Data Structures & Algorithms

def binary_search(items, target):
    lo, hi = 0, len(items) - 1
    while lo <= hi:
        mid = (lo + hi) // 2
        if items[mid] == target:
            return mid
        if items[mid] < target:
            lo = mid + 1
        else:
            hi = mid - 1
    return -1

from collections import deque

def shortest_path(graph, start, goal):
    queue = deque([[start]])
    seen = {start}
    while queue:
        path = queue.popleft()
        if path[-1] == goal:
            return path
        for nxt in graph[path[-1]]:
            if nxt not in seen:
                seen.add(nxt)
                queue.append(path + [nxt])
    return None