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307.range-sum-query-mutable.py
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162 lines (135 loc) · 4.83 KB
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# Tag: Array, Design, Binary Indexed Tree, Segment Tree
# Time: O(logN)
# Space: O(N)
# Ref: -
# Note: -
# Given an integer array nums, handle multiple queries of the following types:
#
# Update the value of an element in nums.
# 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.
#
#
class segmentTree:
def __init__(self, a: list):
n = len(a)
self.seg = [0 for i in range(4 * n)]
self.build(a, 1, 0, n - 1)
print(self.seg)
def build(self, a: list, v: int, i: int, j: int):
if i == j:
self.seg[v] = a[i]
return
m = (i + j) // 2
self.build(a, 2 * v, i, m)
self.build(a, 2 * v + 1, m + 1, j)
self.seg[v] = self.seg[2 * v] + self.seg[2 * v + 1]
def query(self, v: int, i: int, j: int, l: int, r: int) -> int:
if l > r:
return 0
if l == i and r == j:
return self.seg[v]
m = (i + j) // 2
left = self.query(2 * v, i, m, l, min(m, r))
right = self.query(2 * v + 1, m + 1, j, max(m + 1, l), r)
return left + right
def update(self, v: int, i: int, j: int, pos: int, val: int):
if i == j:
self.seg[v] = val
return
m = (i + j) // 2
if pos <= m:
self.update(2 * v, i, m, pos, val)
else:
self.update(2 * v + 1, m + 1, j, pos, val)
self.seg[v] = self.seg[2 * v] + self.seg[2 * v + 1]
class NumArray:
def __init__(self, nums: List[int]):
self.n = len(nums)
self.seg = segmentTree(nums)
def update(self, index: int, val: int) -> None:
self.seg.update(1, 0, self.n - 1, index, val)
def sumRange(self, left: int, right: int) -> int:
return self.seg.query(1, 0, self.n - 1, left, right)
class SegmentTreeNode:
def __init__(self, start: int, end: int, val: int):
self.start = start
self.end = end
self.val = val
self.left = None
self.right = None
class SegmentTree:
def __init__(self, nums: list):
self.root = self.build(nums, 0, len(nums) - 1)
def build(self, nums: list, start: int, end: int):
node = SegmentTreeNode(start, end, nums[start])
if start == end:
return node
mid = (start + end) // 2
node.left = self.build(nums, start, mid)
node.right = self.build(nums, mid + 1, end)
node.val = node.left.val + node.right.val
return node
def update(self, node: SegmentTreeNode, index: int, val: int):
if index == node.start and index == node.end:
node.val = val
return
mid = (node.start + node.end) // 2
if index <= mid:
self.update(node.left, index, val)
else:
self.update(node.right, index, val)
node.val = node.left.val + node.right.val
def query(self, node: SegmentTreeNode, start: int, end: int) -> int:
if start == node.start and end == node.end:
return node.val
mid = (node.start + node.end) // 2
if end <= mid:
return self.query(node.left, start, end)
elif start > mid:
return self.query(node.right, start, end)
else:
left_val = self.query(node.left, start, mid)
right_val = self.query(node.right, mid + 1, end)
return left_val + right_val
class NumArray:
def __init__(self, nums: List[int]):
self.tree = SegmentTree(nums)
def update(self, index: int, val: int) -> None:
self.tree.update(self.tree.root, index, val)
def sumRange(self, left: int, right: int) -> int:
return self.tree.query(self.tree.root, 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)