Why set the size of the first array (temp) equal to the length of the input array?

Setting the size of the temporary array (temp) equal to the length of the input array is often done to simplify the algorithm, ensuring that temp has enough space for all elements that may be needed during processing.

For example, in merge sort, the temporary array is used to store intermediate results. The size of temp is equal to the length of the original array to avoid overflow and to prevent dynamic memory allocation during recursion.

This allows:

• To avoid reallocating memory on each function call.
• To simplify the logic of copying elements.

Example:

void mergeSort(int[] arr) {
    int[] temp = new int[arr.length];
    mergeSortHelper(arr, temp, 0, arr.length - 1);
}

void mergeSortHelper(int[] arr, int[] temp, int left, int right) {
    if (left >= right) return;
    int mid = (left + right) / 2;
    mergeSortHelper(arr, temp, left, mid);
    mergeSortHelper(arr, temp, mid + 1, right);
    merge(arr, temp, left, mid, right);
}

Thus, setting temp size to the input array length is for efficiency and ease of implementation.