LeetCode 28: Find the Index of the First Occurrence in a String — Python Solution

Solve LeetCode 28: Find the Index of the First Occurrence in a String in Python with a substring scan approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Check every feasible starting position and return the first slice equal to the needle.

Algorithm

1. Check every feasible starting position and return the first slice equal to the needle.
2. Maintain this invariant: All starts before the current position have already been proven not to match.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def strStr(self, haystack, needle):
        if needle == "":
            return 0
        for start in range(len(haystack) - len(needle) + 1):
            if haystack[start:start + len(needle)] == needle:
                return start
        return -1

Why this is correct

The proof follows the maintained state: All starts before the current position have already been proven not to match. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O((n-m+1)m) worst-case time and O(1) extra space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

An empty needle matches at zero; a longer needle cannot match.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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