CPMagical CP Library

Problem solution · Python

Count of Smaller Numbers After Self

Count of Smaller Numbers After Self: a Python solution using sorting and greedy selection. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Sorting and greedy selection
Source
walkccc LeetCode Solutions
Length
41 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

Sorting and greedy selection

For Count of Smaller Numbers After Self, the implementation first exposes a useful order, then scans that order while making locally justified choices.

  1. Choose the key that reveals the greedy or grouping structure.
  2. Sort the relevant records by that key.
  3. Scan in order, maintaining the invariant that makes each local choice safe.

Code notes

  • 41 lines of Python from the credited upstream file 315.py.
  • The implementation visibly relies on sequence storage, hash lookup, ordered lookup.
  • No explicit loop blocks detected.

Complexity

Sorting is typically the dominant term unless the subsequent scan uses a more expensive nested operation.

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

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeCount of Smaller Numbers After Self · PythonPython
Use this to learn the idea, then write your own version.
class FenwickTree:  def __init__(self, n: int):    self.sums = [0] * (n + 1)   def add(self, i: int, delta: int) -> None:    while i < len(self.sums):      self.sums[i] += delta      i += FenwickTree.lowbit(i)   def get(self, i: int) -> int:    summ = 0    while i > 0:      summ += self.sums[i]      i -= FenwickTree.lowbit(i)    return summ   @staticmethod  def lowbit(i: int) -> int:    return i & -i  class Solution:  def countSmaller(self, nums: list[int]) -> list[int]:    ans = []    ranks = self._getRanks(nums)    tree = FenwickTree(len(ranks))     for num in reversed(nums):      ans.append(tree.get(ranks[num] - 1))      tree.add(ranks[num], 1)     return ans[::-1]   def _getRanks(self, nums: list[int]) -> dict[int, int]:    ranks = collections.Counter()    rank = 0    for num in sorted(set(nums)):      rank += 1      ranks[num] = rank    return ranks

Keep practising

Did this explanation save you time? I'm a Grade 11 student building this free library to make difficult algorithms easier to understand.

Buy me a coffee ↗