Merge Sort

Stats

Worst Case Performance: O(n log n)

Best Case Performance: O(n log n)

Algorithm

• Conceptually, a merge sort works as follows:
  1. Divide the unsorted list into n sublists, each containing 1 element (a list of 1 element is considered sorted).
  2. Repeatedly merge sublists to produce new sorted sublists until there is only 1 sublist remaining. This will be the sorted list.

Psuedocode

/* Array A[] has the items to sort; array B[] is a work array */
function BottomUpSort(int n, int A[], int B[]) {
  int width;
  /* Each 1-element run in A is already "sorted". */
  /* Make successively longer sorted runs of length 2, 4, 8, 16... until whole array is sorted. */
  for(width = 1; width < n; width = 2 * width) {
    int i;
    /* Array A is full of runs of length width. */
    for(i = 0; i < n; i = i + 2 * width) {
      /* Merge two runs: A[i:i+width-1] and A[i+width:i+2*width-1] to B[] */
      /* or copy A[i:n-1] to B[] ( if(i+width >= n) ) */
      BottomUpMerge(A, i, min(i+width, n), min(i+2*width, n), B);
    }
  }
}

BottomUpMerge(int A[], int iLeft, int iRight, int iEnd, int B[]) {
  int i0 = iLeft;
  int i1 = iRight;
  int j;

  /* While there are elements in the left or right lists */
  for(j = iLeft; j < iEnd; j++) {
    /* If left list head exists and is <= existing right list head */
    if(i0 < iRight && (i1 >= iEnd || A[i0] <= A[i1])) {
      B[j] = A[i0];
      i0 = i0 + 1;
    } else {
      B[j] = A[i1];
      i1 = i1 + 1;
    }
  }
}

Additional Info

Wikipedia Article [http://en.wikipedia.org/wiki/Merge_Sort]