Bottom-up merge sorting algorithm

1, what is the bottom-up of the merge sort?

In the final analysis, whether it is the top-down merge sort or the now speaking of the bottom-up of the merge sort, its essence is to merge.

Take a look at a demonstration process:

This is the sequence of arrays to be sorted.

The array is divided into 4 groups with 2 elements, and each group is internally divided into 2 sub-sequences to merge up

This is the effect after the merger.

Then a group is divided into 2 groups with 4 elements, and each group is internally divided into 2 sub-sequences to merge up

This is the effect after the merger.

Then a group is divided into 1 groups with 8 elements, and each group is internally divided into 2 sub-sequences to merge up

Finally, the whole sequence is programmed in order.

In fact, from this point of view, this is like the front of the top-down sort process in the back of a process.

2. Complexity of Time

Same as top-down merge sort, time complexity is O (NLOGN) level.

3, the implementation of the algorithm (based on C + +)

#define MIN (A, B) ((a) < (b)? (a): (b))

1 /***************************** Bottom-up merge sort algorithm realizes ***********************************/2Template<typename t>3 voidMERGESORTBU (T arr[],intcount)4 {5      for(intSize =1; Size <= count; Size + = size) {//Outer Loop Grouping of sub-sequences6          for(inti =0; i + size < count; i + = size + size) {//the inner loop iterates through all the sub-sequences of the well-grouped groups and merges them up sequentially7__merge<t> (arr, I, i + Size-1, MIN (i + size + size-1, Count-1));//This function is implemented in the top-down merge sort __merge function9         }Ten     } One } A /*******************************************************************************************/

4. Performance test (compared to optimized top-down merge sorting algorithm)

Test Data Volume 50000:

Test Data Volume 100000:

5. Algorithm optimization

In fact, the optimization algorithm is the same as the top-down merge sort

1 /*optimization ********************************** of **************************** bottom-up merging sorting algorithm*/2Template<typename t>3 voidMERGESORTBU (T arr[],intcount)4 {5      for(intSize =1; Size <= count; Size + = size) {//Outer Loop Grouping of sub-sequences6          for(inti =0; i + size < count; i + = size + size) {//the inner loop iterates through all the sub-sequences of the well-grouped groups and merges them up sequentially7             if(MIN (i + size + size-1, Count-1)-I < -) {//Optimization measures 28__insertsortmg<t> (arr, I, MIN (i + size + size-1, Count-1));//This function is the __INSERTSORTMG function implemented in the top-down merge sort9                 Continue;Ten             } One  A             if(Arr[i + Size-1] > arr[i + size]) {//Optimization measures 1 -__merge<t> (arr, I, i + Size-1, MIN (i + size + size-1, Count-1));//This function is implemented in the top-down merge sort __merge function -             }    the         } -     } - } - /*******************************************************************************************/

Performance testing after optimization:

Test Data Volume 50000:

Test Data Volume 100000:

Summary: From the above data can be seen, after optimization, the performance of the bottom-up sorting has been a great improvement, but still more than the top-down merge sort slow,

There is a reason for this, and there is no analysis here.

It is also worth mentioning that the code of the non-optimized algorithm shows that the code does not use the attributes of the array (using the index to find the corresponding element), so we can

Sort a list by the bottom-up merge sort.

Bottom-up merge sorting algorithm