2.2: FastArrayStack - An Optimized ArrayStack

Much of the work done by an ArrayStack involves shifting (by \(\mathtt{add(i,x)}\) and \(\mathtt{remove(i)}\)) and copying (by \(\mathtt{resize()}\)) of data. In the implementations shown above, this was done using \(\mathtt{for}\) loops. It turns out that many programming environments have specific functions that are very efficient at copying and moving blocks of data. In the C programming language, there are the \(\mathtt{memcpy(d,s,n)}\) and \(\mathtt{memmove(d,s,n)}\) functions. In the C++ language there is the \(\texttt{std::copy(a0,a1,b)}\) algorithm. In Java there is the \(\texttt{System.arraycopy}\mathtt{(s,i,d,j,n)}\) method.

    void resize() {
        T[] b = newArray(Math.max(2*n,1));
        System.arraycopy(a, 0, b, 0, n);
        a = b;
    }
    void add(int i, T x) {
        if (i < 0 || i > n) throw new IndexOutOfBoundsException();
        if (n + 1 > a.length) resize();
        System.arraycopy(a, i, a, i+1, n-i); 
        a[i] = x;
        n++;
    }
    T remove(int i) {
        if (i < 0 || i > n - 1) throw new IndexOutOfBoundsException();
        T x = a[i];
        System.arraycopy(a, i+1, a, i, n-i-1);
        n--; 
        if (a.length >= 3*n) resize();
        return x;
    }

These functions are usually highly optimized and may even use special machine instructions that can do this copying much faster than we could by using a \(\mathtt{for}\) loop. Although using these functions does not asymptotically decrease the running times, it can still be a worthwhile optimization.

In the Java implementations here, the use of the native \(\texttt{System.arraycopy}\mathtt{(s,i,d,j,n)}\) resulted in speedups of a factor between 2 and 3, depending on the types of operations performed. Your mileage may vary.

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