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I'm trying to code a program that can tell apart real and fake credit card numbers using Luhn's algorithm in C, which is
Multiply every other digit by 2, starting with the number’s
second-to-last digit, and then add those products’ digits together.
Add the sum to the sum of the digits that weren’t multiplied by 2.
If the total’s last digit is 0 (or, put more formally, if the total
modulo 10 is congruent to 0), the number is valid!
Then I coded something like this (I already declared all the functions at the top and included all the necessary libraries)
//Luhn's Algorithm
int luhn(long z)
{
int c;
return c = (sumall(z)-sumodd(z)) * 2 + sumaodd(z);
}
//sum of digits in odd position starting from the end
int sumodd(long x)
{
int a;
while(x)
{
a = a + x % 10;
x /= 100;
}
return a;
}
//sum of all digits
int sumall(long y)
{
int b;
while(y)
{
b = b + y % 10;
y /= 10;
}
return b;
}
But somehow it always gives out the wrong answer even though there's no error or bug detected. I came to notice that it works fine when my variable z stands alone, but when it's used multiple times in the same line of code with different functions, their values get messed up (in function luhn). I'm writing this to ask for any fix I can make to make my code run correctly as I intended.
I'd appreciate any help as I'm very new to this, and I'm not a native English speaker so I may have messed up some technical terms, but I hope you'd be able to understand my concerns.
sumall is wrong.
It should be sumeven from:
Add the sum to the sum of the digits that weren’t multiplied by 2.
Your sumall is summing all digits instead of the non-odd (i.e. even) digits.
You should do the * 2 inside sumodd as it should not be applied to the other [even] sum. And, it should be applied to the individual digits [vs the total sum].
Let's start with a proper definition from https://en.wikipedia.org/wiki/Luhn_algorithm
The check digit is computed as follows:
If the number already contains the check digit, drop that digit to form the "payload." The check digit is most often the last digit.
With the payload, start from the rightmost digit. Moving left, double the value of every second digit (including the rightmost digit).
Sum the digits of the resulting value in each position (using the original value where a digit did not get doubled in the previous step).
The check digit is calculated by 10 − ( s mod 10 )
Note that if we have a credit card of 9x where x is the check digit, then the payload is 9.
The correct [odd] sum for that digit is: 9 * 2 --> 18 --> 1 + 8 --> 9
But, sumodd(9x) * 2 --> 9 * 2 --> 18
Here's what I came up with:
// digsum -- calculate sum of digits
static inline int
digsum(int digcur)
{
int sum = 0;
for (; digcur != 0; digcur /= 10)
sum += digcur % 10;
return sum;
}
// luhn -- luhn's algorithm using digits array
int
luhn(long z)
{
char digits[16] = { 0 };
// get check digit and remove from "payload"
int check_expected = z % 10;
z /= 10;
// split into digits (we use little-endian)
int digcnt = 0;
for (digcnt = 0; z != 0; ++digcnt, z /= 10)
digits[digcnt] = z % 10;
int sum = 0;
for (int digidx = 0; digidx < digcnt; ++digidx) {
int digcur = digits[digidx];
if ((digidx & 1) == 0)
sum += digsum(digcur * 2);
else
sum += digcur;
}
int check_actual = 10 - (sum % 10);
return (check_actual == check_expected);
}
// luhn -- luhn's algorithm using long directly
int
luhn2(long z)
{
// get check digit and remove from "payload"
int check_expected = z % 10;
z /= 10;
int sum = 0;
for (int digidx = 0; z != 0; ++digidx, z /= 10) {
int digcur = z % 10;
if ((digidx & 1) == 0)
sum += digsum(digcur * 2);
else
sum += digcur;
}
int check_actual = 10 - (sum % 10);
return (check_actual == check_expected);
}
You've invoked undefined behavior by not initializing a few local variables in your functions, for instance you can remove your undefined behaviour in sumodd() by initializing a to zero like so:
//sum of digits in odd position starting from the end
int sumodd(long x)
{
int a = 0; //Initialize
while(x)
{
a += x % 10; //You can "a += b" instead of "a = a + b"
x /= 100;
}
return a;
}
It's also important to note that long is only required to be a minimum of 4-bytes wide, so it is not guaranteed to be wide enough to represent a decimal-16-digit-integer. Using long long solves this problem.
Alternatively you may find this problem much easier to solve by treating your credit card number as a char[] instead of an integer type altogether, for instance if we assume a 16-digit credit card number:
int luhn(long long z){
char number[16]; //Convert CC number to array of digits and store them here
for(int c = 0; c < 16; ++c){
number[c] = z % 10; //Last digit is at number[0], first digit is at number[15]
z /= 10;
}
int sum = 0;
for(int c = 0; c < 16; c += 2){
sum += number[c] + number[c + 1] * 2; //Sum the even digits and the doubled odd digits
}
return sum;
}
...and you could skip the long long to char[] translation part altogether if you treat the credit card number as an array of digits in the whole program
This expression:
(sumall(z)-sumodd(z)) * 2 + sumall(z);
Should be:
((sumall(z)-sumodd(z)) * 2 + sumodd(z))%10;
Based on your own definition.
But how about:
(sumall(z) * 2 - sumodd(z))%10
If you're trying to be smart and base off sumall(). You don't need to call anything twice.
Also you don't initialise your local variables. You must assign variables values before using them in C.
Also you don't need the local variable c in the luhn() function. It's harmless but unnecessary.
As others mention in a real-world application we can't recommend enough that such 'codes' are held in a character array. The amount of grief caused by people using integer types to represent digit sequence 'codes' and identifiers is vast. Unless a variable represents a numerical quantity of something, don't represent it as an arithmetic type. More issue has been caused in my career by that error than people trying to use double to represent monetary amounts.
#include <stdio.h>
//sum of digits in odd position starting from the end
int sumodd(long x)
{
int a=0;
while(x)
{
a = a + x % 10;
x /= 100;
}
return a;
}
//sum of all digits
int sumall(long y)
{
int b=0;
while(y)
{
b = b + y % 10;
y /= 10;
}
return b;
}
//Luhn's Algorithm
int luhn(long z)
{
return (sumall(z)*2-sumodd(z))%10;
}
int check_luhn(long y,int expect){
int result=luhn(y);
if(result==expect){
return 0;
}
return 1;
}
int check_sumodd(long y,int expect){
int result=sumodd(y);
if(result==expect){
return 0;
}
return 1;
}
int check_sumall(long y,int expect){
int result=sumall(y);
if(result==expect){
return 0;
}
return 1;
}
int main(void) {
int errors=0;
errors+=check_sumall(1,1);
errors+=check_sumall(12,3);
errors+=check_sumall(123456789L,45);
errors+=check_sumall(4273391,4+2+7+3+3+9+1);
errors+=check_sumodd(1,1);
errors+=check_sumodd(91,1);
errors+=check_sumodd(791,8);
errors+=check_sumodd(1213191,1+1+1+1);
errors+=check_sumodd(4273391,15);
errors+=check_luhn(1234567890,((9+7+5+3+1)*2+(0+8+6+4+2))%10);
errors+=check_luhn(9264567897,((9+7+5+6+9)*2+(7+8+6+4+2))%10);
if(errors!=0){
printf("*ERRORS*\n");
}else{
printf("Success\n");
}
return 0;
}
I'm a computer engineering student and next semester I am going to start C course. So in order to prepare myself a bit, I have started learning C by myself and stumbled across an interesting task, designed for, how it seemed to me at first sight, not a very advanced level.
The task is to write a program to compute the value of a given position in Pascal's Triangle. And the formula given to compute it is written as element = row! / ( position! * (row - position)! )
I've written a simple console program that seems to work okay, until I get to testing it with large numbers.
When trying this program with row 16 and position 3, it calculates the value as 0, although it's obvious that there can't be such a value (in fact it should compute the value as 560), all cells of this triangle are supposed to be integers and be greater than one.
I suppose I'm experiencing a problem with storing and processing large numbers. The factorial function seems to work okay, and the formula I used works until I get to trying large numbers
So far the best solution was found here - How do you printf an unsigned long long int(the format specifier for unsigned long long int)? using inttypes.h library with type uint64_t but it still doesn't give me the result I need.
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
void clear_input(void);
uint64_t factorial(int x);
int main()
{
// Printing
printf("This program computes the value of a given position in Pascal's Triangle.\n");
printf("You will be asked for row and position of the value.\n");
printf("Note that the rows and positions starts from 0.\n");
printf("\n");
printf(" 1 * 0 \n");
printf(" 1 1 * 1 \n");
printf(" 1 2 1 * 2 \n");
printf(" 1 3 3 1 * 3 \n");
printf(" 1 4 6 4 1 * 4 \n");
printf(" **************** \n");
printf(" 0 1 2 3 4 \n");
printf("\n");
// Initializing
int row, pos;
// Input Row
printf("Enter the row: ");
scanf("%d", &row);
clear_input();
// Input Position
printf("Enter the position in the row: ");
scanf("%d", &pos);
clear_input();
// Initializing
uint64_t element, element_1, element_2, element_3, element_4;
// Previously written as -> element = ( factorial(row) ) / ( factorial(pos) * factorial(row - pos) );
// Doesn't fix the problem
element_1 = factorial(row);
element_2 = factorial(pos);
element_3 = factorial(row - pos);
element_4 = element_2 * element_3;
element = element_1 / element_4;
// Print result
printf("\n");
printf("%"PRIu64"\n", element_1); // Temporary output
printf("%"PRIu64"\n", element_2); // Temporary output
printf("%"PRIu64"\n", element_3); // Temporary output
printf("%"PRIu64"\n", element_4); // Temporary output
printf("\n");
printf("The element is %"PRIu64"", element);
printf("\n");
return 0;
}
void clear_input(void) // Temporary function to clean input from the keyboard
{
while(getchar() != '\n');
}
uint64_t factorial(int x) // Function to calculate factorial
{
int f = 1, i = x;
if (x == 0) {
return 1;
}
while (i != 1) {
f = f * i;
i = i - 1;
}
return f;
}
Factorials get really big really fast (scroll down a little to see the list). Even a 64-bit number is only good up to 20!. So you have to do a little preprocessing before you start multiplying.
The general idea is to factor the numerator and the denominator, and remove all of the common factors. Since the results of Pascal's Triangle are always integers, you are guaranteed that the denominator will be 1 after all common factors have been removed.
For example let's say you have row=35 and position=10. Then the calculation is
element = 35! / (10! * 25!)
which is
35 * 34 * 33 * ... * 26 * 25 * 24 * ... * 3 * 2 * 1
---------------------------------------------------
10! * 25 * 24 * ... * 3 * 2 * 1
So the first simplification is that the larger factorial in the denominator cancels all of the smaller terms of the numerator. Which leaves
35 * 34 * 33 * ... * 26
-----------------------
10 * 9 * 8 * ... * 1
Now we need to remove the remaining common factors in the numerator and denominator. It helps to put all the number of the numerator in an array. Then, for each number in the denominator, compute the greatest common divisor (gcd) and divide the numerator and denominator by the gcd.
The following code demonstrates the technique.
array[10] = { 35, 34, 33, 32, 31, 30, 29, 28, 27, 26 };
for ( d = 10; d >= 2; d-- )
{
temp = d;
for ( i = 0; i < 10 && temp > 1; i++ )
{
common = gcd( array[i], temp );
array[i] /= common;
temp /= common;
}
}
Here's what the code does step by step
d=10 i=0 temp=10 array[0]=35 ==> gcd(35,10)=5, so array[0]=35/5=7 and temp=10/5=2
d=10 i=1 temp=2 array[1]=34 ==> gcd(34, 2)=2, so array[1]=34/2=17 and temp=2/2=1
inner loop breaks because temp==1
d=9 i=0 temp=9 array[0]=7 ==> gcd(7,9)=1, so nothing changes
d=9 i=1 temp=9 array[1]=17 ==> gcd(17,9)=1, so nothing changes
d=9 i=2 temp=9 array[2]=33 ==> gcd(33,9)=3, so array[2]=11 and temp=3
d=9 i=3 ==> gcd(32,3)=1
d=9 i=4 ==> gcd(31,3)=1
d=9 i=5 temp=3 array[5]=30 ==> gcd(30,3)=3, so array[5]=10 and temp=1
inner loop breaks
When all is said and done the array ends up as
array[10] = { 1, 17, 11, 1, 31, 1, 29, 14, 3, 26 }
Multiply those numbers together and the answer is 183579396, and the entire calculation could be performed using 32-bit ints. In general, as long as the answer fits into 32-bits, the calculations can be done with 32-bits.
(my C is rusty, so this may not be super accurate)
Your factorial function is returning a uint64_t, but it's doing the computation with regular ints. If you changed f and i to uint64_t I think you'll avoid your current integer overflow issue.
However, you're still going to run into overflow pretty quickly (uint64_t will overflow around 21!). To avoid this you can be a bit smarter with the algorithm. With row=16 and position=3, you need 16! / (3! * 13!). You can cancel out most of the terms (16!/13! is just 14*15*16) and end up with 14*15*16 / (1*2*3). This'll let your program go a lot further than row 21.
When you are calculating the factorial, even though you are returning a 64-bit integer it won't make a difference if you are using regular int variables for your intermediate calculations. Change to this:
uint64_t factorial(uint64_t x)
{
uint64_t f = 1, i = x;
if (x == 0) {
return 1;
}
while (i != 1) {
f = f * i;
i = i - 1;
}
return f;
}
Also, think about how you can rearrange the equation so that you don't have to calculate really large intermediate values. For example you could rearrange to this:
element = ( factorial(row) / factorial(pos) ) / factorial(row - pos);
Then you won't be multiplying two factorials together and getting a really large number.
Also, when you compute factorial(row) / factorial(pos) you can eliminate terms that will be in both factorial(row) and factorial(pos), so you don't need to calculate the entire factorials.
This will work:
#include <stdio.h>
int main()
{
printf ("\n");
int n = 10;
int i;
int j;
int x[n];
for (i = 0; i < n; i++)
x[i] = 0;
for (i = 1; i <= n; i++)
{
for (j = n - 1; j >= 1; j--)
x[j] = x[j-1] + x[j];
x[0] = 1;
int s = n - i;
for (j = 0; j < s; j++)
printf (" ");
for (j = 0; j < n; j++)
{
if (x[j] != 0)
printf (" %3d", x[j]);
}
printf ("\n");
}
printf ("\n");
return 0;
}
I'm a computer engineering student and next semester I am going to start C course. So in order to prepare myself a bit, I have started learning C by myself and stumbled across an interesting task, designed for, how it seemed to me at first sight, not a very advanced level.
The task is to write a program to compute the value of a given position in Pascal's Triangle. And the formula given to compute it is written as element = row! / ( position! * (row - position)! )
I've written a simple console program that seems to work okay, until I get to testing it with large numbers.
When trying this program with row 16 and position 3, it calculates the value as 0, although it's obvious that there can't be such a value (in fact it should compute the value as 560), all cells of this triangle are supposed to be integers and be greater than one.
I suppose I'm experiencing a problem with storing and processing large numbers. The factorial function seems to work okay, and the formula I used works until I get to trying large numbers
So far the best solution was found here - How do you printf an unsigned long long int(the format specifier for unsigned long long int)? using inttypes.h library with type uint64_t but it still doesn't give me the result I need.
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
void clear_input(void);
uint64_t factorial(int x);
int main()
{
// Printing
printf("This program computes the value of a given position in Pascal's Triangle.\n");
printf("You will be asked for row and position of the value.\n");
printf("Note that the rows and positions starts from 0.\n");
printf("\n");
printf(" 1 * 0 \n");
printf(" 1 1 * 1 \n");
printf(" 1 2 1 * 2 \n");
printf(" 1 3 3 1 * 3 \n");
printf(" 1 4 6 4 1 * 4 \n");
printf(" **************** \n");
printf(" 0 1 2 3 4 \n");
printf("\n");
// Initializing
int row, pos;
// Input Row
printf("Enter the row: ");
scanf("%d", &row);
clear_input();
// Input Position
printf("Enter the position in the row: ");
scanf("%d", &pos);
clear_input();
// Initializing
uint64_t element, element_1, element_2, element_3, element_4;
// Previously written as -> element = ( factorial(row) ) / ( factorial(pos) * factorial(row - pos) );
// Doesn't fix the problem
element_1 = factorial(row);
element_2 = factorial(pos);
element_3 = factorial(row - pos);
element_4 = element_2 * element_3;
element = element_1 / element_4;
// Print result
printf("\n");
printf("%"PRIu64"\n", element_1); // Temporary output
printf("%"PRIu64"\n", element_2); // Temporary output
printf("%"PRIu64"\n", element_3); // Temporary output
printf("%"PRIu64"\n", element_4); // Temporary output
printf("\n");
printf("The element is %"PRIu64"", element);
printf("\n");
return 0;
}
void clear_input(void) // Temporary function to clean input from the keyboard
{
while(getchar() != '\n');
}
uint64_t factorial(int x) // Function to calculate factorial
{
int f = 1, i = x;
if (x == 0) {
return 1;
}
while (i != 1) {
f = f * i;
i = i - 1;
}
return f;
}
Factorials get really big really fast (scroll down a little to see the list). Even a 64-bit number is only good up to 20!. So you have to do a little preprocessing before you start multiplying.
The general idea is to factor the numerator and the denominator, and remove all of the common factors. Since the results of Pascal's Triangle are always integers, you are guaranteed that the denominator will be 1 after all common factors have been removed.
For example let's say you have row=35 and position=10. Then the calculation is
element = 35! / (10! * 25!)
which is
35 * 34 * 33 * ... * 26 * 25 * 24 * ... * 3 * 2 * 1
---------------------------------------------------
10! * 25 * 24 * ... * 3 * 2 * 1
So the first simplification is that the larger factorial in the denominator cancels all of the smaller terms of the numerator. Which leaves
35 * 34 * 33 * ... * 26
-----------------------
10 * 9 * 8 * ... * 1
Now we need to remove the remaining common factors in the numerator and denominator. It helps to put all the number of the numerator in an array. Then, for each number in the denominator, compute the greatest common divisor (gcd) and divide the numerator and denominator by the gcd.
The following code demonstrates the technique.
array[10] = { 35, 34, 33, 32, 31, 30, 29, 28, 27, 26 };
for ( d = 10; d >= 2; d-- )
{
temp = d;
for ( i = 0; i < 10 && temp > 1; i++ )
{
common = gcd( array[i], temp );
array[i] /= common;
temp /= common;
}
}
Here's what the code does step by step
d=10 i=0 temp=10 array[0]=35 ==> gcd(35,10)=5, so array[0]=35/5=7 and temp=10/5=2
d=10 i=1 temp=2 array[1]=34 ==> gcd(34, 2)=2, so array[1]=34/2=17 and temp=2/2=1
inner loop breaks because temp==1
d=9 i=0 temp=9 array[0]=7 ==> gcd(7,9)=1, so nothing changes
d=9 i=1 temp=9 array[1]=17 ==> gcd(17,9)=1, so nothing changes
d=9 i=2 temp=9 array[2]=33 ==> gcd(33,9)=3, so array[2]=11 and temp=3
d=9 i=3 ==> gcd(32,3)=1
d=9 i=4 ==> gcd(31,3)=1
d=9 i=5 temp=3 array[5]=30 ==> gcd(30,3)=3, so array[5]=10 and temp=1
inner loop breaks
When all is said and done the array ends up as
array[10] = { 1, 17, 11, 1, 31, 1, 29, 14, 3, 26 }
Multiply those numbers together and the answer is 183579396, and the entire calculation could be performed using 32-bit ints. In general, as long as the answer fits into 32-bits, the calculations can be done with 32-bits.
(my C is rusty, so this may not be super accurate)
Your factorial function is returning a uint64_t, but it's doing the computation with regular ints. If you changed f and i to uint64_t I think you'll avoid your current integer overflow issue.
However, you're still going to run into overflow pretty quickly (uint64_t will overflow around 21!). To avoid this you can be a bit smarter with the algorithm. With row=16 and position=3, you need 16! / (3! * 13!). You can cancel out most of the terms (16!/13! is just 14*15*16) and end up with 14*15*16 / (1*2*3). This'll let your program go a lot further than row 21.
When you are calculating the factorial, even though you are returning a 64-bit integer it won't make a difference if you are using regular int variables for your intermediate calculations. Change to this:
uint64_t factorial(uint64_t x)
{
uint64_t f = 1, i = x;
if (x == 0) {
return 1;
}
while (i != 1) {
f = f * i;
i = i - 1;
}
return f;
}
Also, think about how you can rearrange the equation so that you don't have to calculate really large intermediate values. For example you could rearrange to this:
element = ( factorial(row) / factorial(pos) ) / factorial(row - pos);
Then you won't be multiplying two factorials together and getting a really large number.
Also, when you compute factorial(row) / factorial(pos) you can eliminate terms that will be in both factorial(row) and factorial(pos), so you don't need to calculate the entire factorials.
This will work:
#include <stdio.h>
int main()
{
printf ("\n");
int n = 10;
int i;
int j;
int x[n];
for (i = 0; i < n; i++)
x[i] = 0;
for (i = 1; i <= n; i++)
{
for (j = n - 1; j >= 1; j--)
x[j] = x[j-1] + x[j];
x[0] = 1;
int s = n - i;
for (j = 0; j < s; j++)
printf (" ");
for (j = 0; j < n; j++)
{
if (x[j] != 0)
printf (" %3d", x[j]);
}
printf ("\n");
}
printf ("\n");
return 0;
}
I am writing a program to see if a user entered number is Armstrong or not, here is my code:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main(){
int x = 0;
printf("Enter a natural number: ");
scanf("%d", &x);
int ans = x;
// Digit Counter
int counter = 0; //Variable for number of digits in the user entered number
int b = x; //For each time number can be divided by 10 and isnt 0
for (int i = 1; i <= x; i++){ // Then counter variable is incremented by 1
b /= 10;
if (b != 0){
counter += 1;
}
}
++counter;
//Digit Counter
int sum = 0;
// Digit Finder
int D;
for (int j = 1; j <= x; j++){
D = x % 10; //Shows remainder of number (last digit) when divided by 10
sum += pow(D, counter); //Raises Digit found by counter and adds to sum
printf("%d\n", sum);
x /= 10; // Divides user entered number by 10 to get rid of digit found
}
if (sum == ans){
printf("%d is a Armstrong number! :)", ans);
}else
printf("%d is not an Armstrong number :(", ans);
//Digit Finder
return 0;
}
My problem is that the program works fine apart from one point, when the program is given a Armstrong number which does not start with 1 then it behaves normally and indicates if it is an Armstrong number or not, but when i input a Armstrong number which start with 1 then it will print out the Armstrong number but -1.
For example: If i input something such as 371 which is an Armstrong number it will show that it is an Armstrong number. However if i input 1634 it will output 1633 which is 1 less than 1634.
How can i fix this problem?, also by the way could someone comment on my code and tell me if it seems good and professional/efficient because i am a beginner in C and would like someone else's opinion on my code.
How can I fix this problem.
You know the number of iterations you want to make once you have calculated the digit count. So instead of looping till you reach the value of x:
for (int j = 1; j <= x; j++){
use the digit counter instead:
for (int j = 1; j <= counter; j++) {
also by the way could someone comment on my code and tell me if it seems good and professional/efficient because i am a beginner in C and would like someone else's opinion on my code.
There's a number of things you can do to improve your code.
First and foremost, any piece of code should be properly indented and formatted. Right now your code has no indenting, which makes it more difficult to read and it just looks ugly in general. So, always indent your code properly. Use an IDE or a good text editor, it will help you.
Be consistent in your code style. If you are writing
if (some_cond) {
...
}
else
//do this
It is not consistent. Wrap the else in braces as well.
Always check the return value of a function you use, especially for scanf. It will save you from many bugs in the future.
if (scanf("%d", &x) == 1)
//...all OK...
else
// ...EOF or conversion failure...
exit(EXIT_FAILURE);
Your first for loop will iterate x times uselessly. You can stop when you know that you have hit 0:
for (int i = 1; i <= x; i++){ // Then counter variable is incremented by 1
b /= 10;
if (b == 0){
break;
}
counter += 1;
}
C has ++ operator. Use that instead of doing counter += 1
int D; you create this, but don't initialize it. Always initialize your variables as soon as possible
C has const qualifier keyword, which makes a value immutable. This makes your code more readable, as the reader can immediately tell that this value will not change. In your code, you can change ans variable and make it a const int because it never changes:
const int ans = x;
Use more descriptive names for your variables. ans, D don't tell me anything. Use proper names, so that the reader of your code can easily understand your code.
These are some of the things that in my opinion you should do and keep doing to improve your code and coding skills. I am sure there can be more things though. Keep your code readable and as simple as possible.
The condition in this loop
for (int i = 1; i <= x; i++){ // Then counter variable is incremented by 1
b /= 10;
if (b != 0){
counter += 1;
}
}
does not make sense because there will be numerous redundant iterations of the loop.
For example if x is equal to 153 that is contains only 3 digits the loop will iterate exactly 153 times.
Also additional increment of the variable counter after the loop
++counter;
makes the code logically inconsistent.
Instead of the loop you could write at least the following way
int counter = 0;
int b = x;
do
{
++counter;
} while ( b /= 10 );
This loop iterates exactly the number of times equal to the number of digits in a given number.
In this loop
for (int j = 1; j <= x; j++){
D = x % 10; //Shows remainder of number (last digit) when divided by 10
sum += pow(D, counter); //Raises Digit found by counter and adds to sum
printf("%d\n", sum);
x /= 10; // Divides user entered number by 10 to get rid of digit found
}
it seems you did not take into account that the variable x is decreased inside the body of the loop
x /= 10; // Divides user entered number by 10 to get rid of digit found
So the loop can interrupt its iterations too early. In any case the condition of the loop again does not make great sense the same way as the condition of the first loop and only adds a bug.
The type of used variables that store a given number should be unsigned integer type. Otherwise the user can enter a negative number.
You could write a separate function that checks whether a given number is an Armstrong number.
Here you are.
#include <stdio.h>
int is_armstrong( unsigned int x )
{
const unsigned int Base = 10;
size_t n = 0;
unsigned int tmp = x;
do
{
++n;
} while ( tmp /= Base );
unsigned int sum = 0;
tmp = x;
do
{
unsigned int digit = tmp % Base;
unsigned int power = digit;
for ( size_t i = 1; i < n; i++ ) power *= digit;
sum += power;
} while ( ( tmp /= Base ) != 0 && !( x < sum ) );
return tmp == 0 && x == sum;
}
int main(void)
{
unsigned int a[] =
{
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407,
1634, 8208, 9474, 54748, 92727, 93084, 548834
};
const size_t N = sizeof( a ) / sizeof( *a );
for ( size_t i = 0; i < N; i++ )
{
printf( "%u is %san Armstrong number.\n", a[i], is_armstrong( a[i] ) ? "": "not " );
}
return 0;
}
The program output is
0 is an Armstrong number.
1 is an Armstrong number.
2 is an Armstrong number.
3 is an Armstrong number.
4 is an Armstrong number.
5 is an Armstrong number.
6 is an Armstrong number.
7 is an Armstrong number.
8 is an Armstrong number.
9 is an Armstrong number.
153 is an Armstrong number.
370 is an Armstrong number.
371 is an Armstrong number.
407 is an Armstrong number.
1634 is an Armstrong number.
8208 is an Armstrong number.
9474 is an Armstrong number.
54748 is an Armstrong number.
92727 is an Armstrong number.
93084 is an Armstrong number.
548834 is an Armstrong number.
Please remove j++ from 2nd loop for (int j = 1; j <= x; j++)
I tried this:
void armstrong(int x)
{
// count digits
int counter = 0, temp = x, sum = 0;
while(temp != 0)
{
temp = temp/10;
++counter; // Note: pre increment faster
}
// printf("count %d\n",counter);
temp = x;
while(temp != 0)
{
sum += pow(temp % 10, counter);
temp = temp/10;
}
// printf("sum %d\n",sum);
if(x == sum)
{
printf("Armstrong\n");
}
else
{
printf("No Armstrong\n");
}
}
int main(){
armstrong(371);
armstrong(1634);
return 0;
}
Let's take this and add the ability to handle multiple numeric bases while we're at it. Why? BECAUSE WE CAN!!!! :-)
#include <stdio.h>
#include <math.h>
double log_base(int b, double n)
{
return log(n) / log((double)b);
}
int is_armstrong_number(int b, /* base */
int n)
{
int num_digits = trunc(log_base(b, (double)n)) + 1;
int sum = 0;
int remainder = n;
while(remainder > 0)
{
sum = sum + pow(remainder % b, num_digits);
remainder = (int) (remainder / b);
}
return sum == n;
}
int main()
{
printf("All the following are valid Armstrong numbers\n");
printf(" 407 base 10 - result = %d\n", is_armstrong_number(10, 407));
printf(" 0xEA1 base 16 - result = %d\n", is_armstrong_number(16, 0xEA1));
printf(" 371 base 10 - result = %d\n", is_armstrong_number(10, 371));
printf(" 1634 base 10 - result = %d\n", is_armstrong_number(10, 1634));
printf(" 0463 base 8 - result = %d\n", is_armstrong_number(8, 0463));
printf("All the following are NOT valid Armstrong numbers\n");
printf(" 123 base 10 - result = %d\n", is_armstrong_number(10, 123));
printf(" 0x2446 base 16 - result = %d\n", is_armstrong_number(16, 0x2446));
printf(" 022222 base 8 - result = %d\n", is_armstrong_number(8, 022222));
}
At the start of is_armstrong_number we compute the number of digits directly instead of looping through the number. We then loop through the digits of n in base b, summing up the value of the digit raised to the number of digits in the number, for the given numeric base. Once the remainder hits zero we know there are no more digits to compute and we return a flag indicating if the given number is an Armstrong number in the given base.
I am trying to solve an online judge problem: http://opc.iarcs.org.in/index.php/problems/LEAFEAT
The problem in short:
If we are given an integer L and a set of N integers s1,s2,s3..sN, we have to find how many numbers there are from 0 to L-1 which are not divisible by any of the 'si's.
For example, if we are given, L = 20 and S = {3,2,5} then there are 6 numbers from 0 to 19 which are not divisible by 3,2 or 5.
L <= 1000000000 and N <= 20.
I used the Inclusion-Exclusion principle to solve this problem:
/*Let 'T' be the number of integers that are divisible by any of the 'si's in the
given range*/
for i in range 1 to N
for all subsets A of length i
if i is odd then:
T += 1 + (L-1)/lcm(all the elements of A)
else
T -= 1 + (L-1)/lcm(all the elements of A)
return T
Here is my code to solve this problem
#include <stdio.h>
int N;
long long int L;
int C[30];
typedef struct{int i, key;}subset_e;
subset_e A[30];
int k;
int gcd(a,b){
int t;
while(b != 0){
t = a%b;
a = b;
b = t;
}
return a;
}
long long int lcm(int a, int b){
return (a*b)/gcd(a,b);
}
long long int getlcm(int n){
if(n == 1){
return A[0].key;
}
int i;
long long int rlcm = lcm(A[0].key,A[1].key);
for(i = 2;i < n; i++){
rlcm = lcm(rlcm,A[i].key);
}
return rlcm;
}
int next_subset(int n){
if(k == n-1 && A[k].i == N-1){
if(k == 0){
return 0;
}
k--;
}
while(k < n-1 && A[k].i == A[k+1].i-1){
if(k <= 0){
return 0;
}
k--;
}
A[k].key = C[A[k].i+1];
A[k].i++;
return 1;
}
int main(){
int i,j,add;
long long int sum = 0,g,temp;
scanf("%lld%d",&L,&N);
for(i = 0;i < N; i++){
scanf("%d",&C[i]);
}
for(i = 1; i <= N; i++){
add = i%2;
for(j = 0;j < i; j++){
A[j].key = C[j];
A[j].i = j;
}
temp = getlcm(i);
g = 1 + (L-1)/temp;
if(add){
sum += g;
} else {
sum -= g;
}
k = i-1;
while(next_subset(i)){
temp = getlcm(i);
g = 1 + (L-1)/temp;
if(add){
sum += g;
} else {
sum -= g;
}
}
}
printf("%lld",L-sum);
return 0;
}
The next_subset(n) generates the next subset of size n in the array A, if there is no subset it returns 0 otherwise it returns 1. It is based on the algorithm described by the accepted answer in this stackoverflow question.
The lcm(a,b) function returns the lcm of a and b.
The get_lcm(n) function returns the lcm of all the elements in A.
It uses the property : LCM(a,b,c) = LCM(LCM(a,b),c)
When I submit the problem on the judge it gives my a 'Time Limit Exceeded'. If we solve this using brute force we get only 50% of the marks.
As there can be upto 2^20 subsets my algorithm might be slow, hence I need a better algorithm to solve this problem.
EDIT:
After editing my code and changing the function to the Euclidean algorithm, I am getting a wrong answer, but my code runs within the time limit. It gives me a correct answer to the example test but not to any other test cases; here is a link to ideone where I ran my code, the first output is correct but the second is not.
Is my approach to this problem correct? If it is then I have made a mistake in my code, and I'll find it; otherwise can anyone please explain what is wrong?
You could also try changing your lcm function to use the Euclidean algorithm.
int gcd(int a, int b) {
int t;
while (b != 0) {
t = b;
b = a % t;
a = t;
}
return a;
}
int lcm(int a, int b) {
return (a * b) / gcd(a, b);
}
At least with Python, the speed differences between the two are pretty large:
>>> %timeit lcm1(103, 2013)
100000 loops, best of 3: 9.21 us per loop
>>> %timeit lcm2(103, 2013)
1000000 loops, best of 3: 1.02 us per loop
Typically, the lowest common multiple of a subset of k of the s_i will exceed L for k much smaller than 20. So you need to stop early.
Probably, just inserting
if (temp >= L) {
break;
}
after
while(next_subset(i)){
temp = getlcm(i);
will be sufficient.
Also, shortcut if there are any 1s among the s_i, all numbers are divisible by 1.
I think the following will be faster:
unsigned gcd(unsigned a, unsigned b) {
unsigned r;
while(b) {
r = a%b;
a = b;
b = r;
}
return a;
}
unsigned recur(unsigned *arr, unsigned len, unsigned idx, unsigned cumul, unsigned bound) {
if (idx >= len || bound == 0) {
return bound;
}
unsigned i, g, s = arr[idx], result;
g = s/gcd(cumul,s);
result = bound/g;
for(i = idx+1; i < len; ++i) {
result -= recur(arr, len, i, cumul*g, bound/g);
}
return result;
}
unsigned inex(unsigned *arr, unsigned len, unsigned bound) {
unsigned i, result = bound, t;
for(i = 0; i < len; ++i) {
result -= recur(arr, len, i, 1, bound);
}
return result;
}
call it with
unsigned S[N] = {...};
inex(S, N, L-1);
You need not add the 1 for the 0 anywhere, since 0 is divisible by all numbers, compute the count of numbers 1 <= k < L which are not divisible by any s_i.
Create an array of flags with L entries. Then mark each touched leaf:
for(each size in list of sizes) {
length = 0;
while(length < L) {
array[length] = TOUCHED;
length += size;
}
}
Then find the untouched leaves:
for(length = 0; length < L; length++) {
if(array[length] != TOUCHED) { /* Untouched leaf! */ }
}
Note that there is no multiplication and no division involved; but you will need up to about 1 GiB of RAM. If RAM is a problem the you can use an array of bits (max. 120 MiB).
This is only a beginning though, as there are repeating patterns that can be copied instead of generated. The first pattern is from 0 to S1*S2, the next is from 0 to S1*S2*S3, the next is from 0 to S1*S2*S3*S4, etc.
Basically, you can set all values touched by S1 and then S2 from 0 to S1*S2; then copy the pattern from 0 to S1*S2 until you get to S1*S2*S3 and set all the S3's between S3 and S1*S2*S3; then copy that pattern until you get to S1*S2*S3*S4 and set all the S4's between S4 and S1*S2*S3*S4 and so on.
Next; if S1*S2*...Sn is smaller than L, you know the pattern will repeat and can generate the results for lengths from S1*S2*...Sn to L from the pattern. In this case the size of the array only needs to be S1*S2*...Sn and doesn't need to be L.
Finally, if S1*S2*...Sn is larger than L; then you could generate the pattern for S1*S2*...(Sn-1) and use that pattern to create the results from S1*S2*...(Sn-1) to S1*S2*...Sn. In this case if S1*S2*...(Sn-1) is smaller than L then the array doesn't need to be as large as L.
I'm afraid your problem understanding is maybe not correct.
You have L. You have a set S of K elements. You must count the sum of quotient of L / Si. For L = 20, K = 1, S = { 5 }, the answer is simply 16 (20 - 20 / 5). But K > 1, so you must consider the common multiples also.
Why loop through a list of subsets? It doesn't involve subset calculation, only division and multiple.
You have K distinct integers. Each number could be a prime number. You must consider common multiples. That's all.
EDIT
L = 20 and S = {3,2,5}
Leaves could be eaten by 3 = 6
Leaves could be eaten by 2 = 10
Leaves could be eaten by 5 = 4
Common multiples of S, less than L, not in S = 6, 10, 15
Actually eaten leaves = 20/3 + 20/2 + 20/5 - 20/6 - 20/10 - 20/15 = 6
You can keep track of the distance until then next touched leaf for each size. The distance to the next touched leaf will be whichever distance happens to be smallest, and you'd subtract this distance from all the others (and wrap whenever the distance is zero).
For example:
int sizes[4] = {2, 5, 7, 9};
int distances[4];
int currentLength = 0;
for(size = 0 to 3) {
distances[size] = sizes[size];
}
while(currentLength < L) {
smallest = INT_MAX;
for(size = 0 to 3) {
if(distances[size] < smallest) smallest = distances[size];
}
for(size = 0 to 3) {
distances[size] -= smallest;
if(distances[size] == 0) distances[size] = sizes[size];
}
while( (smallest > 1) && (currentLength < L) ) {
currentLength++;
printf("%d\n", currentLength;
smallest--;
}
}
#A.06: u r the one with username linkinmew on opc, rite?
Anyways, the answer just requires u to make all possible subsets, and then apply inclusion exclusion principle. This will fall well within the time bounds for the data given. For making all possible subsets, u can easily define a recursive function.
i don't know about programming but in math there is a single theorem which works on a set that has GCD 1
L=20, S=(3,2,5)
(1-1/p)(1-1/q)(1-1/r).....and so on
(1-1/3)(1-1/2)(1-1/5)=(2/3)(1/2)(4/5)=4/15
4/15 means there are 4 numbers in each set of 15 number which are not divisible by any number rest of it can be count manually eg.
16, 17, 18, 19, 20 (only 17 and 19 means there are only 2 numbers thatr can't be divided by any S)
4+2=6
6/20 means there are only 6 numbers in first 20 numbers that can't be divided by any s