This is the Merge-Sort implementation written in Objective-C.

MergeSort.h

/**
 * Divide and Conque Algorithm.
 */
- (NSArray *)mergesort:(NSArray *)array

MergeSort.m

/**
 * The following two implementation introduced a few Objective-C knowledge hints I used to miss.
 * 1st, Objective-C is just like C language, it pass-by-value instead of pass-by-reference, 
 *      even pass a pointer address, it's still a value. You can't assign a new address to it.
 * 2nd, [[NSMutableArray alloc] initWithCapacity:count]; would create an empty mutable array, which has nothing in it. You could either addObject: to it,
 *      or set the first unsigned index to an object.
 * E.g, If you just send the message "initWithCapacity:", it's an empty mutable array, you could addObject: which add the object to the array,
 *      and its index is 0. Or, you could just assign the 0th index with the object. You can't assign the object to other index at this moment.
 *      Like, you could not assign 1st index with object, otherwise, a runtime error will popup when you run it.
 */
- (NSArray *)mergesort:(NSArray *)array
{
    NSInteger count = array.count;
    NSMutableArray *helper = [[NSMutableArray alloc] initWithCapacity:count];
    NSMutableArray *ret = [array mutableCopy];
    [self mergesort:ret withHelperArray:helper from:0 to:count-1];
    return ret;
}

- (void)mergesort:(NSMutableArray *)array withHelperArray:(NSMutableArray *)helper from:(NSInteger)low to:(NSInteger)high
{
    if (low >= high) return;
    NSInteger mid = (low + high) / 2;
    [self mergesort:array withHelperArray:helper from:low to:mid];
    [self mergesort:array withHelperArray:helper from:mid+1 to:high];
    [self merge:array withHelperArray:helper from:low mid:mid to:high];
}

- (void)merge:(NSMutableArray *)array withHelperArray:(NSMutableArray *)helper from:(NSInteger)low mid:(NSInteger)mid to:(NSInteger)high
{
    for(NSInteger i = low; i<= high; i++) {
        helper[i] = array[i];
    }
    
    NSInteger left1 = low;
    NSInteger left2 = mid + 1;
    NSInteger index = low;
    while(left1 <= mid || left2 <= high) {
        if(left1 <= mid && left2 <= high) {
            if ([helper[left1] integerValue] <= [helper[left2] integerValue]) {
                array[index] = helper[left1];
                left1++;
            } else {
                array[index] = helper[left2];
                left2++;
            }
            index++;
        } else if (left1 <= mid) {
            array[index] = helper[left1];
            left1++;
            index++;
        } else if (left2 <= high) {
            array[index] = helper[left2];
            left2++;
            index++;
        }
    }
}

- (NSArray *)mergesort:(NSArray *)array
{
    NSMutableArray *ret = [array mutableCopy];
    [self mergesort:ret from:0 to:array.count-1];
    return ret;
}

- (void)mergesort:(NSMutableArray *)array from:(NSInteger)low to:(NSInteger)high
{
    if (low >= high) return;
    NSInteger mid = (low + high) / 2;
    [self mergesort:array from:low to:mid];
    [self mergesort:array from:mid+1 to:high];
    [self merge:array from:low mid:mid to:high];
}

- (void)merge:(NSMutableArray *)array from:(NSInteger)low mid:(NSInteger)mid to:(NSInteger)high
{
    NSMutableArray *helper = [[NSMutableArray alloc] initWithCapacity:array.count];
    for(NSInteger i = 0; i< array.count; i++) {
        [helper addObject:array[i]];
    }
    
    NSInteger left1 = low;
    NSInteger left2 = mid + 1;
    NSInteger index = low;
    while(left1 <= mid || left2 <= high) {
        if(left1 <= mid && left2 <= high) {
            if ([helper[left1] integerValue] <= [helper[left2] integerValue]) {
                array[index] = helper[left1];
                left1++;
            } else {
                array[index] = helper[left2];
                left2++;
            }
            index++;
        } else if (left1 <= mid) {
            array[index] = helper[left1];
            left1++;
            index++;
        } else if (left2 <= high) {
            array[index] = helper[left2];
            left2++;
            index++;
        }
    }
}