAnsiEscapeCodes()) { if (std.io.getStdErr().supportsAnsiEscapeCodes()) {
@ -172,7 +172,7 @@ pub fn build(b: *Build) !void {
// Named build mode: verifies a single exercise. // Named build mode: verifies a single exercise.
if (n == 0 or n > exercises.len - 1) { if (n == 0 or n > exercises.len - 1) {
print("unknown exercise number: {}\n", .{n}); print("unknown exercise number: {}\n", .{n});
std.process.exit(2); std.os.exit(2);
} }
const ex = exercises[n - 1]; const ex = exercises[n - 1];
@ -262,7 +262,7 @@ const ZiglingStep = struct {
print("\n{s}Ziglings hint: {s}{s}", .{ bold_text, hint, reset_text }); print("\n{s}Ziglings hint: {s}{s}", .{ bold_text, hint, reset_text });
self.help(); self.help();
std.process.exit(2); std.os.exit(2);
}; };
self.run(exe_path.?, prog_node) catch { self.run(exe_path.?, prog_node) catch {
@ -272,7 +272,7 @@ const ZiglingStep = struct {
print("\n{s}Ziglings hint: {s}{s}", .{ bold_text, hint, reset_text }); print("\n{s}Ziglings hint: {s}{s}", .{ bold_text, hint, reset_text });
self.help(); self.help();
std.process.exit(2); std.os.exit(2);
}; };
// Print possible warning/debug messages. // Print possible warning/debug messages.
@ -939,7 +939,7 @@ const exercises = [_]Exercise{
.{ .{
.main_file = "082_anonymous_structs3.zig", .main_file = "082_anonymous_structs3.zig",
.output = .output =
\\"0"(bool):true "1"(bool):false "2"(i32):42 "3"(f32):3.141592e0 \\"0"(bool):true "1"(bool):false "2"(i32):42 "3"(f32):3.14159202e+00
, ,
.hint = "This one is a challenge! But you have everything you need.", .hint = "This one is a challenge! But you have everything you need.",
}, },
@ -1103,24 +1103,6 @@ const exercises = [_]Exercise{
\\This little poem has 15 words! \\This little poem has 15 words!
, ,
}, },
.{
.main_file = "104_threading.zig",
.output =
\\Starting work...
\\thread 1: started.
\\thread 2: started.
\\thread 3: started.
\\Some weird stuff, after starting the threads.
\\thread 2: finished.
\\thread 1: finished.
\\thread 3: finished.
\\Zig is cool!
,
},
.{
.main_file = "105_threading2.zig",
.output = "PI ≈ 3.14159265",
},
.{ .{
.main_file = "999_the_end.zig", .main_file = "999_the_end.zig",
.output = .output =

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@ -88,7 +88,7 @@ pub fn main() void {
for (&aliens) |*alien| { for (&aliens) |*alien| {
// *** Zap the alien with the heat ray here! *** // *** Zap the alien with the heat ray here! ***
heat_ray.zap(alien); ???.zap(???);
// If the alien's health is still above 0, it's still alive. // If the alien's health is still above 0, it's still alive.
if (alien.health > 0) aliens_alive += 1; if (alien.health > 0) aliens_alive += 1;

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@ -54,7 +54,7 @@ fn visitElephants(first_elephant: *Elephant) void {
// This gets the next elephant or stops: // This gets the next elephant or stops:
// which method do we want here? // which method do we want here?
e = if (e.hasTail()) e.getTail() else break; e = if (e.hasTail()) e.??? else break;
} }
} }

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@ -27,13 +27,7 @@ const Elephant = struct {
// Your Elephant trunk methods go here! // Your Elephant trunk methods go here!
// --------------------------------------------------- // ---------------------------------------------------
pub fn getTrunk(self: *Elephant) *Elephant { ???
return self.trunk.?;
}
pub fn hasTrunk(self: *Elephant) bool {
return (self.trunk != null);
}
// --------------------------------------------------- // ---------------------------------------------------

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@ -65,10 +65,10 @@ const std = @import("std");
const Err = error{Cthulhu}; const Err = error{Cthulhu};
pub fn main() void { pub fn main() void {
var first_line1: *const [16]u8 = undefined; var first_line1: *const [16]u8 = ???;
first_line1 = "That is not dead"; first_line1 = "That is not dead";
var first_line2: Err!*const [21]u8 = undefined; var first_line2: Err!*const [21]u8 = ???;
first_line2 = "which can eternal lie"; first_line2 = "which can eternal lie";
// Note we need the "{!s}" format for the error union string. // Note we need the "{!s}" format for the error union string.
@ -77,8 +77,8 @@ pub fn main() void {
printSecondLine(); printSecondLine();
} }
fn printSecondLine() void { fn printSecondLine() ??? {
var second_line2: ?*const [18]u8 = null; var second_line2: ?*const [18]u8 = ???;
second_line2 = "even death may die"; second_line2 = "even death may die";
std.debug.print("And with strange aeons {s}.\n", .{second_line2.?}); std.debug.print("And with strange aeons {s}.\n", .{second_line2.?});

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@ -87,7 +87,7 @@ pub fn main() void {
// Let's assign the std.debug.print function to a const named // Let's assign the std.debug.print function to a const named
// "print" so that we can use this new name later! // "print" so that we can use this new name later!
const print = std.debug.print; const print = ???;
// Now let's look at assigning and pointing to values in Zig. // Now let's look at assigning and pointing to values in Zig.
// //
@ -141,20 +141,9 @@ pub fn main() void {
// //
// Moving along... // Moving along...
// //
// When arguments are passed to a function, // Passing arguments to functions is pretty much exactly like
// they are ALWAYS passed as constants within the function, // making an assignment to a const (since Zig enforces that ALL
// regardless of how they were declared in the calling function. // function parameters are const).
//
// Example:
// fn foo(arg: u8) void {
// arg = 42; // Error, 'arg' is const!
// }
//
// fn bar() void {
// var arg: u8 = 12;
// foo(arg);
// ...
// }
// //
// Knowing this, see if you can make levelUp() work as expected - // Knowing this, see if you can make levelUp() work as expected -
// it should add the specified amount to the supplied character's // it should add the specified amount to the supplied character's
@ -163,13 +152,13 @@ pub fn main() void {
print("XP before:{}, ", .{glorp.experience}); print("XP before:{}, ", .{glorp.experience});
// Fix 1 of 2 goes here: // Fix 1 of 2 goes here:
levelUp(&glorp, reward_xp); levelUp(glorp, reward_xp);
print("after:{}.\n", .{glorp.experience}); print("after:{}.\n", .{glorp.experience});
} }
// Fix 2 of 2 goes here: // Fix 2 of 2 goes here:
fn levelUp(character_access: *Character, xp: u32) void { fn levelUp(character_access: Character, xp: u32) void {
character_access.experience += xp; character_access.experience += xp;
} }

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@ -32,8 +32,8 @@ pub fn main() void {
var cards = [8]u8{ 'A', '4', 'K', '8', '5', '2', 'Q', 'J' }; var cards = [8]u8{ 'A', '4', 'K', '8', '5', '2', 'Q', 'J' };
// Please put the first 4 cards in hand1 and the rest in hand2. // Please put the first 4 cards in hand1 and the rest in hand2.
const hand1: []u8 = cards[0..4]; const hand1: []u8 = cards[???];
const hand2: []u8 = cards[4..8]; const hand2: []u8 = cards[???];
std.debug.print("Hand1: ", .{}); std.debug.print("Hand1: ", .{});
printHand(hand1); printHand(hand1);
@ -43,7 +43,7 @@ pub fn main() void {
} }
// Please lend this function a hand. A u8 slice hand, that is. // Please lend this function a hand. A u8 slice hand, that is.
fn printHand(hand: []u8) void { fn printHand(hand: ???) void {
for (hand) |h| { for (hand) |h| {
std.debug.print("{u} ", .{h}); std.debug.print("{u} ", .{h});
} }

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@ -17,19 +17,19 @@ const std = @import("std");
pub fn main() void { pub fn main() void {
const scrambled = "great base for all your justice are belong to us"; const scrambled = "great base for all your justice are belong to us";
const base1: []const u8 = scrambled[15..23]; const base1: []u8 = scrambled[15..23];
const base2: []const u8 = scrambled[6..10]; const base2: []u8 = scrambled[6..10];
const base3: []const u8 = scrambled[32..]; const base3: []u8 = scrambled[32..];
printPhrase(base1, base2, base3); printPhrase(base1, base2, base3);
const justice1: []const u8 = scrambled[11..14]; const justice1: []u8 = scrambled[11..14];
const justice2: []const u8 = scrambled[0..5]; const justice2: []u8 = scrambled[0..5];
const justice3: []const u8 = scrambled[24..31]; const justice3: []u8 = scrambled[24..31];
printPhrase(justice1, justice2, justice3); printPhrase(justice1, justice2, justice3);
std.debug.print("\n", .{}); std.debug.print("\n", .{});
} }
fn printPhrase(part1: []const u8, part2: []const u8, part3: []const u8) void { fn printPhrase(part1: []u8, part2: []u8, part3: []u8) void {
std.debug.print("'{s} {s} {s}.' ", .{ part1, part2, part3 }); std.debug.print("'{s} {s} {s}.' ", .{ part1, part2, part3 });
} }

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@ -33,7 +33,7 @@ pub fn main() void {
// we can CONVERT IT TO A SLICE. (Hint: we do know the length!) // we can CONVERT IT TO A SLICE. (Hint: we do know the length!)
// //
// Please fix this line so the print statement below can print it: // Please fix this line so the print statement below can print it:
const zen12_string: []const u8 = zen_manyptr[0..21]; const zen12_string: []const u8 = zen_manyptr;
// Here's the moment of truth! // Here's the moment of truth!
std.debug.print("{s}\n", .{zen12_string}); std.debug.print("{s}\n", .{zen12_string});

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@ -59,8 +59,8 @@ pub fn main() void {
std.debug.print("Insect report! ", .{}); std.debug.print("Insect report! ", .{});
// Oops! We've made a mistake here. // Oops! We've made a mistake here.
printInsect(ant, AntOrBee.a); printInsect(ant, AntOrBee.c);
printInsect(bee, AntOrBee.b); printInsect(bee, AntOrBee.c);
std.debug.print("\n", .{}); std.debug.print("\n", .{});
} }

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@ -44,14 +44,14 @@ pub fn main() void {
std.debug.print("Insect report! ", .{}); std.debug.print("Insect report! ", .{});
// Could it really be as simple as just passing the union? // Could it really be as simple as just passing the union?
printInsect(ant); printInsect(???);
printInsect(bee); printInsect(???);
std.debug.print("\n", .{}); std.debug.print("\n", .{});
} }
fn printInsect(insect: Insect) void { fn printInsect(insect: Insect) void {
switch (insect) { switch (???) {
.still_alive => |a| std.debug.print("Ant alive is: {}. ", .{a}), .still_alive => |a| std.debug.print("Ant alive is: {}. ", .{a}),
.flowers_visited => |f| std.debug.print("Bee visited {} flowers. ", .{f}), .flowers_visited => |f| std.debug.print("Bee visited {} flowers. ", .{f}),
} }

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@ -7,7 +7,7 @@
// const a3: u8 = 0o101; // octal // const a3: u8 = 0o101; // octal
// const a4: u8 = 0b1000001; // binary // const a4: u8 = 0b1000001; // binary
// const a5: u8 = 'A'; // ASCII code point literal // const a5: u8 = 'A'; // ASCII code point literal
// const a6: u16 = '\u{0041}'; // Unicode code points can take up to 21 bits // const a6: u16 = 'Ȁ'; // Unicode code points can take up to 21 bits
// //
// You can also place underscores in numbers to aid readability: // You can also place underscores in numbers to aid readability:
// //

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@ -1,26 +1,19 @@
// //
// Often, C functions are used where no equivalent Zig function exists // Often, C functions are used where no equivalent Zig function exists
// yet. Okay, that's getting less and less. ;-) // yet. Since the integration of a C function is very simple, as already
//
// Since the integration of a C function is very simple, as already
// seen in the last exercise, it naturally offers itself to use the // seen in the last exercise, it naturally offers itself to use the
// very large variety of C functions for our own programs. // very large variety of C functions for our own programs.
// As an example: // As an example:
// //
// Let's say we have a given angle of 765.2 degrees. If we want to // Let's say we have a given angle of 765.2 degrees. If we want to
// normalize that, it means that we have to subtract X * 360 degrees // normalize that, it means that we have to subtract X * 360 degrees
// to get the correct angle. // to get the correct angle. How could we do that? A good method is
// How could we do that? A good method is to use the modulo function. // to use the modulo function. But if we write "765.2 % 360", it won't
// But if we write "765.2 % 360", it only works with float values // work, because the standard modulo function works only with integer
// that are known at compile time. // values. In the C library "math", there is a function called "fmod";
// In Zig, we would use %mod(a, b) instead. // the "f" stands for floating and means that we can solve modulo for
// // real numbers. With this function, it should be possible to normalize
// Let us now assume that we cannot do this in Zig, but only with // our angle. Let's go.
// a C function from the standard library. In the library "math",
// there is a function called "fmod"; the "f" stands for floating
// and means that we can solve modulo for real numbers. With this
// function, it should be possible to normalize our angle.
// Let's go.
const std = @import("std"); const std = @import("std");

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@ -1,129 +0,0 @@
//
// Whenever there is a lot to calculate, the question arises as to how
// tasks can be carried out simultaneously. We have already learned about
// one possibility, namely asynchronous processes, in Exercises 84-91.
//
// However, the computing power of the processor is only distributed to
// the started tasks, which always reaches its limits when pure computing
// power is called up.
//
// For example, in blockchains based on proof of work, the miners have
// to find a nonce for a certain character string so that the first m bits
// in the hash of the character string and the nonce are zeros.
// As the miner who can solve the task first receives the reward, everyone
// tries to complete the calculations as quickly as possible.
//
// This is where multithreading comes into play, where tasks are actually
// distributed across several cores of the CPU or GPU, which then really
// means a multiplication of performance.
//
// The following diagram roughly illustrates the difference between the
// various types of process execution.
// The 'Overall Time' column is intended to illustrate how the time is
// affected if, instead of one core as in synchronous and asynchronous
// processing, a second core now helps to complete the work in multithreading.
//
// In the ideal case shown, execution takes only half the time compared
// to the synchronous single thread. And even asynchronous processing
// is only slightly faster in comparison.
//
//
// Synchronous Asynchronous
// Processing Processing Multithreading
//
// Thread 1 Thread 1 Thread 1 Thread 2
// Overall Time
//
//
// T T T T
// a a a a
// s s s s
// k k k k
//
// 1 1 1 3
//
// 5 Sec
//
// Blocking T T T
// a a a
// s s s 8 Sec
// k k k
// T
// a 2 2 4
// s
// k 10 Sec
//
// 1 T
// a
// s
// k
// T
// a 1
// s
// k
//
// 2
//
//
//
//
//
// The diagram was modeled on the one in a blog in which the differences
// between asynchronous processing and multithreading are explained in detail:
// https://blog.devgenius.io/multi-threading-vs-asynchronous-programming-what-is-the-difference-3ebfe1179a5
//
// Our exercise is essentially about clarifying the approach in Zig and
// therefore we try to keep it as simple as possible.
// Multithreading in itself is already difficult enough. ;-)
//
const std = @import("std");
pub fn main() !void {
// This is where the preparatory work takes place
// before the parallel processing begins.
std.debug.print("Starting work...\n", .{});
// These curly brackets are very important, they are necessary
// to enclose the area where the threads are called.
// Without these brackets, the program would not wait for the
// end of the threads and they would continue to run beyond the
// end of the program.
{
// Now we start the first thread, with the number as parameter
const handle = try std.Thread.spawn(.{}, thread_function, .{1});
// Waits for the thread to complete,
// then deallocates any resources created on `spawn()`.
defer handle.join();
// Second thread
const handle2 = try std.Thread.spawn(.{}, thread_function, .{-4}); // that can't be right?
defer handle2.join();
// Third thread
const handle3 = try std.Thread.spawn(.{}, thread_function, .{3});
defer ??? // <-- something is missing
// After the threads have been started,
// they run in parallel and we can still do some work in between.
std.time.sleep((1) * std.time.ns_per_s);
std.debug.print("Some weird stuff, after starting the threads.\n", .{});
}
// After we have left the closed area, we wait until
// the threads have run through, if this has not yet been the case.
std.debug.print("Zig is cool!\n", .{});
}
// This function is started with every thread that we set up.
// In our example, we pass the number of the thread as a parameter.
fn thread_function(num: usize) !void {
std.debug.print("thread {d}: {s}\n", .{ num, "started." });
std.time.sleep((5 - num % 3) * std.time.ns_per_s);
std.debug.print("thread {d}: {s}\n", .{ num, "finished." });
}
// This is the easiest way to run threads in parallel.
// In general, however, more management effort is required,
// e.g. by setting up a pool and allowing the threads to communicate
// with each other using semaphores.
//
// But that's a topic for another exercise.

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@ -1,107 +0,0 @@
//
// Now that we are familiar with the principles of multi threading, we
// boldly venture into a practical example from mathematics.
// We will determine the circle number PI with sufficient accuracy.
//
// There are different methods for this, and some of them are several
// hundred years old. For us, the dusty procedures are surprisingly well
// suited to our exercise. Because the mathematicians of the time didn't
// have fancy computers with which we can calculate something like this
// in seconds today.
// Whereby, of course, it depends on the accuracy, i.e. how many digits
// after the decimal point we are interested in.
// But these old procedures can still be tackled with paper and pencil,
// which is why they are easier for us to understand.
// At least for me. ;-)
//
// So let's take a mental leap back a few years.
// Around 1672 (if you want to know and read about it in detail, you can
// do so on Wikipedia, for example), various mathematicians once again
// discovered a method of approaching the circle number PI.
// There were the Scottish mathematician Gregory and the German
// mathematician Leibniz, and even a few hundred years earlier the Indian
// mathematician Madhava. All of them independently developed the same
// formula, which was published by Leibnitz in 1682 in the journal
// "Acta Eruditorum".
// This is why this method has become known as the "Leibnitz series",
// although the other names are also often used today.
// We will not go into the formula and its derivation in detail, but
// will deal with the series straight away:
//
// 4 4 4 4 4
// PI = --- - --- + --- - --- + --- ...
// 1 3 5 7 9
//
// As you can clearly see, the series starts with the whole number 4 and
// approaches the circle number by subtracting and adding smaller and
// smaller parts of 4. Pretty much everyone has learned PI = 3.14 at school,
// but very few people remember other digits, and this is rarely necessary
// in practice. Because either you don't need the precision, or you use a
// calculator in which the number is stored as a very precise constant.
// But at some point this constant was calculated and we are doing the same
// now.The question at this point is, how many partial values do we have
// to calculate for which accuracy?
//
// The answer is chewing, to get 8 digits after the decimal point we need
// 1,000,000,000 partial values. And for each additional digit we have to
// add a zero.
// Even fast computers - and I mean really fast computers - get a bit warmer
// on the CPU when it comes to really many diggits. But the 8 digits are
// enough for us for now, because we want to understand the principle and
// nothing more, right?
//
// As we have already discovered, the Leibnitz series is a series with a
// fixed distance of 2 between the individual partial values. This makes
// it easy to apply a simple loop to it, because if we start with n = 1
// (which is not necessarily useful now) we always have to add 2 in each
// round.
// But wait! The partial values are alternately added and subtracted.
// This could also be achieved with one loop, but not very elegantly.
// It also makes sense to split this between two CPUs, one calculates
// the positive values and the other the negative values. And so we can
// simply start two threads and add everything up at the end and we're
// done.
// We just have to remember that if only the positive or negative values
// are calculated, the distances are twice as large, i.e. 4.
//
// So that the whole thing has a real learning effect, the first thread
// call is specified and you have to make the second.
// But don't worry, it will work out. :-)
//
const std = @import("std");
pub fn main() !void {
const count = 1_000_000_000;
var pi_plus: f64 = 0;
var pi_minus: f64 = 0;
{
// First thread to calculate the plus numbers.
const handle1 = try std.Thread.spawn(.{}, thread_pi, .{ &pi_plus, 5, count });
defer handle1.join();
// Second thread to calculate the minus numbers.
???
}
// Here we add up the results.
std.debug.print("PI ≈ {d:.8}\n", .{4 + pi_plus - pi_minus});
}
fn thread_pi(pi: *f64, begin: u64, end: u64) !void {
var n: u64 = begin;
while (n < end) : (n += 4) {
pi.* += 4 / @as(f64, @floatFromInt(n));
}
}
// If you wish, you can increase the number of loop passes, which
// improves the number of digits.
//
// But be careful:
// In order for parallel processing to really show its strengths,
// the compiler must be given the "-O ReleaseFast" flag when it
// is created. Otherwise the debug functions slow down the speed
// to such an extent that seconds become minutes during execution.
//
// And you should remove the formatting restriction in "print",
// otherwise you will not be able to see the additional diggits.

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@ -1,5 +1,5 @@
--- exercises/051_values.zig 2024-03-14 23:25:42.695020607 +0100 --- exercises/051_values.zig 2023-10-03 22:15:22.122241138 +0200
+++ answers/051_values.zig 2024-03-14 23:28:34.525109174 +0100 +++ answers/051_values.zig 2023-10-05 20:04:07.072767194 +0200
@@ -87,7 +87,7 @@ @@ -87,7 +87,7 @@
// Let's assign the std.debug.print function to a const named // Let's assign the std.debug.print function to a const named
// "print" so that we can use this new name later! // "print" so that we can use this new name later!
@ -9,7 +9,7 @@
// Now let's look at assigning and pointing to values in Zig. // Now let's look at assigning and pointing to values in Zig.
// //
@@ -163,13 +163,13 @@ @@ -152,13 +152,13 @@
print("XP before:{}, ", .{glorp.experience}); print("XP before:{}, ", .{glorp.experience});
// Fix 1 of 2 goes here: // Fix 1 of 2 goes here:

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@ -1,6 +1,6 @@
--- exercises/094_c_math.zig 2024-02-28 12:50:35.789939935 +0100 --- exercises/094_c_math.zig 2023-10-22 14:00:02.909379696 +0200
+++ answers/094_c_math.zig 2024-02-28 12:53:57.910309471 +0100 +++ answers/094_c_math.zig 2023-10-22 14:02:46.709025235 +0200
@@ -26,7 +26,7 @@ @@ -19,7 +19,7 @@
const c = @cImport({ const c = @cImport({
// What do we need here? // What do we need here?

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@ -1,17 +0,0 @@
--- exercises/104_threading.zig 2024-03-05 09:09:04.013974229 +0100
+++ answers/104_threading.zig 2024-03-05 09:12:03.987162883 +0100
@@ -97,12 +97,12 @@
defer handle.join();
// Second thread
- const handle2 = try std.Thread.spawn(.{}, thread_function, .{-4}); // that can't be right?
+ const handle2 = try std.Thread.spawn(.{}, thread_function, .{2});
defer handle2.join();
// Third thread
const handle3 = try std.Thread.spawn(.{}, thread_function, .{3});
- defer ??? // <-- something is missing
+ defer handle3.join();
// After the threads have been started,
// they run in parallel and we can still do some work in between.

View file

@ -1,13 +0,0 @@
--- exercises/105_threading2.zig 2024-03-23 16:35:14.754540802 +0100
+++ answers/105_threading2.zig 2024-03-23 16:38:00.577539733 +0100
@@ -81,8 +81,8 @@
defer handle1.join();
// Second thread to calculate the minus numbers.
- ???
-
+ const handle2 = try std.Thread.spawn(.{}, thread_pi, .{ &pi_minus, 3, count });
+ defer handle2.join();
}
// Here we add up the results.
std.debug.print("PI ≈ {d:.8}\n", .{4 + pi_plus - pi_minus});