Solved some Mathematics/Fundamentals tests.

Author: jonasraoni

README.md

@@ -92,12 +92,24 @@ Note: Few codes were solved in C# (I've written them a long time ago), I'll conv
 ## [Functional Programming](functional-programming)
 
 - [Solve Me First FP](functional-programming/introduction/solveMeFirst.cs)
+
 ### [Introduction](functional-programming/introduction)
 
+## [Mathematics](mathematics)
+
+### [Fundamentals](mathematics/fundamentals)
+
+- [Army Game](mathematics/fundamentals/gameWithCells.js)
+- [Find the Point](mathematics/fundamentals/findPoint.js)
+- [Handshake](mathematics/fundamentals/handshake.js)
+- [Is Fibo](mathematics/fundamentals/solve.js)
+- [Leonardo's Prime Factors](mathematics/fundamentals/primeCount.js)
+- [Maximum Draws](mathematics/fundamentals/maximumDraws.js)
+- [Minimum Height Triangle](mathematics/fundamentals/lowestTriangle.js)
+
 ## [Tutorials](tutorials)
 
 ### [Cracking The Code Interview](tutorials/cracking-the-code-interview)
-Merge Sort: Counting Inversions
 - [Arrays: Left Rotation](tutorials/cracking-the-code-interview/rotLeft.js)
 - [Hash Tables: Ice Cream Parlor](tutorials/cracking-the-code-interview/whatFlavors.js)
 - [Hash Tables: Ransom Note Solution](tutorials/cracking-the-code-interview/checkMagazine.js)
@@ -107,5 +119,4 @@ Merge Sort: Counting Inversions
 - [Sorting: Bubble Sort](tutorials/cracking-the-code-interview/countSwaps.js)
 - [Sorting: Comparator](tutorials/cracking-the-code-interview/compare.js)
 - [Strings: Making Anagrams](tutorials/cracking-the-code-interview/makeAnagram.js)
-- [Time Complexity: Primality](tutorials/cracking-the-code-interview/primality.js)
-
+- [Time Complexity: Primality](tutorials/cracking-the-code-interview/primality.js)

mathematics/fundamentals/findPoint.js

@@ -0,0 +1,6 @@
+//+ Jonas Raoni Soares Silva
+//@ http://raoni.org
+
+function findPoint(px, py, qx, qy) {
+	return [qx * 2 - px, qy * 2 - py];
+}

mathematics/fundamentals/gameWithCells.js

@@ -0,0 +1,8 @@
+//+ Jonas Raoni Soares Silva
+//@ http://raoni.org
+
+function gameWithCells(n, m){
+	const squares = (n >> 1) * (m >> 1);
+	const conectors = Math.ceil((n * m - squares * 4) / 2);
+	return squares + conectors;
+}

mathematics/fundamentals/handshake.js

@@ -0,0 +1,6 @@
+//+ Jonas Raoni Soares Silva
+//@ http://raoni.org
+
+function handshake(n) {
+	return n * (n - 1) / 2;
+}

mathematics/fundamentals/lowestTriangle.js

@@ -0,0 +1,6 @@
+//+ Jonas Raoni Soares Silva
+//@ http://raoni.org
+
+function lowestTriangle(base, area){
+	return Math.ceil(2 * area / base);
+}

mathematics/fundamentals/maximumDraws.js

@@ -0,0 +1,6 @@
+//+ Jonas Raoni Soares Silva
+//@ http://raoni.org
+
+function maximumDraws(n) {
+	return n + 1;
+}

mathematics/fundamentals/primeCount.js

@@ -0,0 +1,22 @@
+//+ Jonas Raoni Soares Silva
+//@ http://raoni.org
+
+// My solution will fail without updating the "main()", I've replaced the `parseInt(readLine(), 10)` by `BigInt(readLine())` =]
+function primeCount(n) {
+	if (n <= 1)
+		return 0;
+	let count = 1;
+	// Generate and multiply each prime, to know what's the max factor that can be built with them within the given interval
+	next:
+	for (let current = 2n, i = 1; (i += 2) <= n; ) {
+		// Reducing the number of checks
+		const end = Math.sqrt(i) >> 0;
+		for (let j = 1; ++j <= end; )
+			if (!(i % j))
+				continue next;
+		if ((current *= BigInt(i)) > n)
+			break;
+		++count;
+	}
+	return count;
+}

mathematics/fundamentals/solve.js

@@ -0,0 +1,10 @@
+//+ Jonas Raoni Soares Silva
+//@ http://raoni.org
+
+function solve(n) {
+	// I would add some caching here, to continue from the biggest found, but it wasn't needed :D
+	let last = 1;
+	for (let penultimate = 0, i = 0; last < n;)
+		last = penultimate + (penultimate = last);
+	return last === n ? 'IsFibo' : 'IsNotFibo';
+}

tutorials/cracking-the-code-interview/fibonacci.js

@@ -2,6 +2,10 @@
 //@ http://raoni.org
 
 function fibonacci(n) {
+	return Math.round(Math.pow((Math.sqrt(5) + 1) / 2, Math.abs(n)) / Math.sqrt(5)) * (n < 0 && n % 2 ? -1 : 1);
+}
+
+function fibonacci2(n) {
 	if (n < 2)
 		return n;
 	let last = 1;