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Commitde6a24e

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Minor code style fixes for bitwise multiplication.
1 parentbc8943d commitde6a24e

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5 files changed

+41
-17
lines changed

5 files changed

+41
-17
lines changed

‎src/algorithms/math/bits/README.md

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Original file line numberDiff line numberDiff line change
@@ -38,12 +38,14 @@ This method is a combination of "Clear Bit" and "Set Bit" methods.
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####isEven
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This method determines if the number provided is even.
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It is based on the fact that odd numbers have their last
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right bit to be set to 1.
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```
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Number: 5
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```text
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Number: 5 = 0b0101
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isEven: false
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Number: 4
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Number: 4 = 0b0100
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isEven: true
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```
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@@ -108,18 +110,19 @@ inverting all of the bits of the number and adding 1 to it.
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####Multiply Two Signed Numbers
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This method multiplies two signed integer numbers using bitwise operators.
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This method is based on the following :
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This method is based on the followingfacts:
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```text
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a * b can be written in the below formats
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a * b can be written in the below formats:
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0 if a is zero or b is zero or both a and b are zeroes
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2a * (b/2) if b is even
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2a * (b - 1)/2 + a if b is odd and positive
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2a * (b + 1)/2 - a if b is odd and negative
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```
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The advantage of this approach is that in each recursive step one of the operands reduces to half its original value.
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Hence, the run time complexity is O(log b) where b is the operand that reduces to half on each recursive step.
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The advantage of this approach is that in each recursive step one of the operands
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reduces to half its original value. Hence, the run time complexity is`O(log(b)` where`b` is
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the operand that reduces to half on each recursive step.
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>See[multiply.js](multiply.js) for further details.
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‎src/algorithms/math/bits/__test__/isEven.test.js

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@@ -7,5 +7,13 @@ describe('isEven', () => {
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expect(isEven(-2)).toBe(true);
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expect(isEven(1)).toBe(false);
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expect(isEven(-1)).toBe(false);
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expect(isEven(-3)).toBe(false);
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expect(isEven(3)).toBe(false);
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expect(isEven(8)).toBe(true);
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expect(isEven(9)).toBe(false);
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expect(isEven(121)).toBe(false);
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expect(isEven(122)).toBe(true);
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expect(isEven(1201)).toBe(false);
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expect(isEven(1202)).toBe(true);
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});
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});

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

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@@ -12,5 +12,7 @@ describe('multiply', () => {
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expect(multiply(4,-2)).toBe(-8);
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expect(multiply(-4,-4)).toBe(16);
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expect(multiply(4,-5)).toBe(-20);
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expect(multiply(2,121)).toBe(242);
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expect(multiply(121,2)).toBe(242);
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});
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});

‎src/algorithms/math/bits/isEven.js

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@@ -1,6 +1,6 @@
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/**
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*@param {number} number
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*@returnbool
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*@return{boolean}
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*/
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exportdefaultfunctionisEven(number){
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return(number&1)===0;

‎src/algorithms/math/bits/multiply.js

Lines changed: 20 additions & 9 deletions
Original file line numberDiff line numberDiff line change
@@ -1,27 +1,38 @@
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importmultiplyByTwofrom'./multiplyByTwo';
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importdivideByTwofrom'./divideByTwo';
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importisEvenfrom'./isEven';
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importmultiplyByTwofrom'./multiplyByTwo';
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/**
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* FUNCTION DEFINITION
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* multiply(a, b) = 0 if a is zero or b is zero or if both a and b are zeros
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* multiply(a, b) = multiply(2a, b/2) if b is even
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* multiply(a, b) = multiply(2a, (b-1)/2) + a if b is odd and b is positive
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* multiply(a, b) = multiply(2a, (b+1)/2) - a if b is odd and b is negative
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* Multiply two signed numbers using bitwise operations.
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*
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* If a is zero or b is zero or if both a and b are zeros:
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* multiply(a, b) = 0
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*
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* If b is even:
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* multiply(a, b) = multiply(2a, b/2)
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*
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* If b is odd and b is positive:
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* multiply(a, b) = multiply(2a, (b-1)/2) + a
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*
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* If b is odd and b is negative:
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* multiply(a, b) = multiply(2a, (b+1)/2) - a
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*
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* Time complexity: O(log b)
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*
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* COMPLEXITY
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* O(log b)
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*@param {number} a
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*@param {number} b
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*@return {number} a * b
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*@return {number}
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*/
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exportdefaultfunctionmultiply(a,b){
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// If a is zero or b is zero or if both a and b are zeros then the production is also zero.
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if(b===0||a===0){
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return0;
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}
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// Otherwise we will have four different cases that are described above.
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constmultiplyByOddPositive=()=>multiply(multiplyByTwo(a),divideByTwo(b-1))+a;
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constmultiplyByOddNegative=()=>multiply(multiplyByTwo(a),divideByTwo(b+1))-a;
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constmultiplyByEven=()=>multiply(multiplyByTwo(a),divideByTwo(b));
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constmultiplyByOdd=()=>(b>0 ?multiplyByOddPositive() :multiplyByOddNegative());
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