Difference of two large numbers

https://blog.csdn.net/lichong_87/article/details/6860329

https://www.geeksforgeeks.org/difference-of-two-large-numbers/

Given two numbers as strings. The numbers may be very large (may not fit in long long int), the task is to find difference of these two numbers.

We can avoid the first two string reverse operations by traversing them from end. Below is optimized solution.

static boolean isSmaller(String str1, String str2)

{

    // Calculate lengths of both string

    int n1 = str1.length(), n2 = str2.length();

  

    if (n1 < n2)

        return true;

    if (n2 > n1)

        return false;

  

    for (int i = 0; i < n1; i++)

    {

        if (str1.charAt(i) < str2.charAt(i))

            return true;

        else if (str1.charAt(i) > str2.charAt(i))

            return false;

    }

    return false;

}

  

// Function for finding difference of larger numbers

static String findDiff(String str1, String str2)

{

    // Before proceeding further, make sure str1

    // is not smaller

    if (isSmaller(str1, str2))

    {

        String t = str1; 

        str1 = str2;

        str2 = t;

    }

  

    // Take an empty string for storing result

    String str = "";

  

    // Calculate lengths of both string

    int n1 = str1.length(), n2 = str2.length();

    int diff = n1 - n2;

  

    // Initially take carry zero

    int carry = 0;

  

    // Traverse from end of both strings

    for (int i = n2 - 1; i >= 0; i--)

    {

        // Do school mathematics, compute difference of

        // current digits and carry

        int sub = (((int)str1.charAt(i + diff) - (int)'0') -

                    ((int)str2.charAt(i) - (int)'0') - carry);

        if (sub < 0)

        {

            sub = sub+10;

            carry = 1;

        }

        else

            carry = 0;

  

        str += String.valueOf(sub);

    }

  

    // subtract remaining digits of str1[]

    for (int i = n1 - n2 - 1; i >= 0; i--)

    {

        if (str1.charAt(i) == '0' && carry > 0)

        {

            str += "9";

            continue;

        }

        int sub = (((int)str1.charAt(i) - (int)'0') - carry);

        if (i > 0 || sub > 0) // remove preceding 0's

            str += String.valueOf(sub);

        carry = 0;

  

    }

  

    // reverse resultant string 

    return new StringBuilder(str).reverse().toString();

}




This is simple based on school mathematics. We traverse both strings from end, one by one subtract digits.
1) Reverse both strings.
2) Keep subtracting digits one by one from 0’th index (in reversed strings) to end of smaller string, append the diff if it’s positive to end of result. If difference(diff) is negative then add 10 and keep track of carry as 1 if it’s positive then carry is 0.
3) Finally reverse the result.

// Function for find difference of larger numbers

static String findDiff(String str1, String str2)

{

    // Before proceeding further, make sure str1

    // is not smaller

    if (isSmaller(str1, str2))

    {

        String t = str1;

        str1 = str2;

        str2 = t;

    }

  

    // Take an empty string for storing result

    String str = "";

  

    // Calculate length of both string

    int n1 = str1.length(), n2 = str2.length();

  

    // Reverse both of strings

    str1 = new StringBuilder(str1).reverse().toString();

    str2 = new StringBuilder(str2).reverse().toString();

      

    int carry = 0;

  

    // Run loop till small string length

    // and subtract digit of str1 to str2

    for (int i = 0; i < n2; i++)

    {

        // Do school mathematics, compute difference of

        // current digits

        int sub = ((int)(str1.charAt(i)-'0') - 

                   (int)(str2.charAt(i)-'0')-carry);

          

        // If subtraction is less then zero

        // we add then we add 10 into sub and

        // take carry as 1 for calculating next step

        if (sub < 0)

        {

            sub = sub + 10;

            carry = 1;

        }

        else

            carry = 0;

  

        str += (char)(sub + '0');

    }

  

    // subtract remaining digits of larger number

    for (int i = n2; i < n1; i++)

    {

        int sub = ((int)(str1.charAt(i) - '0') - carry);

          

        // if the sub value is -ve, then make it positive

        if (sub < 0)

        {

            sub = sub + 10;

            carry = 1;

        }

        else

            carry = 0;

              

        str += (char)(sub + '0');

    }

  

    // reverse resultant string

    return new StringBuilder(str).reverse().toString();

}