Explain the sorting algorithm MergeSort, presented below, considering the example of a = {5, 3, 4, 7, 1, 2} while noting down all intermediate steps. Explain the principle of “divide and conquer” with this algorithm. // auxiliary function for recursive sorting by merging private static void _mergeSort(int a[], int copy[], int start, int end){ if (start < end) { int mid = (start + end) / 2; mergeSort(a, copy, start, mid); mergeSort(a, copy, mid + 1, end); merge(a, copy, start, mid, end); } } private static void merge(int a[], int copy[], int start, int m, int end) { int i = 0, j = start, k; while (j <= m) copy[i++] = a[j++]; i = 0; k = start; while (k < j && j <= end) { if (copy[i] <= a[j]) a[k++] = copy[i++]; else a[k++] = a[j++]; } while (k < j) a[k++] = copy[i++]; } public static void mergeSort(int[] a) { mergeSort(a, new int[a.length], 0, a.length - 1)\ } 2. Why does this algorithm require less space than that one presented during the lecture? 3. Is this MergeSort algorithm stable? Give reasons for your answer

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Explain the sorting algorithm MergeSort, presented below, considering the example of a =
{5, 3, 4, 7, 1, 2} while noting down all intermediate steps. Explain the principle of “divide
and conquer” with this algorithm.
// auxiliary function for recursive sorting by merging
private static void _mergeSort(int a[], int copy[], int start, int end){
if (start < end) {
int mid = (start + end) / 2;
mergeSort(a, copy, start, mid);
mergeSort(a, copy, mid + 1, end);
merge(a, copy, start, mid, end);
}
}
private static void merge(int a[], int copy[], int start, int m, int end) {
int i = 0, j = start, k;
while (j <= m)
copy[i++] = a[j++];
i = 0;
k = start;
while (k < j && j <= end) {
if (copy[i] <= a[j])
a[k++] = copy[i++];
else
a[k++] = a[j++];
}
while (k < j)
a[k++] = copy[i++];
}
public static void mergeSort(int[] a) {
mergeSort(a, new int[a.length], 0, a.length - 1)\
}
2. Why does this algorithm require less space than that one presented during the lecture?
3. Is this MergeSort algorithm stable? Give reasons for your answer.

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