Update merge (#1)

* chore: ignore .DS_Store in git (trekhleb#65)

* Fix BST removal method.

* Simplify combineWithoutRepetition algorithm.

* add recursive solution to permutations with repetitions problem (trekhleb#52)

* add recursive solution to permutations with repetitions problem

* fix untested function, failing test

* add comments

* Add recursive way of generating permutations with repetitions.

* Code style fixes.

* Update javascript-algorithms-and-data-structures version.

* fix unbound knapsack problem with items more than 1(default value) (trekhleb#73)

* Code style fixes.

* Correct a comment (trekhleb#66)

* Fix LinkedList

* Fix the prepend method for the LinkedList

* Fix the remove method for the MinHeap

* Correct a comment

* Add algorithms complexity to README.

* Update README.

* Z algorithm implementation (trekhleb#77)

* Implemented Z algorithm

* Fixed bugs in implementation and added tests

* Added README explaining z algorithm

* Code style fixes.

* Add comments.

* Add comments.

* Fix BST removal method (trekhleb#74)

* Fix LinkedList

* Fix the prepend method for the LinkedList

* Fix the remove method for the MinHeap

* Correct a comment

* Fix BST removal method

* Add setValue and nodeCopy methods to binary tree node.

* Corrected explanations and included an example (trekhleb#75)

* Update README for integer partition.

* Added Complexity of Each Algorithm in Sorting/ directory. (trekhleb#76)

* Added Complexity to Bubble Sort README.md

* Added Complexity to Counting-Sort README.md

* Italicized n in Bubble Sort README.md

* Added Complexity to Heap Sort README.md

* Added Complexity to Insertion Sort README.md

* Added Complexity to Merge Sort README.md

* Added Complexity to Quick Sort README.md

* Added Complexity to Radix Sort README.md

* Added Complexity to Selection Sort README.md

* Added Complexity to SHell Sort README.md

* Update READMEs.

* Update READMEs.

* Update READMEs.

* Update READMEs.

* Update READMEs.

* Update READMEs.

* Update READMEs.

* Update READMEs.

* Update READMEs.

* Update READMEs.

* Add Levenshtein Distance algorithm explanations.

*  Fix the findEdge method of the graph (trekhleb#80)

* Fix LinkedList

* Fix the prepend method for the LinkedList

* Fix the remove method for the MinHeap

* Correct a comment

* Fix BST removal method

* Fix the findEdge method of the graph

* Code style fix.

* Add regular expression matching algorithm.

* Fix the value returned by DisjointSet union (trekhleb#81)

* Fix LinkedList

* Fix the prepend method for the LinkedList

* Fix the remove method for the MinHeap

* Correct a comment

* Fix BST removal method

* Fix the findEdge method of the graph

* Fix the value returned by DisjointSet union

* Add bit manipulation section.

* Add more bit manipulation functions.

* Add more bit manipulation functions.

* Fix typo.

* Simplify combineWithoutRepetitions function.

* Simplify combineWithRepetitions function.

* Add recursive factorial function (trekhleb#85)

* Fix LinkedList

* Fix the prepend method for the LinkedList

* Fix the remove method for the MinHeap

* Correct a comment

* Fix BST removal method

* Fix the findEdge method of the graph

* Fix the value returned by DisjointSet union

* Add recursive factorial function

* Simplify permutateWithRepetitions algorithm.

Author: tstillwell

.gitignore

@@ -2,3 +2,4 @@ node_modules
 .idea
 coverage
 .vscode
+.DS_Store

README.md

@@ -0,0 +1,99 @@
+# Bit Manipulation
+
+#### Get Bit
+
+This method shifts `1` over by `bitPosition` bits, creating a 
+value that looks like `00100`. Then we perform `AND` operation
+that clears all bits from the original number except the
+`bitPosition` one. Then we compare the result with zero. If 
+result is zero that would mean that original number has `0` at
+position `bitPosition`.
+
+> See `getBit` function for further details.
+
+#### Set Bit
+
+This method shifts `1` over by `bitPosition` bits, creating a
+value that looks like `00100`. Then we perform `OR` operation
+that sets specific bit into `1` but it does not affect on
+other bits of the number.
+
+> See `setBit` function for further details.
+
+#### Clear Bit
+
+This method shifts `1` over by `bitPosition` bits, creating a
+value that looks like `00100`. Than it inverts this mask to get
+the number that looks like `11011`. Then `AND` operation is
+being applied to both the number and the mask. That operation 
+unsets the bit.
+
+> See `clearBit` function for further details.
+
+#### Update Bit
+
+This method is a combination of "Clear Bit" and "Set Bit" methods.
+
+> See `updateBit` function for further details.
+
+#### Multiply By Two
+
+This method shifts original number by one bit to the left.
+Thus all binary number components (powers of two) are being
+multiplying by two and thus the number itself is being 
+multiplied by two.
+
+```
+Before the shift
+Number: 0b0101 = 5
+Powers of two: 0 + 2^2 + 0 + 2^0 
+
+After the shift
+Number: 0b1010 = 10
+Powers of two: 2^3 + 0 + 2^1 + 0 
+```
+
+> See `multiplyByTwo` function for further details.
+
+#### Divide By Two
+
+This method shifts original number by one bit to the right.
+Thus all binary number components (powers of two) are being
+divided by two and thus the number itself is being 
+divided by two without remainder.
+
+```
+Before the shift
+Number: 0b0101 = 5
+Powers of two: 0 + 2^2 + 0 + 2^0 
+
+After the shift
+Number: 0b0010 = 2
+Powers of two: 0 + 0 + 2^1 + 0 
+```
+
+> See `divideByTwo` function for further details.
+
+#### Switch Sign
+
+This method make positive numbers to be negative and backwards.
+To do so it uses "Twos Complement" approach which does it by
+inverting all of the bits of the number and adding 1 to it.
+
+```
+1101 -3
+1110 -2
+1111 -1
+0000  0
+0001  1
+0010  2
+0011  3
+``` 
+
+> See `switchSign` function for further details.
+
+## References
+
+- [Bit Manipulation on YouTube](https://www.youtube.com/watch?v=NLKQEOgBAnw&t=0s&index=28&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [Negative Numbers in binary on YouTube](https://www.youtube.com/watch?v=4qH4unVtJkE&t=0s&index=30&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [Bit Hacks on stanford.edu](https://graphics.stanford.edu/~seander/bithacks.html)

README.zh-CN.md

@@ -0,0 +1,15 @@
+import clearBit from '../clearBit';
+
+describe('clearBit', () => {
+  it('should clear bit at specific position', () => {
+    // 1 = 0b0001
+    expect(clearBit(1, 0)).toBe(0);
+    expect(clearBit(1, 1)).toBe(1);
+    expect(clearBit(1, 2)).toBe(1);
+
+    // 10 = 0b1010
+    expect(clearBit(10, 0)).toBe(10);
+    expect(clearBit(10, 1)).toBe(8);
+    expect(clearBit(10, 3)).toBe(2);
+  });
+});

README.zh-TW.md

@@ -0,0 +1,12 @@
+import divideByTwo from '../divideByTwo';
+
+describe('divideByTwo', () => {
+  it('should divide numbers by two using bitwise operations', () => {
+    expect(divideByTwo(0)).toBe(0);
+    expect(divideByTwo(1)).toBe(0);
+    expect(divideByTwo(3)).toBe(1);
+    expect(divideByTwo(10)).toBe(5);
+    expect(divideByTwo(17)).toBe(8);
+    expect(divideByTwo(125)).toBe(62);
+  });
+});

package-lock.json

@@ -0,0 +1,23 @@
+import getBit from '../getBit';
+
+describe('getBit', () => {
+  it('should get bit at specific position', () => {
+    // 1 = 0b0001
+    expect(getBit(1, 0)).toBe(1);
+    expect(getBit(1, 1)).toBe(0);
+
+    // 2 = 0b0010
+    expect(getBit(2, 0)).toBe(0);
+    expect(getBit(2, 1)).toBe(1);
+
+    // 3 = 0b0011
+    expect(getBit(3, 0)).toBe(1);
+    expect(getBit(3, 1)).toBe(1);
+
+    // 10 = 0b1010
+    expect(getBit(10, 0)).toBe(0);
+    expect(getBit(10, 1)).toBe(1);
+    expect(getBit(10, 2)).toBe(0);
+    expect(getBit(10, 3)).toBe(1);
+  });
+});

src/algorithms/math/bits/README.md

@@ -0,0 +1,12 @@
+import multiplyByTwo from '../multiplyByTwo';
+
+describe('multiplyByTwo', () => {
+  it('should multiply numbers by two using bitwise operations', () => {
+    expect(multiplyByTwo(0)).toBe(0);
+    expect(multiplyByTwo(1)).toBe(2);
+    expect(multiplyByTwo(3)).toBe(6);
+    expect(multiplyByTwo(10)).toBe(20);
+    expect(multiplyByTwo(17)).toBe(34);
+    expect(multiplyByTwo(125)).toBe(250);
+  });
+});

src/algorithms/math/bits/__test__/clearBit.test.js

@@ -0,0 +1,15 @@
+import setBit from '../setBit';
+
+describe('setBit', () => {
+  it('should set bit at specific position', () => {
+    // 1 = 0b0001
+    expect(setBit(1, 0)).toBe(1);
+    expect(setBit(1, 1)).toBe(3);
+    expect(setBit(1, 2)).toBe(5);
+
+    // 10 = 0b1010
+    expect(setBit(10, 0)).toBe(11);
+    expect(setBit(10, 1)).toBe(10);
+    expect(setBit(10, 2)).toBe(14);
+  });
+});

src/algorithms/math/bits/__test__/divideByTwo.test.js

@@ -0,0 +1,13 @@
+import switchSign from '../switchSign';
+
+describe('switchSign', () => {
+  it('should switch the sign of the number using twos complement approach', () => {
+    expect(switchSign(0)).toBe(0);
+    expect(switchSign(1)).toBe(-1);
+    expect(switchSign(-1)).toBe(1);
+    expect(switchSign(32)).toBe(-32);
+    expect(switchSign(-32)).toBe(32);
+    expect(switchSign(23)).toBe(-23);
+    expect(switchSign(-23)).toBe(23);
+  });
+});

src/algorithms/math/bits/__test__/getBit.test.js

@@ -0,0 +1,19 @@
+import updateBit from '../updateBit';
+
+describe('updateBit', () => {
+  it('should update bit at specific position', () => {
+    // 1 = 0b0001
+    expect(updateBit(1, 0, 1)).toBe(1);
+    expect(updateBit(1, 0, 0)).toBe(0);
+    expect(updateBit(1, 1, 1)).toBe(3);
+    expect(updateBit(1, 2, 1)).toBe(5);
+
+    // 10 = 0b1010
+    expect(updateBit(10, 0, 1)).toBe(11);
+    expect(updateBit(10, 0, 0)).toBe(10);
+    expect(updateBit(10, 1, 1)).toBe(10);
+    expect(updateBit(10, 1, 0)).toBe(8);
+    expect(updateBit(10, 2, 1)).toBe(14);
+    expect(updateBit(10, 2, 0)).toBe(10);
+  });
+});

src/algorithms/math/bits/__test__/multiplyByTwo.test.js

@@ -0,0 +1,10 @@
+/**
+ * @param {number} number
+ * @param {number} bitPosition - zero based.
+ * @return {number}
+ */
+export default function clearBit(number, bitPosition) {
+  const mask = ~(1 << bitPosition);
+
+  return number & mask;
+}

src/algorithms/math/bits/__test__/setBit.test.js

@@ -0,0 +1,7 @@
+/**
+ * @param {number} number
+ * @return {number}
+ */
+export default function divideByTwo(number) {
+  return number >> 1;
+}

src/algorithms/math/bits/__test__/switchSign.test.js

@@ -0,0 +1,8 @@
+/**
+ * @param {number} number
+ * @param {number} bitPosition - zero based.
+ * @return {number}
+ */
+export default function getBit(number, bitPosition) {
+  return (number & (1 << bitPosition)) === 0 ? 0 : 1;
+}

src/algorithms/math/bits/__test__/updateBit.test.js

@@ -0,0 +1,7 @@
+/**
+ * @param {number} number
+ * @return {number}
+ */
+export default function multiplyByTwo(number) {
+  return number << 1;
+}

src/algorithms/math/bits/clearBit.js

@@ -0,0 +1,8 @@
+/**
+ * @param {number} number
+ * @param {number} bitPosition - zero based.
+ * @return {number}
+ */
+export default function setBit(number, bitPosition) {
+  return number | (1 << bitPosition);
+}

src/algorithms/math/bits/divideByTwo.js

@@ -0,0 +1,8 @@
+/**
+ * Switch the sign of the number using "Twos Complement" approach.
+ * @param {number} number
+ * @return {number}
+ */
+export default function switchSign(number) {
+  return ~number + 1;
+}

src/algorithms/math/bits/getBit.js

@@ -0,0 +1,16 @@
+/**
+ * @param {number} number
+ * @param {number} bitPosition - zero based.
+ * @param {number} bitValue - 0 or 1.
+ * @return {number}
+ */
+export default function updateBit(number, bitPosition, bitValue) {
+  // Normalized bit value.
+  const bitValueNormalized = bitValue ? 1 : 0;
+
+  // Init clear mask.
+  const clearMask = ~(1 << bitPosition);
+
+  // Clear bit value and then set it up to required value.
+  return (number & clearMask) | (bitValueNormalized << bitPosition);
+}

src/algorithms/math/bits/multiplyByTwo.js

@@ -0,0 +1,11 @@
+import factorialRecursive from '../factorialRecursive';
+
+describe('factorialRecursive', () => {
+  it('should calculate factorial', () => {
+    expect(factorialRecursive(0)).toBe(1);
+    expect(factorialRecursive(1)).toBe(1);
+    expect(factorialRecursive(5)).toBe(120);
+    expect(factorialRecursive(8)).toBe(40320);
+    expect(factorialRecursive(10)).toBe(3628800);
+  });
+});

src/algorithms/math/bits/setBit.js

@@ -0,0 +1,7 @@
+/**
+ * @param {number} number
+ * @return {number}
+ */
+export default function factorialRecursive(number) {
+  return number > 1 ? number * factorialRecursive(number - 1) : 1;
+}

src/algorithms/math/bits/switchSign.js

@@ -18,7 +18,7 @@ export default function fibonacci(n) {
 
   while (iterationsCounter) {
     currentValue += previousValue;
-    previousValue = (currentValue - previousValue);
+    previousValue = currentValue - previousValue;
 
     fibSequence.push(currentValue);
 

src/algorithms/math/bits/updateBit.js

@@ -16,7 +16,7 @@ export default function fibonacciNth(n) {
 
   while (iterationsCounter) {
     currentValue += previousValue;
-    previousValue = (currentValue - previousValue);
+    previousValue = currentValue - previousValue;
 
     iterationsCounter -= 1;
   }

src/algorithms/math/factorial/__test__/factorialRecursive.test.js

@@ -17,9 +17,10 @@ export default function integerPartition(number) {
     partitionMatrix[0][numberIndex] = 0;
   }
 
-  // Let's fill the first row. It represents the number of way of how we can form
-  // number zero out of numbers 0, 1, 2, ... Obviously there is only one way we could
-  // form number 0 and it is with number 0 itself.
+  // Let's fill the first column. It represents the number of ways we can form
+  // number zero out of numbers 0, 0 and 1, 0 and 1 and 2, 0 and 1 and 2 and 3, ...
+  // Obviously there is only one way we could form number 0
+  // and it is with number 0 itself.
   for (let summandIndex = 0; summandIndex <= number; summandIndex += 1) {
     partitionMatrix[summandIndex][0] = 1;
   }
@@ -33,9 +34,17 @@ export default function integerPartition(number) {
         // any new ways of forming the number. Thus we may just copy the number from row above.
         partitionMatrix[summandIndex][numberIndex] = partitionMatrix[summandIndex - 1][numberIndex];
       } else {
-        // The number of combinations would equal to number of combinations of forming the same
-        // number but WITHOUT current summand number plus number of combinations of forming the
-        // previous number but WITH current summand.
+        /*
+         * The number of combinations would equal to number of combinations of forming the same
+         * number but WITHOUT current summand number PLUS number of combinations of forming the
+         * <current number - current summand> number but WITH current summand.
+         *
+         * Example:
+         * Number of ways to form 5 using summands {0, 1, 2} would equal the SUM of:
+         * - number of ways to form 5 using summands {0, 1} (we've excluded summand 2)
+         * - number of ways to form 3 (because 5 - 2 = 3) using summands {0, 1, 2}
+         * (we've included summand 2)
+        */
         const combosWithoutSummand = partitionMatrix[summandIndex - 1][numberIndex];
         const combosWithSummand = partitionMatrix[summandIndex][numberIndex - summandIndex];