I'm working on a problem in which I have an input array, sorted positive unique integers, and have to try to find all possible triples \$(x,y,z)\$ which satisfy \$x+y>z\$ and \$x<y<z\$. For example, \$(1,2,3)\$ is not a valid triple since \$1+2\$ is not \$> 3\$, and \$(3,4,5)\$ is a valid triple since \$3<4<5\$ and \$3+4>5\$.

This code leverages binary search, and I'm wondering if this can be improved in terms of time complexity. Please also help to point out any code issues/bugs or improvement areas.

Implementation

# find upper bound of value, including value itself
def findUpperBound(numbers, value, start):
    if not numbers:
        raise 'value eror'
    low = start
    high = len(numbers) - 1
    while low <= high:
        mid = (low + high) // 2
        if numbers[mid] == value:
            return mid
        elif numbers[mid] > value:
            high = mid - 1
        else:
            low = mid + 1
    # if reach here, means find an upper bound
    return low

if __name__ == "__main__":

    result = set()
    numbers=[1,2,4,5,6,7,8,10]
    for i in range(0, len(numbers)-2):
        for j in range(i+1, len(numbers)-1):
            k = findUpperBound(numbers, numbers[i] + numbers[j], j+1)
            for p in range(j+1, k):
                result.add((numbers[i], numbers[j], numbers[p]))

    print result

Output

set([(5, 7, 10), (4, 6, 8), (5, 7, 8), (4, 8, 10), (6, 8, 10), (2, 6, 7), (5, 6, 7), (4, 5, 6), (5, 6, 8), (2, 4, 5), (5, 6, 10), (2, 7, 8), (5, 8, 10), (4, 7, 8), (7, 8, 10), (6, 7, 8), (2, 5, 6), (6, 7, 10), (4, 5, 7), (4, 5, 8), (4, 6, 7), (4, 7, 10)])