Sorting a sequence by swapping adjacent elements using minimum swaps

Question

We have an unsorted sequence of N numbers (1, 2, 3, 4, ... N). We can sort the whole sequence by swapping adjacent elements in a specific order. Given a sequence, how do I c

Answer 1

Thanks @Ivaylo Strandjev's explanation, to make the answer more complete, here is Java implementation:

// http://stackoverflow.com/questions/20990127/sorting-a-sequence-by-swapping-adjacent-elements-using-minimum-swaps
// The minimum number if swaps is equal to the number of inversions in the array
public static long sortWithSwap(int [] a) {
    return invCount(a, 0, a.length-1);
}

private static long invCount(int[] a, int left, int right) {
    if(left >= right)   return 0;
    int mid = left + (right-left)/2;
    long cnt = invCount(a, left, mid) + invCount(a, mid+1, right);
    cnt += merge(a, left, mid, right);
    return cnt;
}

private static long merge(int[] a, int left, int mid, int right) {
    long cnt = 0;
    int i = left, j = mid+1, k = left;
    int[] b = new int[a.length];
    while(i<=mid && j<=right) {
        if(a[i] <= a[j])    b[k++] = a[i++];
        else {
            b[k++] = a[j++];
            cnt += mid - i + 1;
        }
    }

    while(i <= mid) {
        b[k++] = a[i++];
    }
    while(j <= right) {
        b[k++] = a[j++];
    }

    for(i=left; i<=right; i++)  a[i] = b[i];
    return cnt;
}