Given an empty set of intervals, implement a data structure that can:
- Add an interval to the set of intervals.
- Count the number of integers that are present in at least one interval.
Implement the CountIntervals class:
CountIntervals()Initializes the object with an empty set of intervals.void add(int left, int right)Adds the interval[left, right]to the set of intervals.int count()Returns the number of integers that are present in at least one interval.
Note that an interval [left, right] denotes all the integers x where left <= x <= right.
Example 1:
Input
["CountIntervals", "add", "add", "count", "add", "count"]
[[], [2, 3], [7, 10], [], [5, 8], []]
Output
[null, null, null, 6, null, 8]
Explanation
CountIntervals countIntervals = new CountIntervals(); // initialize the object with an empty set of intervals.
countIntervals.add(2, 3); // add [2, 3] to the set of intervals.
countIntervals.add(7, 10); // add [7, 10] to the set of intervals.
countIntervals.count(); // return 6
// the integers 2 and 3 are present in the interval [2, 3].
// the integers 7, 8, 9, and 10 are present in the interval [7, 10].
countIntervals.add(5, 8); // add [5, 8] to the set of intervals.
countIntervals.count(); // return 8
// the integers 2 and 3 are present in the interval [2, 3].
// the integers 5 and 6 are present in the interval [5, 8].
// the integers 7 and 8 are present in the intervals [5, 8] and [7, 10].
// the integers 9 and 10 are present in the interval [7, 10].
Constraints:
1 <= left <= right <= 109- At most
105calls in total will be made toaddandcount. - At least one call will be made to
count.
class Node:
def __init__(self):
self.tag = 0
self.tot = 0
self.left = None
self.right = None
def update(self, l, r, a, b):
if self.tag == 1:
return
mid = (a + b) >> 1
if l == a and r == b:
self.tag = 1
self.tot = b - a + 1
return
if not self.left:
self.left = Node()
if not self.right:
self.right = Node()
if mid >= l:
self.left.update(l, min(mid, r), a, mid)
if mid + 1 <= r:
self.right.update(max(mid + 1, l), r, mid + 1, b)
self.tag = 0
self.tot = self.left.tot + self.right.tot
class CountIntervals:
def __init__(self):
self.tree = Node()
def add(self, left: int, right: int) -> None:
self.tree.update(left, right, 0, 1000000010)
def count(self) -> int:
return self.tree.tot
# Your CountIntervals object will be instantiated and called as such:
# obj = CountIntervals()
# obj.add(left,right)
# param_2 = obj.count()class Node {
Node left;
Node right;
int l;
int r;
int mid;
int v;
int add;
public Node(int l, int r) {
this.l = l;
this.r = r;
this.mid = (l + r) >> 1;
}
}
class SegmentTree {
private Node root = new Node(1, (int) 1e9 + 1);
public SegmentTree() {
}
public void modify(int l, int r, int v) {
modify(l, r, v, root);
}
public void modify(int l, int r, int v, Node node) {
if (l > r) {
return;
}
if (node.l >= l && node.r <= r) {
node.v = node.r - node.l + 1;
node.add = v;
return;
}
pushdown(node);
if (l <= node.mid) {
modify(l, r, v, node.left);
}
if (r > node.mid) {
modify(l, r, v, node.right);
}
pushup(node);
}
public int query(int l, int r) {
return query(l, r, root);
}
public int query(int l, int r, Node node) {
if (l > r) {
return 0;
}
if (node.l >= l && node.r <= r) {
return node.v;
}
pushdown(node);
int v = 0;
if (l <= node.mid) {
v += query(l, r, node.left);
}
if (r > node.mid) {
v += query(l, r, node.right);
}
return v;
}
public void pushup(Node node) {
node.v = node.left.v + node.right.v;
}
public void pushdown(Node node) {
if (node.left == null) {
node.left = new Node(node.l, node.mid);
}
if (node.right == null) {
node.right = new Node(node.mid + 1, node.r);
}
if (node.add != 0) {
Node left = node.left, right = node.right;
left.add = node.add;
right.add = node.add;
left.v = left.r - left.l + 1;
right.v = right.r - right.l + 1;
node.add = 0;
}
}
}
class CountIntervals {
private SegmentTree tree = new SegmentTree();
public CountIntervals() {
}
public void add(int left, int right) {
tree.modify(left, right, 1);
}
public int count() {
return tree.query(1, (int) 1e9);
}
}
/**
* Your CountIntervals object will be instantiated and called as such:
* CountIntervals obj = new CountIntervals();
* obj.add(left,right);
* int param_2 = obj.count();
*/class CountIntervals {
left: null | CountIntervals;
right: null | CountIntervals;
start: number;
end: number;
sum: number;
constructor(start: number = 0, end: number = 10 ** 9) {
this.left = null;
this.right = null;
this.start = start;
this.end = end;
this.sum = 0;
}
add(left: number, right: number): void {
if (this.sum == this.end - this.start + 1) return;
if (left <= this.start && right >= this.end) {
this.sum = this.end - this.start + 1;
return;
}
let mid = (this.start + this.end) >> 1;
if (!this.left) this.left = new CountIntervals(this.start, mid);
if (!this.right) this.right = new CountIntervals(mid + 1, this.end);
if (left <= mid) this.left.add(left, right);
if (right > mid) this.right.add(left, right);
this.sum = this.left.sum + this.right.sum;
}
count(): number {
return this.sum;
}
}
/**
* Your CountIntervals object will be instantiated and called as such:
* var obj = new CountIntervals()
* obj.add(left,right)
* var param_2 = obj.count()
*/