Here are the heap, deque, tree, and graph operations you'll actually write in an interview, and how fast each one runs.

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What's on the sheet

• Heap. You want the smallest (or largest) item ready in O(1), and you don't need the rest sorted.
• Deque. You need a queue or a stack, and a deque gives you O(1) at both ends with one class to remember.
• Tree. You're walking parent and child links top-down, one level or one branch at a time.
• Graph. You've got nodes and edges you look up by key, so build an adjacency list first.

Watch out

• Heap: Tuples compare left to right, so two equal priorities fall through to the second value. If that value can't be compared (like a dict), Python throws a TypeError. Push a counter in the middle, (priority, count, item), so the tie never reaches it.
• Deque: A list only tracks one end efficiently. Popping from the front slides every remaining item over, which costs O(n). A deque tracks both ends directly, so popleft() finishes in O(1) no matter how long the queue is.
• Tree: BFS holds a whole level in its queue at once, which is O(w) space for the widest level. DFS only holds the current branch, which is O(h) for the height. A wide, shallow tree favors DFS, and a deep, narrow one favors BFS.
• Graph: A tree only has one path in, but a graph can loop back on itself. Skip the visited set and a cycle spins the traversal forever. Mark a node visited the moment you enqueue or recurse into it, not when you finally process it.

How to get it

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The ten pattern sheets work differently. You earn each one by solving half of that pattern's problems. See the pattern sheets.

Every pattern has a sheet too. See the full set.