Basic Operations

Data Structures and Algorithms with Object-Oriented Design Patterns in Java

Basic Operations

Program defines the constructor for the SetAsBitVector class as well as the three basic operations--insert, isMember, and withdraw. The constructor takes a single argument , which specifies the universe and, consequently, the number of bits needed in the bit array. The constructor creates an array of ints of length , where is the number of bits in an int, and sets the elements of the array to zero. The running time of the constructor is .

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Program: SetAsBitVector class constructor, insert, withdraw, and isMember methods.

To insert an item into the set, we need to change the appropriate bit in the array of bits to one. The bit of the bit array is bit of word . Thus, the insert method is implemented using a bitwise or operation to change the bit to one as shown in Program . Even though it is slightly more complicated than the corresponding operation for the SetAsArray class, the running time for this operation is still O(1). Since is a power of two, it is possible to replace the division and modulo operations, / and %, with shifts and masks like this:

vector [item >> shift] |= 1 << (item & mask);

for a suitable definition of the constants shift and mask. Depending on the compiler and machine architecture, doing so may improve the performance of the insert operation by a constant factor. Of course, its asymptotic performance is still O(1).

To withdraw an item from the set, we need to clear the appropriate bit in the array of bits and to test if an item is a member of the set, we test the corresponding bit. The isMember and withdraw methods in Program show how this can be done. Like insert, both these methods have constant worst-case running times.