feat: add ex11

README.md

@@ -912,6 +912,49 @@ We know that the two inputs will not exceed $2^{16}$ each, so we can concatenate
 
 > 💡 We can use the `u32` type to store this number.
 
+### Steps
+
+1. **Shift `x` to the left by $16$ bits**.
+2. **Perform a bitwise OR** between `x` and `y`.
+3. **Divide the result by $2^{32} - 1$** to get a number between $0$ and $1$.
+
+And that's it! You have your solution.
+
+## 11 - Curve Inverse
+
+```rust
+fn reverse_map(n: f64) -> (u16, u16);
+```
+
+> You must write the inverse function $f^{−1}$ of the function $f$ from the previous exercise (so this time, this is a space-filling curve, used to decode data from a line into a space).
+>
+> Let $f$ and $A$ be the function and set from the previous exercise, then:
+>
+> $$f^{-1} : A \rightarrow [[0; 2^{16} - 1]]^2 \subset \mathbb{N}^2$$
+>
+> The above function must be implemented such that the following expressions are true for values that are in range:
+>
+> $$(f^{-1} \circ f)(x, y) = (x, y)$$
+> $$(f \circ f^{-1})(x) = x$$
+
+---
+
+Let's decrypt the mathematical notation.
+
+- The function $f^{-1}$ takes a floating-point number $n$ in the set $A$, and returns a pair of integers $(x, y)$ comprised between $0$ and $2^{16} - 1$.
+
+- If you apply $f$ to a pair of integers $(x, y)$, and then apply $f^{-1}$ to the result, you should get back $(x, y)$.
+
+- If you apply $f^{-1}$ to a floating-point number $n$, and then apply $f$ to the result, you should get back $n$.
+
+So basically, you need to reverse the operation you did in the previous exercise.
+
+### Steps
+
+1. **Multiply `n` by $2^{32} - 1$** to get a number between $0$ and $2^{32} - 1$.
+2. **Shift `n` to the right by $16$ bits** to get the original `x`.
+3. **Shift `n` to the left by $16$ bits, then again to the right by $16$ bits** to get the original `y`.
+
 # Resources
 
 - [📺 Add Two Numbers Without The "+" Sign (Bit Shifting Basics)](https://www.youtube.com/watch?v=qq64FrA2UXQ)

src/ex11.rs

@@ -0,0 +1,7 @@
+pub fn reverse_map(n: f64) -> (u16, u16) {
+	let n: u32 = (n * u32::MAX as f64) as u32;
+	let x: u16 = (n >> 16) as u16;
+	let y: u16 = ((n << 16) >> 16) as u16;
+
+	return (x, y);
+}

src/main.rs

@@ -37,8 +37,8 @@ use ex09::eval_set;
 mod ex10;
 use ex10::map;
 
-// mod ex11;
-// use ex11::reverse_map;
+mod ex11;
+use ex11::reverse_map;
 
 fn main() {
 	println!("\n{}", "EX00 - ADDER".bold());
@@ -236,10 +236,7 @@ fn main() {
 		);
 
 		println!("Formula: {}", formula.bold());
-		println!(
-			"RPN output: {}",
-			conjunctive_normal_form(formula).bold()
-		);
+		println!("RPN output: {}", conjunctive_normal_form(formula).bold());
 		println!();
 	}
 
@@ -295,30 +292,12 @@ fn main() {
 
 	println!("\n{}", "EX09 - EVAL SET".bold());
 	let sets: Vec<Vec<Vec<i32>>> = vec![
-		vec![
-			vec![0, 1, 2],
-			vec![0, 3, 4]
-		],
-		vec![
-			vec![0, 1, 2],
-			vec![3, 4, 5]
-		],
-		vec![
-			vec![0, 1, 2]
-		],
-		vec![
-			vec![0, 1, 2],
-			vec![3, 4, 5],
-			vec![6, 7, 3]
-		],
-		vec![
-			vec![42, 43],
-			vec![44, 45, 46],
-		],
-		vec![
-			vec![42, 43],
-			vec![44, 45, 46],
-		],
+		vec![vec![0, 1, 2], vec![0, 3, 4]],
+		vec![vec![0, 1, 2], vec![3, 4, 5]],
+		vec![vec![0, 1, 2]],
+		vec![vec![0, 1, 2], vec![3, 4, 5], vec![6, 7, 3]],
+		vec![vec![42, 43], vec![44, 45, 46]],
+		vec![vec![42, 43], vec![44, 45, 46]],
 	];
 	let formulas: Vec<(&str, Vec<i32>)> = vec![
 		("AB&", vec![0]),
@@ -351,16 +330,30 @@ fn main() {
 		((u16::MAX, u16::MAX), 1.0),
 	];
 
-	for coord in coordinates {
+	for coord in &coordinates {
 		println!(
 			"{}\t{:?} → {}",
-			if map(coord.0.0, coord.0.1) == coord.1 {
+			if map(coord.0 .0, coord.0 .1) == coord.1 {
 				"OK".green().bold()
 			} else {
 				"KO".red().bold()
 			},
 			coord.0,
-			map(coord.0.0, coord.0.1)
+			map(coord.0 .0, coord.0 .1)
+		);
+	}
+
+	println!("\n{}", "EX11 - INVERSE FUNCTION".bold());
+	for coord in &coordinates {
+		println!(
+			"{}\t{} → {:?}",
+			if reverse_map(coord.1) == (coord.0 .0, coord.0 .1) {
+				"OK".green().bold()
+			} else {
+				"KO".red().bold()
+			},
+			coord.1,
+			reverse_map(coord.1)
 		);
 	}
 }