Question

When sorting using merge sort, I get confused about what going on. Consider the following array A = [7,5,2,8,9,1] and the following code:

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int merge_sort(int *input, int start, int end)
{
if (start < end)
{
int middle = (start + end ) / 2;
merge_sort(input, start, middle);
merge_sort(input, middle+1, end);
merge(input, start, middle, end);
}

return 0;
}
int merge(int *input, int left, int middle, int right)
{
// determine lenghts
int length1 = middle - left + 1;
int length2 = right - middle;
// create helper arrays
int subarray1[length1];
int subarray2[length2];
// fill helper arrays
int i;
for (i=0; i<length1; ++i)
{
subarray1[i] = input[left + i];
}
for (i=0; i<length2; ++i)
{
subarray2[i] = input[middle + 1 + i];
}
subarray1[length1] = 100;
subarray2[length2] = 100;

int j,k;
j = 0;
i = 0;

// go through subarray and insert into main array
for (k=left; k<=right; ++k)
{
if (subarray1[i] <= subarray2[j])
{
input[k] = subarray1[i];
++i;
}
else if (subarray1[i] > subarray2[j])
{
input[k] = subarray2[j];
++j;
}
}

return 0;
}
-------------------------------------------------------------------------------------

Since merge-sort () is called first on array A, the left side of this array would recursively divided using, merge-sort(input, start , middle) until base case (start <end) is met resulting into:

<7,5,2,8,9,1>

<7,5,2>

<7,5>

<7>

Then we can deal with the right using merge-sort(input, middle + 1, end)

<7,5>

<5>

<7,5,2>

<2>

<8,9,1>

<8,9>

...

until we get something like: < 7 > < 5 > < 2 > < 8 > < 9 > < 1 >

This where we should merge(at least I think) using merge (input, start, middle, end)

Which would sort 7 and 5 into < 5 , 7 >

Which would make the first iteration of Merge Sort = [5, 7 , 2 , 8 , 9 , 1]

Am I right, or am I missing something? I have used visualalgo to visualize how Merge sot works, and it is different from the visuals from "introduction to algorithms." I would assume that since we recursively call merge-sort using merge-sort(input, start, middle) the left side is "divided" first since programming works top to bottom, and when the base case is met start >=end that is when we can move to the next recursive call on the right side, aka merge-sort(input, middle + 1, end). Then we can finally "conquer" and "combine" by calling merge(input, start, middle, end), which will create subarrays (1 and 2) of different sizes ( based on what is the size of what we want to sort, aka left, middle and right). Sorry for the rambling, by I hope by giving my approach on how I see this, someone can better assist me with figuring out how the first iteration or pass of Merge sort looks like.  

Answer 1

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