Cracking the Coding Interview - Fooo

Solutions to Chapter 10 | Mathematical
10 4 Write a method to implement *, - , / operations You should use only the + operator
SOLUTION
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pg 68
With an understanding of what each operation (minus, times, divide) does, this problem can
be approached logically
» Subtraction should be relatively straightforward, as we all know that a - b is the same
thing as a + (-1)*b
» Multiplication: we have to go back to what we learned in grade school: 21 * 3 = 21 + 21
+ 21 It’s slow, but it works
» Division is the trickiest, because we usually think of 21 / 3 as something like “if you divide
a 21 foot board into 3 pieces, how big is each piece?” If we think about it the other way
around, it’s a little easier: “I divided a 21 foot board in x pieces and got pieces of 3 feet
each, how many pieces were there?” From here, we can see that if we continuously subtract
3 feet from 21 feet, we’ll know how many pieces there are That is, we continuously
subtract b from a and count how many times we can do that
1 /* Flip a positive sign to negative, or a negative sign to pos */
2 public static int FnNegate(int a) {
3 int neg = 0;
4 int d = a < 0 ? 1 : -1;
5 while (a != 0) {
6 neg += d;
7 a += d;
8 }
9 return neg;
10 }
11
12 /* Subtract two numbers by negating b and adding them */
13 public static int FnMinus(int a, int b) {
14 return a + FnNegate(b);
15 }
16
17 /* Check if a and b are different signs */
18 public static boolean DifferentSigns(int a, int b) {
19 return ((a < 0 && b > 0) || (a > 0 && b < 0)) ? true : false;
20 }
21
22 /* Return absolute value */
23 public static int abs(int a) {
24 if (a < 0) return FnNegate(a);
25 else return a;
26 }
1 9 0