Find Duplicates

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 4 kilobytes of memory available, how would you print all duplicate elements in the array?

Solution

We have 4 kilobytes 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 on integer

Complexity

时间复杂度 O(n),空间复杂度 O(n)

Code

void checkDuplicates(int[] array){
    BitSet bs = new BitSet(32000);
    for (int i = 0; i < array.length; i++){
        int num = array[i];
        int num0 = num - 1; // bitset starts at 0, numbers start at 1
        if (bs.get(num0)){
            System.out.println(num);
        }
        else{
            bs.set(num0);
        }
    }
}

class BitSet{
    int[] bitset;

    public BitSet(int size){
        bitset = new int[(size >> 5) + 1]; // divide by 32
    }

    boolean get(int pos){
        int wordNumber = (pos >> 5); // divide by 32
        int bitNumber = (pos & 0x1F); // mod 32
        return (bitset[wordNumber] & (1 << bitNumber)) != 0;
    }

    void set(int pos){
        int wordNumber = (pos >> 5); // divide by 32
        int bitNumber = (pos & 0x1F); // mod 32
        bitset[wordNumber] |= 1<< bitNumber;
    }
}