307. Range Sum Query - Mutable

Medium (Trung bình) Python 🔗 Xem trên LeetCode

📋 Đề Bài

Given an integer array nums, handle multiple queries of the following types:

  1. Update the value of an element in nums.
  2. Calculate the sum of the elements of nums between indices left and right inclusive where left <= right.

Implement the NumArray class:

  • NumArray(int[] nums) Initializes the object with the integer array nums.
  • void update(int index, int val) Updates the value of nums[index] to be val.
  • int sumRange(int left, int right) Returns the sum of the elements of nums between indices left and right inclusive (i.e. nums[left] + nums[left + 1] + ... + nums[right]).

 

Example 1:

Input
["NumArray", "sumRange", "update", "sumRange"]
[[[1, 3, 5]], [0, 2], [1, 2], [0, 2]]
Output
[null, 9, null, 8]

Explanation
NumArray numArray = new NumArray([1, 3, 5]);
numArray.sumRange(0, 2); // return 1 + 3 + 5 = 9
numArray.update(1, 2);   // nums = [1, 2, 5]
numArray.sumRange(0, 2); // return 1 + 2 + 5 = 8

 

Constraints:

  • 1 <= nums.length <= 3 * 104
  • -100 <= nums[i] <= 100
  • 0 <= index < nums.length
  • -100 <= val <= 100
  • 0 <= left <= right < nums.length
  • At most 3 * 104 calls will be made to update and sumRange.

🧠 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 0307-range-sum-query-mutable.py 
class SegmentTree:
    def __init__(self, nums):
        self.n = len(nums)
        self.tree = [0] * 4 * self.n
        for idx, val in enumerate(nums):
            self.update(1, 0, self.n - 1, idx, val)
        
    def update(self, node, left, right, index, val):
        if not left <= index <= right:
            return
        if left == right:
            self.tree[node] = val
            return
        mid = (left + right) >> 1
        self.update(node * 2, left, mid, index, val)
        self.update(node * 2 + 1, mid + 1, right, index, val)
        self.tree[node] = self.tree[node * 2] + self.tree[node * 2 + 1]
        
    def sumRange(self, node, left, right, qleft, qright):
        if qleft > right or left > qright:
            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 NumArray:

    def __init__(self, nums: List[int]):
        self.n = len(nums)
        self.it = SegmentTree(nums)

    def update(self, index: int, val: int) -> None:
        self.it.update(1, 0, self.n - 1, index, val)

    def sumRange(self, left: int, right: int) -> int:
        return self.it.sumRange(1, 0, self.n - 1, left, right)


# Your NumArray object will be instantiated and called as such:
# obj = NumArray(nums)
# obj.update(index,val)
# param_2 = obj.sumRange(left,right)