Related
For instance, whenever my count is equal to 4294967295 + 1 I want that the count restart from 0.
Basically I`m trying to simulate a unsigned 32 bits in java that has range [0, 4294967295]. The methods that I'm trying to create is ADD and MULTIPLE.
For example, if I have the number 4294967295 and I multiple by 2, I will get the result 4294967294.
Since Java does not have a unsigned int, I need to create that class to "simulate" the C int uint32_t in Java.
If I multiple 1103527590 * 1103515245 the result should be 4294967294, but my code is giving the result 2524872877
public class Unsigned32BitsInt {
private long limit; // Upper bound 4294967295
public Unsigned32BitsInt(long limit) {
this.limit = limit;
}
public long add(long x, long y) {
long result = 0L;
if (x + y < this.limit) {
if ((x + y) % this.limit == 0) {
result = (x + y) / 2;
} else {
result = (x + y) % this.limit;
}
} else {
if ((x + y) % this.limit == 0) {
result = (x + y) / (Math.max(x, y) / Math.min(x, y)) - 1;
} else {
result = (x + y) % this.limit - 1;
}
}
return result;
}
public long multiple(long x, long y) {
long result = 1L;
long r = x*y;
long c = result = (x * y) % this.limit;
if (x * y < this.limit) {
if ((x * y) % this.limit == 0) {
result = (x + y) / 2;
} else {
result = (x * y) % this.limit;
}
} else {
if ((x * y) % this.limit == 0) {
result = (x * y) / 2 - 1;
} else {
result = (x * y) % this.limit - 1;
}
}
return result;
}
}
Int's are only signed from the standpoint of comparisons and display. Internally signed and unsigned are no different.
So when the count is 4294967295 that is -1 in twos complement form. So you add 1 and you get 0 as required. You can print it unsigned by casting it to a long like so.
int s = -1;
// prints 4294967295
System.out.println(((long)s)&0xffff_ffffL);
If count is Integer.MAX_VALUE you have count = 2147483647 you can add 1 and get 2147483648. You can cast it to a long to print it as unsigned instead of the normal -2147483648.
To do general comparisons, use the built-in method
Integer.unsignedCompare(int x, int y);
to compare two integers as 32 bit unsigned values.
And finally,
int a = 1_103_527_590;
int b = 1_103_515_245;
System.out.println((long)(a*b) & 0xffff_ffffL);
prints
2524872878
Update
As pointed out by Andrey Tyukin instead of the casting to long and masking of the value, the Integer class method Integer.toUnsignedString() can be used to print the unsigned value. For more useful methods check out the Integer class in the Java API.
The answer from #WJS makes a good point:
[Integers] are only signed from the standpoint of comparisons and display. Internally signed and unsigned are no different.
In Java, doing arithmetic on integer types does not result in overflow.[1] The values wrap around. Along with ~unsigned methods in some of the the APIs, such as the Integer API, this makes it easy to do unsigned arithmetic.
Even so, it might be convenient to have unsigned classes. Here is part of one for a 32-bit integer:
public final class Unsigned32BitInt implements
Comparable<Unsigned32BitInt> {
public static final Unsigned32BitInt ZERO = new
Unsigned32BitInt (0);
public static final Unsigned32BitInt ONE = new
Unsigned32BitInt (1);
private final int value; // [2]
public Unsigned32BitInt () { value = 0; }
public Unsigned32BitInt (long v) {
value = (int) v ;
}
public Unsigned32BitInt (int v) {
value = v;
}
#Override
public int compareTo (Unsigned32BitInt other) {
return Integer.compareUnsigned (this.value, other.value);
}
#Override
public boolean equals (Object other) {
if (this == other) return true;
if (other == null) return false;
if ( ! (other instanceof Unsigned32BitInt )) return false;
return Integer.compareUnsigned
(this.value, ((Unsigned32BitInt) other).value) == 0;
}
#Override
public int hashCode () { return value; }
public Unsigned32BitInt add (Unsigned32BitInt i) { // [3]
return new Unsigned32BitInt (i.value + this.value);
}
public Unsigned32BitInt multiply (Unsigned32BitInt i) {
long a = i.value;
long b = value;
return new Unsigned32BitInt (a * b);
}
#Override
public String toString () {
return Integer.toUnsignedString(value);
}
}
You can continue, adding methods, including overriden methods and overloaded methods, to fit your needs.
In some cases, as shown in toString and compareTo here, methods will be wrappers for methods in the Byte, Short, Integer, or Long APIs.
NOTES:
[1] If you need arithmetic that can throw an ArithmeticException on overflow, there are ~Exact methods in the Math API
[2] I made Objects of type Unsigned32BitInt immutable. I kept the values as 32 bit integers.
[3] My preference would be to have the arithmetic operations be instance methods, e.g. c = a.add(b);, sum = sum.add(a);. From your example, you might prefer static methods. One such method might look like this:
public static Unsigned32BitInt add
(Unsigned32BitInt a, Unsigned32BitInt b) {
return new Unsigned32BitInt (a.value + b.value);
}
I got bored and decided to dive into remaking the square root function without referencing any of the Math.java functions. I have gotten to this point:
package sqrt;
public class SquareRoot {
public static void main(String[] args) {
System.out.println(sqrtOf(8));
}
public static double sqrtOf(double n){
double x = log(n,2);
return powerOf(2, x/2);
}
public static double log(double n, double base)
{
return (Math.log(n)/Math.log(base));
}
public static double powerOf(double x, double y) {
return powerOf(e(),y * log(x, e()));
}
public static int factorial(int n){
if(n <= 1){
return 1;
}else{
return n * factorial((n-1));
}
}
public static double e(){
return 1/factorial(1);
}
public static double e(int precision){
return 1/factorial(precision);
}
}
As you may very well see, I came to the point in my powerOf() function that infinitely recalls itself. I could replace that and use Math.exp(y * log(x, e()), so I dived into the Math source code to see how it handled my problem, resulting in a goose chase.
public static double exp(double a) {
return StrictMath.exp(a); // default impl. delegates to StrictMath
}
which leads to:
public static double exp(double x)
{
if (x != x)
return x;
if (x > EXP_LIMIT_H)
return Double.POSITIVE_INFINITY;
if (x < EXP_LIMIT_L)
return 0;
// Argument reduction.
double hi;
double lo;
int k;
double t = abs(x);
if (t > 0.5 * LN2)
{
if (t < 1.5 * LN2)
{
hi = t - LN2_H;
lo = LN2_L;
k = 1;
}
else
{
k = (int) (INV_LN2 * t + 0.5);
hi = t - k * LN2_H;
lo = k * LN2_L;
}
if (x < 0)
{
hi = -hi;
lo = -lo;
k = -k;
}
x = hi - lo;
}
else if (t < 1 / TWO_28)
return 1;
else
lo = hi = k = 0;
// Now x is in primary range.
t = x * x;
double c = x - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
if (k == 0)
return 1 - (x * c / (c - 2) - x);
double y = 1 - (lo - x * c / (2 - c) - hi);
return scale(y, k);
}
Values that are referenced:
LN2 = 0.6931471805599453, // Long bits 0x3fe62e42fefa39efL.
LN2_H = 0.6931471803691238, // Long bits 0x3fe62e42fee00000L.
LN2_L = 1.9082149292705877e-10, // Long bits 0x3dea39ef35793c76L.
INV_LN2 = 1.4426950408889634, // Long bits 0x3ff71547652b82feL.
INV_LN2_H = 1.4426950216293335, // Long bits 0x3ff7154760000000L.
INV_LN2_L = 1.9259629911266175e-8; // Long bits 0x3e54ae0bf85ddf44L.
P1 = 0.16666666666666602, // Long bits 0x3fc555555555553eL.
P2 = -2.7777777777015593e-3, // Long bits 0xbf66c16c16bebd93L.
P3 = 6.613756321437934e-5, // Long bits 0x3f11566aaf25de2cL.
P4 = -1.6533902205465252e-6, // Long bits 0xbebbbd41c5d26bf1L.
P5 = 4.1381367970572385e-8, // Long bits 0x3e66376972bea4d0L.
TWO_28 = 0x10000000, // Long bits 0x41b0000000000000L
Here is where I'm starting to get lost. But I can make a few assumptions that so far the answer is starting to become estimated. I then find myself here:
private static double scale(double x, int n)
{
if (Configuration.DEBUG && abs(n) >= 2048)
throw new InternalError("Assertion failure");
if (x == 0 || x == Double.NEGATIVE_INFINITY
|| ! (x < Double.POSITIVE_INFINITY) || n == 0)
return x;
long bits = Double.doubleToLongBits(x);
int exp = (int) (bits >> 52) & 0x7ff;
if (exp == 0) // Subnormal x.
{
x *= TWO_54;
exp = ((int) (Double.doubleToLongBits(x) >> 52) & 0x7ff) - 54;
}
exp += n;
if (exp > 0x7fe) // Overflow.
return Double.POSITIVE_INFINITY * x;
if (exp > 0) // Normal.
return Double.longBitsToDouble((bits & 0x800fffffffffffffL)
| ((long) exp << 52));
if (exp <= -54)
return 0 * x; // Underflow.
exp += 54; // Subnormal result.
x = Double.longBitsToDouble((bits & 0x800fffffffffffffL)
| ((long) exp << 52));
return x * (1 / TWO_54);
}
TWO_54 = 0x40000000000000L
While I am, I would say, very understanding of math and programming, I hit the point to where I find myself at a Frankenstein monster mix of the two. I noticed the intrinsic switch to bits (which I have little to no experience with), and I was hoping someone could explain to me the processes that are occurring "under the hood" so to speak. Specifically where I got lost is from "Now x is in primary range" in the exp() method on wards and what the values that are being referenced really represent. I'm was asking for someone to help me understand not only the methods themselves, but also how they arrive to the answer. Feel free to go as in depth as needed.
edit:
if someone could maybe make this tag: "strictMath" that would be great. I believe that its size and for the Math library deriving from it justifies its existence.
To the exponential function:
What happens is that
exp(x) = 2^k * exp(x-k*log(2))
is exploited for positive x. Some magic is used to get more consistent results for large x where the reduction x-k*log(2) will introduce cancellation errors.
On the reduced x a rational approximation with minimized maximal error over the interval 0.5..1.5 is used, see Pade approximations and similar. This is based on the symmetric formula
exp(x) = exp(x/2)/exp(-x/2) = (c(x²)+x)/(c(x²)-x)
(note that the c in the code is x+c(x)-2). When using Taylor series, approximations for c(x*x)=x*coth(x/2) are based on
c(u)=2 + 1/6*u - 1/360*u^2 + 1/15120*u^3 - 1/604800*u^4 + 1/23950080*u^5 - 691/653837184000*u^6
The scale(x,n) function implements the multiplication x*2^n by directly manipulating the exponent in the bit assembly of the double floating point format.
Computing square roots
To compute square roots it would be more advantageous to compute them directly. First reduce the interval of approximation arguments via
sqrt(x)=2^k*sqrt(x/4^k)
which can again be done efficiently by directly manipulating the bit format of double.
After x is reduced to the interval 0.5..2.0 one can then employ formulas of the form
u = (x-1)/(x+1)
y = (c(u*u)+u) / (c(u*u)-u)
based on
sqrt(x)=sqrt(1+u)/sqrt(1-u)
and
c(v) = 1+sqrt(1-v) = 2 - 1/2*v - 1/8*v^2 - 1/16*v^3 - 5/128*v^4 - 7/256*v^5 - 21/1024*v^6 - 33/2048*v^7 - ...
In a program without bit manipulations this could look like
double my_sqrt(double x) {
double c,u,v,y,scale=1;
int k=0;
if(x<0) return NaN;
while(x>2 ) { x/=4; scale *=2; k++; }
while(x<0.5) { x*=4; scale /=2; k--; }
// rational approximation of sqrt
u = (x-1)/(x+1);
v = u*u;
c = 2 - v/2*(1 + v/4*(1 + v/2));
y = 1 + 2*u/(c-u); // = (c+u)/(c-u);
// one Halley iteration
y = y*(1+8*x/(3*(3*y*y+x))) // = y*(y*y+3*x)/(3*y*y+x)
// reconstruct original scale
return y*scale;
}
One could replace the Halley step with two Newton steps, or
with a better uniform approximation in c one could replace the Halley step with one Newton step, or ...
today i heard about this website called codility where a user can give various programming test to check their code's performance.
When I started, they presented me with this sample test,
Task description A small frog wants to get to the other side of the
road. The frog is currently located at position X and wants to get to
a position greater than or equal to Y. The small frog always jumps a
fixed distance, D. Count the minimal number of jumps that the small
frog must perform to reach its target.
Write a function:
class Solution { public int solution(int X, int Y, int D); }
that, given three integers X, Y and D, returns the minimal number of jumps from position X to a position equal to or greater than Y.
For example,
given:
X = 10
Y = 85
D = 30 the function should return 3,
because the frog will be positioned as follows:
after the first jump,
at position 10 + 30 = 40
after the second jump, at position 10 + 30 + 30 = 70
after the third jump, at position 10 + 30 + 30 + 30 = 100
Assume that: X, Y and D are integers within the range
[1..1,000,000,000]; X ≤ Y. Complexity: expected worst-case time
complexity is O(1); expected worst-case space complexity is O(1).
The question was pretty straight forward and it took me like 2 minutes to write the solution, which is following,
class Solution {
public int solution(int X, int Y, int D) {
int p = 0;
while (X < Y){
p++;
X = X + D;
}
return p;
}
}
However, the test result shows that the performance of my code is just 20% and I scored just 55%,
Here is the link to result, https://codility.com/demo/results/demo66WP2H-K25/
That was so simple code, where I have just used a single while loop, how could it possibly be make much faster ?
Basic math:
X + nD >= Y
nD >= Y - X
n >= (Y - X) / D
The minimum value for n will be the result of rounding up the division of (Y - X) by D.
Big O analysis for this operation:
Complexity: O(1). It's a difference, a division and a round up
Worst-case space complexity is O(1): you can have at most 3 more variables:
Difference for Y - X, let's assign this into Z.
Division between Z by D, let's assign this into E.
Rounding E up, let's assign this into R (from result).
Java(One Line), Correctness 100%, Performance 100%, Task score 100%
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int X, int Y, int D) {
return (int) Math.ceil((double) (Y - X) / (double) D);
}
}
Here is the 100% total score Python solution:
def solution(X, Y, D):
# write your code in Python 3.6
s = (Y-X)/D
return int(-(-s // 1))
class Solution {
public int solution(int x, int y, int d) {
return (y - x + d - 1) / d;
}
}
class Solution {
public int solution(int x, int y, int d) {
// write your code in Java SE 8
System.out.println("this is a debug message"+(y-x)%d);
if((y-x)%d == 0)
return ((y-x)/d);
else
return (((y-x)/d)+1);
}
}
C# got 100 out of 100 points
using System;
// you can also use other imports, for example:
// using System.Collections.Generic;
// you can write to stdout for debugging purposes, e.g.
// Console.WriteLine("this is a debug message");
class Solution {
public int solution(int X, int Y, int D) {
int Len= Y-X;
if (Len%D==0)
{
return Len/D;
}
else
{
return (Len/D)+1;
}
}
}
Here's Scala solution:
def solution(X: Int, Y: Int, D: Int): Int = {
//divide distance (Y-X) with fixed jump distance. If there is reminder then add 1 to result to
// cover that part with one jump
val jumps = (Y-X) / D + (if(((Y-X) % D) >0 ) 1 else 0)
jumps
}
Performance: https://codility.com/demo/results/trainingTQS547-ZQW/
Javascript solution, 100/100, and shorter than the existing answer:
function solution(Y, Y, D) {
return Math.ceil((Y - X) / D);
}
Here is a solution that brings the test performance to 100%
class Solution {
public int solution(int X, int Y, int D) {
if (X >= Y) return 0;
if (D == 0) return -1;
int minJump = 0;
if ((Y - X) % D == 0) {
minJump = (Y - X) / D;
} else minJump= (Y - X) / D +1;
return minJump;
}
}
JavaScript solution 100/100
function solution (x,y,d) {
if ((y-x) % d === 0) {
return (y-x)/d;
} else {
return Math.ceil((y-x)/d);
}
}
Using Java perfect code
100 score code in Java
public int solution(int X, int Y, int D) {
if(X<0 && Y<0)
return 0;
if(X==Y)
return 0;
if((Y-X)%D==0)
return (Y-X)/D;
else
return (((Y-X)/D)+1);
}
this is corrected code using java giving 91% pass
int solution(int A[]) {
int len = A.length;
if (len == 2) {
return Math.abs(A[1] - A[0]);
}
int[] sumArray = new int[A.length];
int sum = 0;
for (int j = 0; j < A.length; j++) {
sum = sum + A[j];
sumArray[j] = sum;
}
int min = Integer.MAX_VALUE;
for (int j = 0; j < sumArray.length; j++) {
int difference = Math.abs(sum - 2 * sumArray[j]);
// System.out.println(difference);
if (difference < min)
min = difference;
}
return min;
}
This is my solution with 100% (C#):
int result = 0;
if (y <= x || d == 0)
{
result = 0;
}
else
{
result = (y - x + d - 1) / d;
}
return result;
Here is my solution in PHP, 100% performance.
function solution($X, $Y, $D) {
return (int)ceil(($Y-$X)/$D); //ceils returns a float and so we cast (int)
}
Y-X gives you the actual distance object has to be travel ,if that distance is directly divsible by object jump(D) then ans will be (sum/D) if some decimal value is there then we have to add 1 more into it i.e(sum/D)+1
int sum=Y-X;
if(X!=Y && X<Y){
if(sum%D==0){
return (int )(sum/D);
}
else{
return ((int)(sum/D)+1);
}}
else{
return 0;
}
I like all the rest of the solutions, especially "(y - x + d - 1) / d". That was awesome. This is what I came up with.
public int solution(int X, int Y, int D) {
if (X == Y || X > Y || D == 0) {
return 0;
}
int total = (Y - X) / D;
int left = (Y - X) - (D * total);
if (left > 0) {
total++;
}
return total;
}
// you can write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');
function solution(X, Y, D) {
let jumps = 0
//If 0 -> 100 with 2 step
// Answer would be 100/2 = 50
//If 10 -> 100 with 2 step
//Answer would be (100 - 10) / 2 = 45
jumps = Math.ceil((Y - X) / D)
return jumps
}
swift solution 100% PASS - O(1) complexity
import Foundation
import Glibc
public func solution(_ X : Int, _ Y : Int, _ D : Int) -> Int {
if X == Y {
return 0
}
var jumps = (Y-X)/D
if jumps * D + X < Y {
jumps += 1
}
return jumps
}
import math
def solution(X, Y, D):
if (X >= Y): return 0
if (D == 0): return -1
minJump = 0
#if ((Y - X) % D == 0):
minJump = math.ceil((Y - X) / D)
#else:
#minJump = math.ceil((Y - X) / D) +1
return minJump
This solution worked for me in Java 11:
public int solution(int X, int Y, int D) {
return X == Y ? 0 : (Y - X - 1) / D + 1;
}
Correctness 100%, Performance 100%, Task score 100%
#Test
void solution() {
assertThat(task1.solution(0, 0, 30)).isEqualTo(0);
assertThat(task1.solution(10, 10, 10)).isEqualTo(0);
assertThat(task1.solution(10, 10, 30)).isEqualTo(0);
assertThat(task1.solution(10, 30, 30)).isEqualTo(1);
assertThat(task1.solution(10, 40, 30)).isEqualTo(1);
assertThat(task1.solution(10, 45, 30)).isEqualTo(2);
assertThat(task1.solution(10, 70, 30)).isEqualTo(2);
assertThat(task1.solution(10, 75, 30)).isEqualTo(3);
assertThat(task1.solution(10, 80, 30)).isEqualTo(3);
assertThat(task1.solution(10, 85, 30)).isEqualTo(3);
assertThat(task1.solution(10, 100, 30)).isEqualTo(3);
assertThat(task1.solution(10, 101, 30)).isEqualTo(4);
assertThat(task1.solution(10, 105, 30)).isEqualTo(4);
assertThat(task1.solution(10, 110, 30)).isEqualTo(4);
}
Here is the JS implementation
function frogJumbs(x, y, d) {
if ((y - x) % d == 0) {
return Math.floor((y - x) / d);
}
return Math.floor((y - x) / d + 1);
}
console.log(frogJumbs(0, 150, 30));
100% C# solution:
public int solution(int X, int Y, int D)
{
var result = Math.Ceiling((double)(Y - X) / D);
return Convert.ToInt32(result);
}
It divides the total distance by length of a jump and rounds up the result. It came after multiple attempts and some web searches.
Here is the solution in Python giving a score of 100 on Codility:
import math
return math.ceil((Y-X)/D)
Is there any ceil counterpart for Math.floorDiv()
How to calculate it fastest way with what we have?
UPDATE
The code for floorDiv() is follows:
public static long floorDiv(long x, long y) {
long r = x / y;
// if the signs are different and modulo not zero, round down
if ((x ^ y) < 0 && (r * y != x)) {
r--;
}
return r;
}
Can we code ceil the similar way?
UPDATE 2
I saw this answer https://stackoverflow.com/a/7446742/258483 but it seems to have too many unnecessary operations.
There is none in the Math class, but you can easily calculate it
long ceilDiv(long x, long y){
return -Math.floorDiv(-x,y);
}
For example, ceilDiv(1,2) = -floorDiv(-1,2) =-(-1)= 1 (correct answer).
I'd also just use the negation of floorMod, but if you are going to define your own function, you could simply adapt the above code:
public static int ceilDiv(int x, int y) {
int r = x / y;
// if the signs are the same and modulo not zero, round up
if ((x ^ y) >= 0 && (r * y != x)) r++;
return r;
}
You can make use of the floorDiv function and fiddle with that:
int ceilDiv(int x, int y) {
return Math.floorDiv(x, y) + (x % y == 0 ? 0 : 1)
}
Is there any other way in Java to calculate a power of an integer?
I use Math.pow(a, b) now, but it returns a double, and that is usually a lot of work, and looks less clean when you just want to use ints (a power will then also always result in an int).
Is there something as simple as a**b like in Python?
When it's power of 2. Take in mind, that you can use simple and fast shift expression 1 << exponent
example:
22 = 1 << 2 = (int) Math.pow(2, 2)
210 = 1 << 10 = (int) Math.pow(2, 10)
For larger exponents (over 31) use long instead
232 = 1L << 32 = (long) Math.pow(2, 32)
btw. in Kotlin you have shl instead of << so
(java) 1L << 32 = 1L shl 32 (kotlin)
Integers are only 32 bits. This means that its max value is 2^31 -1. As you see, for very small numbers, you quickly have a result which can't be represented by an integer anymore. That's why Math.pow uses double.
If you want arbitrary integer precision, use BigInteger.pow. But it's of course less efficient.
Best the algorithm is based on the recursive power definition of a^b.
long pow (long a, int b)
{
if ( b == 0) return 1;
if ( b == 1) return a;
if (isEven( b )) return pow ( a * a, b/2); //even a=(a^2)^b/2
else return a * pow ( a * a, b/2); //odd a=a*(a^2)^b/2
}
Running time of the operation is O(logb).
Reference:More information
No, there is not something as short as a**b
Here is a simple loop, if you want to avoid doubles:
long result = 1;
for (int i = 1; i <= b; i++) {
result *= a;
}
If you want to use pow and convert the result in to integer, cast the result as follows:
int result = (int)Math.pow(a, b);
Google Guava has math utilities for integers.
IntMath
import java.util.*;
public class Power {
public static void main(String args[])
{
Scanner sc=new Scanner(System.in);
int num = 0;
int pow = 0;
int power = 0;
System.out.print("Enter number: ");
num = sc.nextInt();
System.out.print("Enter power: ");
pow = sc.nextInt();
System.out.print(power(num,pow));
}
public static int power(int a, int b)
{
int power = 1;
for(int c = 0; c < b; c++)
power *= a;
return power;
}
}
Guava's math libraries offer two methods that are useful when calculating exact integer powers:
pow(int b, int k) calculates b to the kth the power, and wraps on overflow
checkedPow(int b, int k) is identical except that it throws ArithmeticException on overflow
Personally checkedPow() meets most of my needs for integer exponentiation and is cleaner and safter than using the double versions and rounding, etc. In almost all the places I want a power function, overflow is an error (or impossible, but I want to be told if the impossible ever becomes possible).
If you want get a long result, you can just use the corresponding LongMath methods and pass int arguments.
Well you can simply use Math.pow(a,b) as you have used earlier and just convert its value by using (int) before it. Below could be used as an example to it.
int x = (int) Math.pow(a,b);
where a and b could be double or int values as you want.
This will simply convert its output to an integer value as you required.
A simple (no checks for overflow or for validity of arguments) implementation for the repeated-squaring algorithm for computing the power:
/** Compute a**p, assume result fits in a 32-bit signed integer */
int pow(int a, int p)
{
int res = 1;
int i1 = 31 - Integer.numberOfLeadingZeros(p); // highest bit index
for (int i = i1; i >= 0; --i) {
res *= res;
if ((p & (1<<i)) > 0)
res *= a;
}
return res;
}
The time complexity is logarithmic to exponent p (i.e. linear to the number of bits required to represent p).
I managed to modify(boundaries, even check, negative nums check) Qx__ answer. Use at your own risk. 0^-1, 0^-2 etc.. returns 0.
private static int pow(int x, int n) {
if (n == 0)
return 1;
if (n == 1)
return x;
if (n < 0) { // always 1^xx = 1 && 2^-1 (=0.5 --> ~ 1 )
if (x == 1 || (x == 2 && n == -1))
return 1;
else
return 0;
}
if ((n & 1) == 0) { //is even
long num = pow(x * x, n / 2);
if (num > Integer.MAX_VALUE) //check bounds
return Integer.MAX_VALUE;
return (int) num;
} else {
long num = x * pow(x * x, n / 2);
if (num > Integer.MAX_VALUE) //check bounds
return Integer.MAX_VALUE;
return (int) num;
}
}
base is the number that you want to power up, n is the power, we return 1 if n is 0, and we return the base if the n is 1, if the conditions are not met, we use the formula base*(powerN(base,n-1)) eg: 2 raised to to using this formula is : 2(base)*2(powerN(base,n-1)).
public int power(int base, int n){
return n == 0 ? 1 : (n == 1 ? base : base*(power(base,n-1)));
}
There some issues with pow method:
We can replace (y & 1) == 0; with y % 2 == 0
bitwise operations always are faster.
Your code always decrements y and performs extra multiplication, including the cases when y is even. It's better to put this part into else clause.
public static long pow(long x, int y) {
long result = 1;
while (y > 0) {
if ((y & 1) == 0) {
x *= x;
y >>>= 1;
} else {
result *= x;
y--;
}
}
return result;
}
Use the below logic to calculate the n power of a.
Normally if we want to calculate n power of a. We will multiply 'a' by n number of times.Time complexity of this approach will be O(n)
Split the power n by 2, calculate Exponentattion = multiply 'a' till n/2 only. Double the value. Now the Time Complexity is reduced to O(n/2).
public int calculatePower1(int a, int b) {
if (b == 0) {
return 1;
}
int val = (b % 2 == 0) ? (b / 2) : (b - 1) / 2;
int temp = 1;
for (int i = 1; i <= val; i++) {
temp *= a;
}
if (b % 2 == 0) {
return temp * temp;
} else {
return a * temp * temp;
}
}
Apache has ArithmeticUtils.pow(int k, int e).
import java.util.Scanner;
class Solution {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int t = sc.nextInt();
for (int i = 0; i < t; i++) {
try {
long x = sc.nextLong();
System.out.println(x + " can be fitted in:");
if (x >= -128 && x <= 127) {
System.out.println("* byte");
}
if (x >= -32768 && x <= 32767) {
//Complete the code
System.out.println("* short");
System.out.println("* int");
System.out.println("* long");
} else if (x >= -Math.pow(2, 31) && x <= Math.pow(2, 31) - 1) {
System.out.println("* int");
System.out.println("* long");
} else {
System.out.println("* long");
}
} catch (Exception e) {
System.out.println(sc.next() + " can't be fitted anywhere.");
}
}
}
}
int arguments are acceptable when there is a double paramter. So Math.pow(a,b) will work for int arguments. It returns double you just need to cast to int.
int i = (int) Math.pow(3,10);
Without using pow function and +ve and -ve pow values.
public class PowFunction {
public static void main(String[] args) {
int x = 5;
int y = -3;
System.out.println( x + " raised to the power of " + y + " is " + Math.pow(x,y));
float temp =1;
if(y>0){
for(;y>0;y--){
temp = temp*x;
}
} else {
for(;y<0;y++){
temp = temp*x;
}
temp = 1/temp;
}
System.out.println("power value without using pow method. :: "+temp);
}
}
Unlike Python (where powers can be calculated by a**b) , JAVA has no such shortcut way of accomplishing the result of the power of two numbers.
Java has function named pow in the Math class, which returns a Double value
double pow(double base, double exponent)
But you can also calculate powers of integer using the same function. In the following program I did the same and finally I am converting the result into an integer (typecasting). Follow the example:
import java.util.*;
import java.lang.*; // CONTAINS THE Math library
public class Main{
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n= sc.nextInt(); // Accept integer n
int m = sc.nextInt(); // Accept integer m
int ans = (int) Math.pow(n,m); // Calculates n ^ m
System.out.println(ans); // prints answers
}
}
Alternatively,
The java.math.BigInteger.pow(int exponent) returns a BigInteger whose value is (this^exponent). The exponent is an integer rather than a BigInteger. Example:
import java.math.*;
public class BigIntegerDemo {
public static void main(String[] args) {
BigInteger bi1, bi2; // create 2 BigInteger objects
int exponent = 2; // create and assign value to exponent
// assign value to bi1
bi1 = new BigInteger("6");
// perform pow operation on bi1 using exponent
bi2 = bi1.pow(exponent);
String str = "Result is " + bi1 + "^" +exponent+ " = " +bi2;
// print bi2 value
System.out.println( str );
}
}