This is the Binary Search implementation written in Objective-C.

BinarySearch.h

/**
 * Standard Binary Search.
 */
- (BOOL)binarySearch:(NSInteger)number inArray:(NSArray *)array;

/**
 * Find the very first element index in an ordered array that satisfy with crateria, then return the index.
 * Otherwise, return -1.
 * This algorithm implemented with binary search.
 */
- (NSInteger)leastXFromIndex:(NSInteger)low
                     toIndex:(NSInteger)high
           withTrueCriterial:(BOOL(^)(NSInteger index))crateria;

/**
 * Find the very last element index in an ordered array that does not satisfy with crateria, then return the index.
 * Otherwise, return -1.
 * This algorithm implemented with binary search.
 */               
- (NSInteger)greatestXFromIndex:(NSInteger)low
                        toIndex:(NSInteger)high
             withFalseCriterial:(BOOL(^)(NSInteger index))crateria;

BinarySearch.m

- (BOOL)binarySearch:(NSInteger)number inArray:(NSArray *)array
{
    NSInteger left = 0;
    NSInteger right = array.count - 1;
    while(left <= right) {
        NSInteger mid = (left + right) / 2;
        if([array[mid] integerValue] < number) {
            left = mid + 1;
        } else if([array[mid] integerValue] > number) {
            right = mid - 1;
        } else {
            return YES;
        }
    }
    return NO;
}

- (NSInteger)leastXFromIndex:(NSInteger)low
                     toIndex:(NSInteger)high
           withTrueCriterial:(BOOL(^)(NSInteger index))crateria
{
    while(low < high) {
        NSInteger mid = (low + high) / 2;
        if (crateria(mid)) {
            high = mid;
        } else {
            low = mid + 1;
        }
    }
    if(!crateria(low)) {
        // Nothing works with this crateria.
        return -1;
    }
    return low;
}

- (NSInteger)greatestXFromIndex:(NSInteger)low
                        toIndex:(NSInteger)high
             withFalseCriterial:(BOOL(^)(NSInteger index))crateria
{
    while(low < high) {
        NSInteger mid = (low + high) / 2;
        if(crateria(mid)) {
            high = mid - 1;
        } else {
            low = mid;
        }
    }
    if(crateria(low)) {
        // Crateria is true for every element in the array.
        return -1;
    }
    return low;
}