Cracking the Coding Interview, 4 Edition - 150 Programming Interview Questions and Solutions

Solutions to Chapter 10 | Mathematical
27
28 /* Multiply a by b by adding a to itself b times */
29 public static int FnTimes(int a, int b) {
30 if (a < b) return FnTimes(b, a); // algo is faster if b < a
31 int sum = 0;
32 for (int iter = abs(b); iter > 0; --iter) sum += a;
33 if (b < 0) sum = FnNegate(sum);
34 return sum;
35 }
36
37 /* Divide a by b by literally counting how many times does b go into
38 * a. That is, count how many times you can subtract b from a until
39 * you hit 0. */
40 public static int FnDivide(int a, int b) throws
41 java.lang.ArithmeticException {
42 if (b == 0) {
43 throw new java.lang.ArithmeticException(“Divide by 0.”);
44 }
45 int quotient = 0;
46 int divisor = FnNegate(abs(b));
47 int divend; /* dividend */
48 for (divend = abs(a); divend >= abs(divisor); divend += divisor) {
49 ++quotient;
50 }
51 if (DifferentSigns(a, b)) quotient = FnNegate(quotient);
52 return quotient;
53 }
OBSERVATIONS AND SUGGESTIONS
»»
A logical approach of going back to what exactly multiplication and division do comes
in handy. Remember that. All (good) interview problems can be approached in a logical,
methodical way!
»»
The interviewer is looking for this sort of logical work-your-way-through-it approach.
»»
This is a great problem to demonstrate your ability to write clean code—specifically,
to show your ability to re-use code. For example, if you were writing this solution and
didn’t put FnNegate in its own method, you should move it out once you see that you’ll
use it multiple times.
» » Be careful about making assumptions while coding. Don’t assume that the numbers are
all positive, or that a is bigger than b.
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Cracking the Coding Interview | Concepts and Algorithms