The Most Efficient Algorithm to Find First Prefix-Match From a Sorted String Array?

Question

Input:

1) A huge sorted array of string SA;

2) A prefix string P;

Output:

The index of the first string matching the input prefix if any. If ther

Answer 1

Here is a possible solution (in Python), which has O(k.log(n)) time complexity and O(1) additional space complexity (considering n strings and k prefix length).

The rationale behind it to perform a binary search which only considers a given character index of the strings. If these are present, continue to the next character index. If any of the prefix characters cannot be found in any string, it returns immediately.

from typing import List

def first(items: List[str], prefix: str, i: int, c: str, left: int, right: int):
    result = -1

    while left <= right:
        mid = left + ((right - left) // 2)
        if ( i >= len(items[mid]) ):
            left = mid + 1
        elif (c < items[mid][i]):
            right = mid - 1
        elif (c > items[mid][i]):
            left = mid + 1
        else:
            result = mid
            right = mid - 1

    return result

def last(items: List[str], prefix: str, i: int, c: str, left: int, right: int):
    result = -1

    while left <= right:
        mid = left + ((right - left) // 2)
        if ( i >= len(items[mid]) ):
            left = mid + 1
        elif (c < items[mid][i]):
            right = mid - 1
        elif (c > items[mid][i]):
            left = mid + 1
        else:
            result = mid
            left = mid + 1

    return result

def is_prefix(items: List[str], prefix: str):
    left = 0
    right = len(items) - 1
    for i in range(len(prefix)):
        c = prefix[i]
        left = first(items, prefix, i, c, left, right)
        right = last(items, prefix, i, c, left, right)

        if (left == -1 or right == -1):
            return False

    return True

# Test cases
a = ['ab', 'abjsiohjd', 'abikshdiu', 'ashdi','abcde Aasioudhf', 'abcdefgOAJ', 'aa', 'aaap', 'aas', 'asd', 'bbbbb', 'bsadiojh', 'iod', '0asdn', 'asdjd', 'bqw', 'ba']
a.sort()
print(a)
print(is_prefix(a, 'abcdf'))
print(is_prefix(a, 'abcde'))
print(is_prefix(a, 'abcdef'))
print(is_prefix(a, 'abcdefg'))
print(is_prefix(a, 'abcdefgh'))
print(is_prefix(a, 'abcde Aa'))
print(is_prefix(a, 'iod'))
print(is_prefix(a, 'ZZZZZZiod'))

This gist is available at https://gist.github.com/lopespm/9790d60492aff25ea0960fe9ed389c0f