How can I remove a certain number of digits in a number so the number obtained is minimal?

Question

Specifically, I want to write a function int remove_digits(int large, int num_digits_to_remove) such that:

Any num_digits_to_remove digits are removed from large as though removing characters from its string representation
The number that is returned has the lowest possible value from removing digits as in step 1

For example, removing 4 digits from 69469813 would give 4613

I would prefer answers written in C.

Welcome to StackOverflow! I edited your question to try to make it more clear what your algorithm is doing. Did I get it right, or are you trying to do something different? — Kevin, Nov 14 '13 at 22:27
In C int division is floor division... so you can / 10 and check %10 over and over, to go through the digits right to left until it is 0. — Grady Player, Nov 14 '13 at 22:41

score 3 · Answer 1 · answered Nov 14 '13 at 22:25

Idea:

char number[] = "69469813";
char digits[ARRAY_SIZE(number)];
size_t i;

// sort digits; complexity O(n * log n);
sort_digits(digits, number);   // -> digits becomes "99866431"

for (i = 0; i < number_of_digits_to_be_removed; ++i) {
     size_t j;
     for (j = 0; j < ARRAY_SIZE(number); ++j) {
         if (number[j] == digits[i]) {
             number[j] = 'X';      // invalidate it
             break;
         }
     }
 }

 for (i = 0; i < ARRAY_SIZE(number); ++i)
     if (number[i] != 'X')
         printf("%c", number[i]);

Whole thing has a complexity of O(n * m);

score 1 · Accepted Answer · answered Nov 15 '13 at 00:31

The basic idea is that if you can only remove one digit, you want to remove the first digit (starting with the most significant digit) that is followed by a smaller digit.

For example, if your number is 123432, you want to remove the 4 (since it is followed by a 3), resulting in 12332.

You then repeat this process for as many digits as you want to remove:

char *num = "69469813";
char *buf = malloc(strlen(num)+1);
size_t to_remove = 4;

while (to_remove --> 0) {
    char *src = num;
    char *dst = buf;

    while (*src < *(src+1)) { *dst++ = *src++; } // Advance until the next digit is less than the current digit
    src++;                                       // Skip it
    while (*dst++ = *src++);                     // Copy the rest

    strcpy(num, buf);
}
printf("%s\n", num); // Prints 4613

Note that ensc's solution doesn't work for, e.g., 319 with one removal. In this case, you want to remove the 3 (as done in my solution), not the 9. — rockhyrax, Nov 15 '13 at 00:38

what is sleep · Answer 3 · 2013-11-14T22:45:49.003

I don't know C but here is how I would do it in java:

String original = "69469813";
String result = "";

int numNeedToBeTaken = 4;
int numLeft = original.length() - numNeedToBeTaken;

while(result.length() < numLeft)
{
    String temp = original.substring(0,original.length()-numNeedToBeTaken+1);
    int smallest= 9;
    int index = 0;
    for(int i = 0; i<temp.length(); i++)
    {
        int number = Integer.parseInt(Character.toString(temp.charAt(i)));
        if( number < smallest)
        {
            smallest = number;
            index = i+1;
        }
    }
    numNeedToBeTaken--;
    result = result.concat(String.valueOf(smallest));
    original = original.substring(index);
}
Log.d("debug","result: "+result); //tested to work with your example, returns 4613

converting this to C should be pretty easy, I only used some basic operations.

How can I remove a certain number of digits in a number so the number obtained is minimal?

3 Answers3