I brute-forced summing of all primes under 2000000. After that, just for fun I tried to parallel my for, but I was a little bit surprised when I saw that Parallel.For gives me an incorrect sum!
Here's my code : (C#)
static class Problem
{
public static long Solution()
{
long sum = 0;
//Correct result is 142913828922
//Parallel.For(2, 2000000, i =>
// {
// if (IsPrime(i)) sum += i;
// });
for (int i = 2; i < 2000000; i++)
{
if (IsPrime(i)) sum += i;
}
return sum;
}
private static bool IsPrime(int value)
{
for (int i = 2; i <= (int)Math.Sqrt(value); i++)
{
if (value % i == 0) return false;
}
return true;
}
}
I know that brute-force is pretty bad solution here but that is not a question about that. I think I've made some very stupid mistake, but I just can't locate it. So, for is calculating correctly, but Parallel.For is not.
You are accessing the variable sum from multiple threads without locking it, so it is possible that the read / write operations become overlapped.
Adding a lock will correct the result (but you will be effectively serializing the computation, losing the benefit you were aiming for).
You should instead calculate a subtotal on each thread and add the sub-totals at the end. See the article How to: Write a Parallel.For Loop That Has Thread-Local Variables on MSDN for more details.
long total = 0;
// Use type parameter to make subtotal a long, not an int
Parallel.For<long>(0, nums.Length, () => 0, (j, loop, subtotal) =>
{
subtotal += nums[j];
return subtotal;
},
(x) => Interlocked.Add(ref total, x)
);
Many thanks to all of you for your quick answers
i changed
sum += i;
to
Interlocked.Add(ref sum,i);
and now it works great.
Related
I'm trying to find the least common multiple of an array of integers, e.g. if there are 2 numbers given (7, 3) then my task is to find the LCM of the numbers 3 through 7 (3,4,5,6,7 in that case).
My solution would be to add the maximum number to a new variable (var common) until the remainders of all of the numbers in the array (common % numBetween[i]) equal 0. There are more efficient ways of doing this, for example applying the Euclidean Algorithm, but I wanted to solve this my way.
The code:
function smallestCommons(arr) {
var numBetween = [];
var max = Math.max.apply(Math, arr);
var min = Math.min.apply(Math, arr);
while (max - min !== -1) {
numBetween.push(min);
min += 1;
} //this loop creates the array of integers, 1 through 13 in this case
var common = max;
var modulus = [1]; //I start with 1, so that the first loop could begin
var modSum = modulus.reduce(function (a, b) {
return a + b;
}, 0);
while (modSum !== 0) {
modulus = [];
for (var i = 0; i < numBetween.length; i++) {
modulus.push(common % numBetween[i]);
}
if (modSum !== 0) {
common += max;
break; //without this, the loop is infinite
}
}
return common;
}
smallestCommons([1,13]);
Now, the loop is either infinite (without break in the if statement) so I guess the modSum never equals 0, because the modulus variable always contains integers other than 0. I wanted to solve this by "resetting" the modulus to an empty array right after the loop starts, with
modulus = [];
and if I include the break, the loop stops after 1 iteration (common = 26). I can't quite grasp why my code isn't working. All comments are appreciated.
Thanks in advance!
I may be false, but do you actually never change modSum within the while-loop? If so, this is your problem. You wanted to do this by using the function .reduce(), but this does not bind the given function, so you have to call the function each time again in the loop.
When you have code like this (written in java, but applicable to any similar language):
public static void main(String[] args) {
int total = 0;
for (int i = 0; i < 50; i++)
total += i * doStuff(i % 2); // multiplies i times doStuff(remainder of i / 2)
}
public static int doStuff(int i) {
// Lots of complicated calculations
}
You can see that there's room for improvement. doStuff(i % 2) only returns two different values - one for doStuff(0) on even numbers and one for doStuff(1) on odd numbers. Therefore you're wasting a lot of computation time/power on recalculating those values each time by saying doStuff(i % 2). You can improve like this:
public static void main(String[] args) {
int total = 0;
boolean[] alreadyCalculated = new boolean[2];
int[] results = new int[2];
for (int i = 0; i < 50; i++) {
if (!alreadyCalculated[i % 2]) {
results[i % 2] = doStuff(i % 2);
alreadyCalculated[i % 2] = true;
}
total += i * results[i % 2];
}
}
Now it accesses a stored value instead of recalculating each time. It might seem silly to keep arrays like that, but for cases like looping from, say, i = 0, i < 500 and you're checking i % 32 each time, or something, an array is an elegant approach.
Is there a term for this kind of code optimization? I'd like to read up more on the different forms and the conventions of it but I'm lacking a concise description.
Is there a term for this kind of code optimization?
Yes, there is:
In computing, memoization is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again.
https://en.wikipedia.org/wiki/Memoization
Common-subexpression-elimination (CSE) is related to this. This case is a combination of that and hoisting a loop-invariant calculation out of a loop.
I'd agree with CBroe that you could call this specific form of caching memoization, esp the way you're implementing it with the clunky alreadyCalculated array. You can optimize that away since you know which calls will be new values and which will be repeats. Normally you'd implement memoization with a static array inside the called function, for the benefit of all callers. Ideally there's a sentinel value you can use to mark entries which don't have a result computed yet, instead of maintaining a separate array for that. Or for a sparse set of input values, just use a hash (instead of e.g. an array with 2^32 entries).
You can also avoid the if in the main loop.
public class Optim
{
public static int doStuff(int i) { return (i+5) << 1; }
public static void main(String[] args)
{
int total = 0;
int results[] = new int[2];
// more interesting if we pretend the loop count isn't known to be > 1, so avoiding calling doStuff(1) for n=1 is useful.
// otherwise you'd just do int[] results = { doStuff(0), doStuff(1) };
int n = 50;
for (int i = 0 ; i < Math.min(n, 2) ; i++) {
results[i] = doStuff(i);
total += i * results[i];
}
for (int i = 2; i < n; i++) { // runs zero times if n < 2
total += i * results[i % 2];
}
System.out.print(total);
}
}
Of course, in this case we can optimize a lot further. sum(0..n) = n * (n+1) / 2, so we can use that to get a closed-form (non-looping) solution in terms of doStuff(0) (sum of the even terms) and doStuff(1) (sum of the odd terms). So we only need the two doStuff() results once each, avoiding any need to memoize.
i have created the recursive call tree by applying brute force technique but when i give this algorithm 100 values it takes trillion of years to compute..
what you guys suggest me to do that it runs fast by giving 100 values
here is what i have done so far
function fib(n) {
if (n =< 1) {
return n;
} else {
return fib(n - 1) + fib(n - 2);
}
}
You can do it also with a loop:
int a = 1;
int b = 1;
for(int i = 2; i < 100; i++){
int temp = a + b;
a = b;
b = temp;
}
System.out.println("Fib 100 is: "+b);
The runtime is linear and avoids the overhead caused by the recursive calls.
EDIT: Please note that the result is wrong. Since Fib(100) is bigger than Integer.MAX_VALUE you have to use BigInteger or similar to get the correct output but the "logic" will stay the same.
You could have a "cache", where you save already computed Fibonacci numbers. Every time you try to compute
fib(n-1) /* or */ fib(n-2) ;
You would first look into your array of already computed numbers. If it's there, you save a whole lot of time.
So every time you do compute a fibonacci number, save it into your array or list, at the corresponding index.
function fib(n)
{
if (n =< 1)
{
return n;
}
if(fiboList[n] != defaultValue)
{
return fiboList[n];
}
else
{
int fibo = fib(n-1) + fib(n-2);
fiboList[n] = fibo;
return fibo;
}
}
You can also do it by dynamic programming:
def fibo(n):
dp = [0,1] + ([0]*n)
def dpfib(n):
return dp[n-1] + dp[n-2]
for i in range(2,n+2):
dp[i] = dpfib(i)
return dp[n]
so i have this method that finds the number of factors of a given number. It works fine and everything but i am using a for loop and my teacher is wanting me to change it into a while loop to make it more efficient, ive tried to change it but i keep getting endless loop here is the code i have using a for loop what might be a good to change it to a while loop without using a break and only having one return statement in the whole method
public static int numberOfFactors(int num){
int i;
int total=0;
for(i=1;i<=num;i++){
if(num%i==0)
total++;
}
return (total);}
I fail to see how:
i = 1;
while(i <= num) {
// do things
i++;
}
Is any more efficient than:
for( i=1; i<=num; i++) {
// do things
}
As far as I can tell? It's not! I'd love to know why your teacher thinks it is.
That said, here's what you can do to make it more efficient:
Calculate the square root of num and put it in sqrtnum as an integer, rounded down.
Change your loop to for(i=1; i<sqrtnum; i++) (note <, not <=)
If num%i==0, increment total by 2, instead of 1.
After the loop, check if sqrtnum*sqrtnum == num - if so, increment total by 1.
In this way, you only have to loop through a fraction of the numbers ;)
Not any more efficient but....
public static int numberOfFactors(int num) {
int total = 0;
int i = 1;
while(i <= num) {
if(num%i == 0)
total++;
i++;
}
return total;
}
I am trying to compare two long bytearrays in VB.NET and have run into a snag. Comparing two 50 megabyte files takes almost two minutes, so I'm clearly doing something wrong. I'm on an x64 machine with tons of memory so there are no issues there. Here is the code that I'm using at the moment and would like to change.
_Bytes and item.Bytes are the two different arrays to compare and are already the same length.
For Each B In item.Bytes
If B <> _Bytes(I) Then
Mismatch = True
Exit For
End If
I += 1
Next
I need to be able to compare as fast as possible files that are potentially hundreds of megabytes and even possibly a gigabyte or two. Any suggests or algorithms that would be able to do this faster?
Item.bytes is an object taken from the database/filesystem that is returned to compare, because its byte length matches the item that the user wants to add. By comparing the two arrays I can then determine if the user has added something new to the DB and if not then I can just map them to the other file and not waste hard disk drive space.
[Update]
I converted the arrays to local variables of Byte() and then did the same comparison, same code and it ran in like one second (I have to benchmark it still and compare it to others), but if you do the same thing with local variables and use a generic array it becomes massively slower. I’m not sure why, but it raises a lot more questions for me about the use of arrays.
What is the _Bytes(I) call doing? It's not loading the file each time, is it? Even with buffering, that would be bad news!
There will be plenty of ways to micro-optimise this in terms of looking at longs at a time, potentially using unsafe code etc - but I'd just concentrate on getting reasonable performance first. Clearly there's something very odd going on.
I suggest you extract the comparison code into a separate function which takes two byte arrays. That way you know you won't be doing anything odd. I'd also use a simple For loop rather than For Each in this case - it'll be simpler. Oh, and check whether the lengths are correct first :)
EDIT: Here's the code (untested, but simple enough) that I'd use. It's in C# for the minute - I'll convert it in a sec:
public static bool Equals(byte[] first, byte[] second)
{
if (first == second)
{
return true;
}
if (first == null || second == null)
{
return false;
}
if (first.Length != second.Length)
{
return false;
}
for (int i=0; i < first.Length; i++)
{
if (first[i] != second[i])
{
return false;
}
}
return true;
}
EDIT: And here's the VB:
Public Shared Function ArraysEqual(ByVal first As Byte(), _
ByVal second As Byte()) As Boolean
If (first Is second) Then
Return True
End If
If (first Is Nothing OrElse second Is Nothing) Then
Return False
End If
If (first.Length <> second.Length) Then
Return False
End If
For i as Integer = 0 To first.Length - 1
If (first(i) <> second(i)) Then
Return False
End If
Next i
Return True
End Function
The fastest way to compare two byte arrays of equal size is to use interop. Run the following code on a console application:
using System;
using System.Runtime.InteropServices;
using System.Security;
namespace CompareByteArray
{
class Program
{
static void Main(string[] args)
{
const int SIZE = 100000;
const int TEST_COUNT = 100;
byte[] arrayA = new byte[SIZE];
byte[] arrayB = new byte[SIZE];
for (int i = 0; i < SIZE; i++)
{
arrayA[i] = 0x22;
arrayB[i] = 0x22;
}
{
DateTime before = DateTime.Now;
for (int i = 0; i < TEST_COUNT; i++)
{
int result = MemCmp_Safe(arrayA, arrayB, (UIntPtr)SIZE);
if (result != 0) throw new Exception();
}
DateTime after = DateTime.Now;
Console.WriteLine("MemCmp_Safe: {0}", after - before);
}
{
DateTime before = DateTime.Now;
for (int i = 0; i < TEST_COUNT; i++)
{
int result = MemCmp_Unsafe(arrayA, arrayB, (UIntPtr)SIZE);
if (result != 0) throw new Exception();
}
DateTime after = DateTime.Now;
Console.WriteLine("MemCmp_Unsafe: {0}", after - before);
}
{
DateTime before = DateTime.Now;
for (int i = 0; i < TEST_COUNT; i++)
{
int result = MemCmp_Pure(arrayA, arrayB, SIZE);
if (result != 0) throw new Exception();
}
DateTime after = DateTime.Now;
Console.WriteLine("MemCmp_Pure: {0}", after - before);
}
return;
}
[DllImport("msvcrt.dll", CallingConvention = CallingConvention.Cdecl, EntryPoint="memcmp", ExactSpelling=true)]
[SuppressUnmanagedCodeSecurity]
static extern int memcmp_1(byte[] b1, byte[] b2, UIntPtr count);
[DllImport("msvcrt.dll", CallingConvention = CallingConvention.Cdecl, EntryPoint = "memcmp", ExactSpelling = true)]
[SuppressUnmanagedCodeSecurity]
static extern unsafe int memcmp_2(byte* b1, byte* b2, UIntPtr count);
public static int MemCmp_Safe(byte[] a, byte[] b, UIntPtr count)
{
return memcmp_1(a, b, count);
}
public unsafe static int MemCmp_Unsafe(byte[] a, byte[] b, UIntPtr count)
{
fixed(byte* p_a = a)
{
fixed (byte* p_b = b)
{
return memcmp_2(p_a, p_b, count);
}
}
}
public static int MemCmp_Pure(byte[] a, byte[] b, int count)
{
int result = 0;
for (int i = 0; i < count && result == 0; i += 1)
{
result = a[0] - b[0];
}
return result;
}
}
}
If you don't need to know the byte, use 64-bit ints that gives you 8 at once. Actually, you can figure out the wrong byte, once you've isolated it to a set of 8.
Use BinaryReader:
saveTime = binReader.ReadInt32()
Or for arrays of ints:
Dim count As Integer = binReader.Read(testArray, 0, 3)
Better approach... If you are just trying to see if the two are different then save some time by not having to go through the entire byte array and generate a hash of each byte array as strings and compare the strings. MD5 should work fine and is pretty efficient.
I see two things that might help:
First, rather than always accessing the second array as item.Bytes, use a local variable to point directly at the array. That is, before starting the loop, do something like this:
array2 = item.Bytes
That will save the overhead of dereferencing from the object each time you want a byte. That could be expensive in Visual Basic, especially if there's a Getter method on that property.
Also, use a "definite loop" instead of "for each". You already know the length of the arrays, so just code the loop using that value. This will avoid the overhead of treating the array as a collection. The loop would look something like this:
For i = 1 to max Step 1
If (array1(i) <> array2(i))
Exit For
EndIf
Next
Not strictly related to the comparison algorithm:
Are you sure your bottleneck is not related to the memory available and the time used to load the byte arrays? Loading two 2 GB byte arrays just to compare them could bring most machines to their knees. If the program design allows, try using streams to read smaller chunks instead.