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Problem solution · Python

All Oone Data Structure

All Oone Data Structure: a Python solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Direct simulation
Source
Kamyu LeetCode Solutions
Length
112 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Direct simulation

For All Oone Data Structure, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 112 lines of Python from the credited upstream file all-oone-data-structure.py.
  • The implementation visibly relies on sequence storage, ordered lookup.
  • No explicit loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from Kamyu LeetCode Solutions by kamyu104 and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeAll Oone Data Structure · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(1), per operation# Space: O(k) class Node(object):    """    double linked list node    """    def __init__(self, value, keys):        self.value = value        self.keys = keys        self.prev = None        self.next = None  class LinkedList(object):    def __init__(self):        self.head, self.tail = Node(0, set()), Node(0, set())        self.head.next, self.tail.prev = self.tail, self.head     def insert(self, pos, node):        node.prev, node.next = pos.prev, pos        pos.prev.next, pos.prev = node, node        return node     def erase(self, node):        node.prev.next, node.next.prev = node.next, node.prev        del node     def empty(self):        return self.head.next is self.tail     def begin(self):        return self.head.next     def end(self):        return self.tail     def front(self):        return self.head.next     def back(self):        return self.tail.prev  class AllOne(object):     def __init__(self):        """        Initialize your data structure here.        """        self.bucket_of_key = {}        self.buckets = LinkedList()     def inc(self, key):        """        Inserts a new key <Key> with value 1. Or increments an existing key by 1.        :type key: str        :rtype: void        """        if key not in self.bucket_of_key:            self.bucket_of_key[key] = self.buckets.insert(self.buckets.begin(), Node(0, set([key])))         bucket, next_bucket = self.bucket_of_key[key], self.bucket_of_key[key].next        if next_bucket is self.buckets.end() or next_bucket.value > bucket.value+1:            next_bucket = self.buckets.insert(next_bucket, Node(bucket.value+1, set()))        next_bucket.keys.add(key)        self.bucket_of_key[key] = next_bucket         bucket.keys.remove(key)        if not bucket.keys:            self.buckets.erase(bucket)     def dec(self, key):        """        Decrements an existing key by 1. If Key's value is 1, remove it from the data structure.        :type key: str        :rtype: void        """        if key not in self.bucket_of_key:            return         bucket, prev_bucket = self.bucket_of_key[key], self.bucket_of_key[key].prev        self.bucket_of_key.pop(key, None)        if bucket.value > 1:            if bucket is self.buckets.begin() or prev_bucket.value < bucket.value-1:                prev_bucket = self.buckets.insert(bucket, Node(bucket.value-1, set()))            prev_bucket.keys.add(key)            self.bucket_of_key[key] = prev_bucket         bucket.keys.remove(key)        if not bucket.keys:            self.buckets.erase(bucket)     def getMaxKey(self):        """        Returns one of the keys with maximal value.        :rtype: str        """        if self.buckets.empty():            return ""        return iter(self.buckets.back().keys).next()     def getMinKey(self):        """        Returns one of the keys with Minimal value.        :rtype: str        """        if self.buckets.empty():            return ""        return iter(self.buckets.front().keys).next()

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