315. Count of Smaller Numbers After Self

Hard (Khó) Python 🔗 Xem trên LeetCode

📋 Đề Bài

Given an integer array nums, return an integer array counts where counts[i] is the number of smaller elements to the right of nums[i].

 

Example 1:

Input: nums = [5,2,6,1]
Output: [2,1,1,0]
Explanation:
To the right of 5 there are 2 smaller elements (2 and 1).
To the right of 2 there is only 1 smaller element (1).
To the right of 6 there is 1 smaller element (1).
To the right of 1 there is 0 smaller element.

Example 2:

Input: nums = [-1]
Output: [0]

Example 3:

Input: nums = [-1,-1]
Output: [0,0]

 

Constraints:

  • 1 <= nums.length <= 105
  • -104 <= nums[i] <= 104

🧠 Thuật Toán & Kỹ Thuật

Binary Search (Tìm kiếm nhị phân)Bit Manipulation (Thao tác bit)
⏱️ Thời gian O(log n)
💾 Không gian O(n)

💻 Lời Giải

Python 0315-count-of-smaller-numbers-after-self.py
class SegmentTree:
    def __init__(self, maxVal):
        self.tree = [0] * 4 * maxVal
        
    def update(self, node, left, right, index):
        if not left <= index <= right:
            return
        if left == right:
            self.tree[node] += 1
            return
        mid = (left + right) >> 1
        self.update(node * 2, left, mid, index)
        self.update(node * 2 + 1, mid + 1, right, index)
        self.tree[node] = self.tree[node * 2] + self.tree[node * 2 + 1]
        
    def sumRange(self, node, left, right, qleft, qright):
        if right < qleft or qright < left:
            return 0
        if qleft <= left and right <= qright:
            return self.tree[node]
        mid = (left + right) >> 1
        sumLeft = self.sumRange(node * 2, left, mid, qleft, qright)
        sumRight = self.sumRange(node * 2 + 1, mid + 1, right, qleft, qright)
        return sumLeft + sumRight
    
class Solution:
    def countSmaller(self, nums: List[int]) -> List[int]:
        n = len(nums)
        
        for i in range(n):
            nums[i] += 10**4 + 1
            
        maxVal = max(nums)
        res = [0 for _ in range(n)]
        it = SegmentTree(maxVal)
        
        for i in range(n - 1, -1, -1):
            res[i] = it.sumRange(1, 1, maxVal, 1, nums[i] - 1)
            it.update(1, 1, maxVal, nums[i])
        
        return res