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

Solutions to Chapter 11 | System Design and Memory Limits
11.4 You have an array with all the numbers from 1 to N, where N is at most 32,000. The
array may have duplicate entries and you do not know what N is. With only 4KB of
memory available, how would you print all duplicate elements in the array?
SOLUTION
pg 72
We have 4KB of memory which means we can address up to 8 * 4 * (2^10) bits. Note that 32*
(2^10) bits is greater than 32000. We can create a bit vector with 32000 bits, where each bit
represents one integer.
NOTE: While this isn’t an especially difficult problem, it’s important to implement this cleanly.
We will define our own bit vector class to hold a large bit vector.
1 public static void checkDuplicates(int[] array) {
2 BitSet bs = new BitSet(32000);
3 for (int i = 0; i < array.length; i++) {
4 int num = array[i];
5 int num0 = num - 1; // bitset starts at 0, numbers start at 1
6 if (bs.get(num0)) {
7 System.out.println(num);
8 } else {
9 bs.set(num0);
10 }
11 }
12 }
13
14 class BitSet {
15 int[] bitset;
16
17 public BitSet(int size) {
18 bitset = new int[size >> 5]; // divide by 32
19 }
20
21 boolean get(int pos) {
22 int wordNumber = (pos >> 5); // divide by 32
23 int bitNumber = (pos & 0x1F); // mod 32
24 return (bitset[wordNumber] & (1 > 5); // divide by 32
29 int bitNumber = (pos & 0x1F); // mod 32
30 bitset[wordNumber] |= 1