Project Euler Problem 9: Solution in C++

Special Pythagorean triplet

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,

a2 + b2 = c2

For example, 32 + 42 = 9 + 16 = 25 = 52.

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.

/*
    Author      :   Sreejith Sreekantan
    Description :   
                    Special Pythagorean triplet
                    Problem 9

                    A Pythagorean triplet is a set of three natural numbers, 
                    a < b < c, for which, a2 + b2 = c2

                    For example, 32 + 42 = 9 + 16 = 25 = 52.

                    There exists exactly one Pythagorean triplet for which 
                    a + b + c = 1000.
                    Find the product abc.

    Eg: for Pythagorean triplets:
    (3, 4, 5 )  (5, 12, 13)     (8, 15, 17)     (7, 24, 25)
    (20, 21, 29)    (12, 35, 37)    ( 9, 40, 41)    (28, 45, 53)
    (11, 60, 61)    (16, 63, 65)    (33, 56, 65)    (48, 55, 73)
    (13, 84, 85)    (36, 77, 85)    (39, 80, 89)    (65, 72, 97)
    (20, 99, 101)   (60, 91, 109)   (15, 112, 113)  (44, 117, 125)
    (88, 105, 137)  (17, 144, 145)  (24, 143, 145)  (51, 140, 149)
    (85, 132, 157)  (119, 120, 169)     (52, 165, 173)  (19, 180, 181)
    (57, 176, 185)  (104, 153, 185)     (95, 168, 193)  (28, 195, 197)
    (84, 187, 205)  (133, 156, 205)     (21, 220, 221)  (140, 171, 221)
    (60, 221, 229)  (105, 208, 233)     (120, 209, 241) (32, 255, 257)
    (23, 264, 265)  (96, 247, 265)  (69, 260, 269)  (115, 252, 277)
    (160, 231, 281)     (161, 240, 289)     (68, 285, 293)

*/
#include 
#include 


using namespace std;

void pythagoreanTriplet(unsigned long sum)
{
    unsigned long m, n, s=sum;
    s /= 2;
    unsigned long sqrt_s = sqrt(s);

    for (int m = 1; m <= sqrt_s ; ++m)
    {
        if (s%m==0)
        {
            n = (s/m)-m;
            if (m>n)
            {
                cout << sum << " : " << pow(m,2)-pow(n,2) << " "  
                << 2*m*n << " "  << pow(m,2)+pow(n,2) << endl;
            }
        }
    }

}


int main(int argc, char const *argv[])
{
    unsigned long sums[] = {12, 30, 40, 56, 70, 84, 90, 126, 132, 
                            144, 176, 182, 1000};
    for (int i = 0; i < sizeof(sums)/sizeof(unsigned long); ++i)
    {
            pythagoreanTriplet(sums[i]);
    }

    cout << " the end..." << endl;
    return 0;
}


C++ Brain Teaser : Virtual Destructor

Hi All,

This time I plan to explain to you a C++ brain teaser I came across. With no further adieu, let me get directly to the question:

C++ Brain Teaser : Virtual Destructor Question

What is the problem with this code, if any?

(Assurance from me: this code will compile and execute fine. ie. no compilation error)

.

.

.

.

.

.

Hope you have put enough thought on it. Some might have already cracked it. For the rest of the folks, let me reveal it.

Yes, this code has some serious problem at run-time. If not compilation-error, what is it?

You are right; the worst nightmare, memory leak! But where is it leaking?

Let pause that question for a few minutes to discuss something in C++ language.

In a scenario where a Child class inherits a Parent class, when a Child object is created, first the Parent-Constructor is invoked and then the Child-Constructor and when the Child object is destroyed, first the Child-Destructor is invoked and then the Parent-Destructor is executed.

In our above program, we use a variable of type “Parent” to point to a “Child” object. Lets use below program to check if the order of invocation of constructor and destructor is followed in this case.

virtual Destructor program with cout

Output of the above program is:

Screen Shot 2014-02-04 at 2.33.23 PM

As you can see, here the child destructor is not invoked, which means, whatever we coded in the Destructor method of Child class is not executed. In our main program, we allocate an array of memory in the Constructor of Child and delete the same in its Destructor. So our main program successfully allocates an array of memory but don’t delete it, which will result in Memory Leak.

So we have answered our question. Now lets see how we can avoid it.

Here is where Virtual-Destructor comes for help. Make the destructor of “Parent” class virtual and this issue is solved.

New implementation of “Parent”:

Virtual Destructor New Parent impNew output:

Virtual Destructor new output

To put it straight, virtual destructor forces the parent class to check for child class destructors and executes it.

Use a virtual destructor if you ever expect a derived class to be destroyed through a pointer to the base class to ensure that the destructor of the most derived classes gets called.

It’s a good practice to make the destructors of all interface classes, ie. any class with at-least one virtual method, as virtual.

Linux Device Driver: 1 of n

Lets try for a “hello world” Linux driver this time. Yeah, I know there are heck lot of tutorials dealing with the same but since I am trying it out myself, I would like to share the steps I followed and the experience I gained out of it.
Drivers, not just in Linux but in all Operating Systems, lie directly on top of hardware, abstracting the device specific operations. This reduces the dependency of Operating System on hardware and thereby it makes easy for an operating system to switch between different hardware.
Didn’t get that? Let me try that once more. Before that let me tell you one fact: devices are categorized into three sets in Linux (this one is specific to Linux and Unix):

  1. Character Devices    – devices which read one byte at a time.
  2. Block Devices        – devices which a block (usually 512 bytes) at a time.
  3. Network Devices        – devices which enables transfer(to be specific, send and receive) of packets over network.

By categorizing devices, Linux expects driver of each category to expose a standard interface. Now what is the use of that? Suppose two devices dev1 and dev2 have its own specific driver driv1 and driv2. If both drivers has a common interface (functions through which it gives out its services), say both implemented f1() and f2() functions, then a program using driv1 one will call f1() and f2() to use the dev1. Suppose at one point of time the user wants to replace dev1 with dev2; since the driver driv2 too follows the standard and has implementation of f1() and f2(), there will be no change in the calling process and it need not be recompiled. Thereby we could isolate the changes to a very small section. This is a good programming practice even outside driver-programming.
In this post, we will try to write our first driver which can be used with Linux. Driver-programming is a little bit different from our usual programming. Program execution in our everyday programming starts in ‘main’ function but in driver-programming main function disappears. Lets see our hello-world without any further ado.

#include <linux/init.h>
#include <linux/module.h>
MODULE_LICENSE(“Dual BSD/GPL”);

static int hello_kernel_init(void)
{
    printk(KERN_ALERT “Hello Kernel, at your service..\n”);
    return 0;
}

static void hello_kernel_exit(void)
{
    printk( KERN_ALERT “Goodbye Kernel, I am no longer at your service..\n”);
}

module_init(hello_kernel_init);
module_exit(hello_kernel_exit);

Don’t worry about the weird function calls: printk. Hope you already got the idea about module_init and module_exit. Those are to register our functions (hello_kernel_init and hello_kernel_exit) as functions to be called at the time of module initialization and exit. Good question: “when does that happen”. A driver module is invoked as part of any software requesting for a hardware service. That request from application goes to operating system and o/s (short form for operating system) loads the driver module specific to that hardware to serve the application. Leave those topics for the time being, we will cover it in coming chapters. ‘printk’ is just a ditto of printf function in C language; the difference is it has an identifier -> KERN_ALERT at the starting of first argument which tells the kernel the priority of the message printed by that printk function. There are other similar identifiers like KERN_INFO, KERN_WARNING, etc . Driver-modules are not supposed to use any library functions other than those implemented in kernel. This is because we wont link our code with libraries at the time of compilation. Linking and loading is the job of kernel. So when kernel links our module, if it sees any reference to functions which it doesn’t implement, it will cause a failure of our code, if not an entire system failure at rare cases.
Forgot to tell you that my development environment is Ubuntu with kernel version 3.2.0
Now I need a makefile to ease my compilation. This simple code of-course should have a simple make-file as well and there it goes:
obj-m := hello_kernel.o
Yes, just one line and the kernel build system will take care of the rest.
At the time of ‘making’ we should give the path of our kernel source. To find that we should firt find the kernel version you are currently running on. Run ‘uname -r‘ at your terminal.

unamer

You will get something like “3.2.0-40-generic”, don’t worry if it’s just numbers. Now the kernel source tree path will be “/lib/modules/3.2.0-40-generic/build”. This will be a soft link to original path and this will do for us.
Now we have our source code in “hello_kernel.c” and make file “Makefile”.
Now run the command
make -C /lib/modules/3.2.0-40-generic/build/ M=`pwd` modules
This command starts by changing its directory to the one provided with -C option, which is your kernel source directory and finds the kernel’s top-level make-file. The M= option is to help the make utility to traverse back to our current directory to build target: modules

make
Now our module is ready to be loaded. Run the below commands.

insmodlsmodrmmod

You need to have sudo privilege since we are messing with kernel. insmod will load the driver module, lsmod will list all the loaded modules and we are grepping our module from the result and rmmod removes the driver.

Hope you notice that we had a few printk statements in our code but nothing appeared in the console. It is because all kernel specific logs go to “/var/log/syslog” file in Ubuntu. Likewise different Linux distros will have its own specific file. You will see whatever we printed out in our driver code in those file. Just run the below command in our case:

cat /var/log/syslog | tail

log

There ends our first step towards mastering Linux Device Drivers. Wait till the next chapter for advanced topics..

Project Euler Problem 8: Solution in C++

/*

Largest product in a series

Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
*/
#include<iostream>

using namespace std;

int main()
{
string s = “7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450”;
//cin >> s;
int max_prod = 1;
int ans_start = 0; // answer ie. 5 consecutive numbers starts at ans_start
for( int i = 0; i < 5; i++ )
{
max_prod *= static_cast(s[i]-‘0’);
}

int prod = max_prod;
for( int i = 5; i < s.size(); i++ )
{

if( static_cast(s[i-5]-‘0’) != 0 )
{
prod /= static_cast(s[i-5]-‘0’);
}
if( static_cast(s[i]-‘0’) == 0 )
{
clog << “skipped ” << “i = ” << i << ” s[i] = ” << s[i] << endl;
continue;
}
clog << “i = ” << i << ” s[i] = ” << s[i];
prod *= static_cast(s[i]-‘0’);
clog << ” prod = ” << prod << ” /= ” << static_cast(s[i-5]-‘0’) << ” *= ” << static_cast(s[i]-‘0’) << ” max_prod = ” << max_prod;
if( max_prod < prod )
{

ans_start = i-4;
max_prod = prod;
}
cout << ” ans_start = ” << ans_start << endl;
}

for( int i = ans_start; i < ans_start+5; i++ )
{
cout << s[i] << ” “;
}
cout << endl << max_prod << endl;
}

//    7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883
//    99879
//    7908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450

// ANSWER IS 40824

Project Euler Problem 7: Solution in C++

/*

10001st prime

*/

#include <iostream>
#include <cmath>

using namespace std;

bool isPrime( long num )
{
switch( num )
{
case 1:
case 4:
case 6:
case 8:
case 9:
return false;
break;
case 2:
case 3:
case 5:
case 7:
return true;
break;
}
if( num % 2 == 0 || num % 3 == 0 )
return false;
long sq_root_of_num = floor( sqrt(num) );
long i = 5;
while( i <= sq_root_of_num )
{
if( num % i == 0 || num % (i+2) == 0 )
{
return false;
}
i += 6;
}

// num is prime
return true;
}

int main()
{
long num = 3;
int index = 1;

while( index < 10001 )
{
if( isPrime( num ) )
{
index++;
}
num += 2;
}
num -= 2;
cout << num << endl;
}

// ANSWER is 404743

Euler Problem: Solution of Problem-6 in C++

Q)The sum of the squares of the first ten natural numbers is,

#include  

#define N 100

using namespace std;

long raiseTo ( const long num, const long n ) {
    int ans = num;
    for ( int i = 1; i < n; i++ ) {
        ans *= num;
    }
    return ans;
}

int main ( int argc, char * argv[] ) {
    long result =     (             ( raiseTo ( N, 4 ) / 4 ) 
                            +     ( raiseTo ( N, 3 ) / 6 ) 
                            -     ( raiseTo ( N, 2 ) / 4 ) 
                            -    ( N / 6 ) 
                    ); 
    cout << result << endl;
}

// 25164150

Euler Problem: Solution of Problem-5 in C++

#include 

#define X 20

using namespace std;

long hcf ( const long & small_num, const long & big_num ) {
    if ( small_num > big_num ) {
        return hcf ( big_num, small_num );
    }
    else {
        if ( big_num % small_num == 0 ) {
            return small_num;
        }
        else {
            return hcf ( big_num % small_num, small_num );
        }
    }
}

int main ( int argc, char *argv[] ) {
    long result = 1;
    long temp_hcf;
    for ( int i = 1; i <= X; i++ ) {
        temp_hcf = hcf ( result, i );
        result /= temp_hcf;
        result *= i;
    }
    cout << "Result = " << result << endl;
    return 0;
}

// Result = 232792560