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

Solutions to Chapter 8 | Recursion
8.7 Given an infinite number of quarters (25 cents), dimes (10 cents), nickels (5 cents) and
pennies (1 cent), write code to calculate the number of ways of representing n cents.
SOLUTION
pg 64
This is a recursive problem, so let’s figure out how to do makeChange(n) using prior solutions
(i.e., sub-problems). Let’s say n = 100, so we want to compute the number of ways of making
change of 100 cents. What’s the relationship to its sub-problems?
We know that makeChange(100):
= makeChange(100 using 0 quarters) + makeChange(100 using 1 quarter) + makeChange(100
using 2 quarter) + makeChange(100 using 3 quarter) + makeChange(100 using 4 quarter)
Can we reduce this further? Yes!
= makeChange(100 using 0 quarters) + makeChange(75 using 0 quarter) + makeChange(50
using 0 quarters) + makeChange(25 using 0 quarters) + 1
Now what? We’ve used up all our quarters, so now we can start applying our next biggest
denomination: dimes.
This leads to a recursive algorithm that looks like this:
1 public static int makeChange(int n, int denom) {
2 int next_denom = 0;
3 switch (denom) {
4 case 25:
5 next_denom = 10;
6 break;
7 case 10:
8 next_denom = 5;
9 break;
10 case 5:
11 next_denom = 1;
12 break;
13 case 1:
14 return 1;
15 }
16 int ways = 0;
17 for (int i = 0; i * denom