1997 Canadian Computing Competition, Stage 1

Problem E: Long Division

In days of yore (circa 1965), mechanical calculators performed division by shifting and repeated subtraction. For example, to divide 987654321 by 3456789, the numbers would first be aligned by their leftmost digit (see Figure 1 below), and the divisor subtracted from the dividend as many times as possible without yielding a negative number. The number of successful subtractions (in this example, 2) is the first digit of the quotient. The divisor, shifted to the right (see Figure 2 below), is subtracted from the remainder several times to yield the next digit, and so on until the remainder is smaller than the divisor.

        987654321
    -   3456789         first successful subtraction
        ========
        641975421
    -   3456789         second successful subtraction
        ========
        296296521       remainder
    -   3456789         unsuccessful subtraction
        ========
        negative

        296296521
   -    3456789
        ========
        261728631
        etc.

Write a program to implement this method of division. See the input and output specifications below.

Input

The first line of the input file contains a positive integer n, n < 20, which represents the number of test cases which follow. Each test case is provided on a pair of lines, with the number on the first line being the dividend, and the number on the second line being the divisor. Each line will contain a positive integer of up to 80 digits in length.

Output

For each pair of input lines, your output file should contain a pair of lines representing the quotient followed by the remainder. Output for different test cases should be separated by a single blank line. Your output should omit unnecessary leading zeros.

Sample Input

3
987654321
3456789
33
11
11
33

Sample Output

285
2469456
 
3
0
 
0
11

All Submissions
Best Solutions

Point Value: 10
Time Limit: 2.00s
Memory Limit: 16M
Added: Sep 29, 2008

Languages Allowed:
C++03, PAS, C, ASM, C#, C++11

Comments (Search)

The subtraction logic is quite confusing.

or should the divisor be shifted one place to the right and then subtract?

Ignore the diagram. Just divide. I can only suppose the diagram is for those people who can program but don't know long division, even though I can't imagine such a person ever making it to stage 2.

Why am I TLEing?

I suggest making your code readable. Does it work on your comp? If not, contact Hanson.

Don't you mean "if so, contact Hanson"?

It works fine on my computer but it TLEs on the judge

Are you allowed to jsut use / and modulo or
do you have to use the method that it says to use

Use the method they say to use.

Well, of course it's not really a secret, but...
there is no automated checking of source, so you are free to use whatever method you want for generating the output. Of course, short of simply hard-coding the output file (which would get you in trouble for sure), the method they gave you is undoubtedly the easiest to implement. The numbers given may be too large to fit in int/long long, so you can't use / and mod to solve this problem.