chore: add example and correct README

README.md

@@ -7,7 +7,7 @@ The implementation of the interval tree in interval_map references "Introduction
 To safely and efficiently handle insertion and deletion operations in Rust, `interval_map` innovatively **uses arrays to simulate pointers** for managing the parent-child references in the red-black tree. This approach also ensures that interval_map has the `Send` and `Unpin` traits, allowing it to be safely transferred between threads and to maintain a fixed memory location during asynchronous operations.
 
 `interval_map` implements an `IntervalMap` struct:
-- It accepts `Interval<T>` as the key, where `T` can be any type that implements `Ord+Clone` trait. Therefore, intervals such as $[1, 2)$ and $["aaa", "bbb")$ are allowed
+- It accepts `Interval<T>` as the key, where `T` can be any type that implements `Ord` trait. Therefore, intervals such as $[1, 2)$ and $["aaa", "bbb")$ are allowed
 - The value can be of any type
 
 `interval_map` supports `insert`, `delete`, and `iter` fns. Traversal is performed in the order of `Interval<T>` . For instance, with intervals of type `Interval<u32>`:
@@ -22,15 +22,16 @@ Currently, `interval_map` only supports half-open intervals, i.e., $[...,...)$.
 
 The benchmark was conducted on a platform with `AMD R7 7840H + DDR5 5600MHz`. The result are as follows:
 1. Only insert
-    | insert          | 100       | 1000      | 10, 000   | 100, 000  |
-    | --------------- | --------- | --------- | --------- | --------- |
-    | Time per insert | 5.4168 µs | 80.518 µs | 2.2823 ms | 36.528 ms |
+    | insert     | 100       | 1000      | 10, 000   | 100, 000  |
+    | ---------- | --------- | --------- | --------- | --------- |
+    | Total time | 5.4168 µs | 80.518 µs | 2.2823 ms | 36.528 ms |
 2. Insert N and remove N
-    | insert_and_remove  | 100       | 1000      | 10, 000   | 100, 000  |
-    | ------------------ | --------- | --------- | --------- | --------- |
-    | Time per operation | 10.333 µs | 223.43 µs | 4.9358 ms | 81.634 ms |
+    | insert_and_remove | 100       | 1000      | 10, 000   | 100, 000  |
+    | ----------------- | --------- | --------- | --------- | --------- |
+    | Total time        | 10.333 µs | 223.43 µs | 4.9358 ms | 81.634 ms |
 
 ## TODO
-- [] Support for $(...,...)$, $[...,...]$ and $(...,...]$ interval types.
-- [] Add more tests like [etcd](https://github.com/etcd-io/etcd/blob/main/pkg/adt/interval_tree_test.go)
-- [] Add Point type for Interval
+- [ ] ~~Support for $(...,...)$, $[...,...]$ and $(...,...]$ interval types.~~ There's no way to support these interval type without performance loss now.
+- [ ] ~~Add Point type for Interval~~ To support Point type, it should also support $[...,...]$, so it couldn't be supported now, either. But you could write code like [examples/new_point](examples/new_point.rs).
+- [x] Add more tests like [etcd](https://github.com/etcd-io/etcd/blob/main/pkg/adt/interval_tree_test.go).
+- [x] Refine iter mod.

examples/new_point.rs

@@ -0,0 +1,27 @@
+use interval_map::{Interval, IntervalMap};
+
+trait Point<T> {
+    fn new_point(x: T) -> Interval<T>;
+}
+
+impl Point<u32> for Interval<u32> {
+    fn new_point(x: u32) -> Self {
+        Interval::new(x, x + 1)
+    }
+}
+
+fn main() {
+    let mut interval_map = IntervalMap::<u32, i32>::new();
+    interval_map.insert(Interval::new(3, 7), 20);
+    interval_map.insert(Interval::new(2, 6), 15);
+
+    let tmp_point = Interval::new_point(5);
+    assert_eq!(tmp_point, Interval::new(5, 6));
+
+    interval_map.insert(tmp_point.clone(), 10);
+    assert_eq!(interval_map.get(&tmp_point).unwrap(), &10);
+    assert_eq!(
+        interval_map.find_all_overlap(&Interval::new_point(5)).len(),
+        3
+    );
+}

examples/string_affine.rs

@@ -0,0 +1,68 @@
+use std::cmp;
+
+use interval_map::{Interval, IntervalMap};
+
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub enum StringAffine {
+    /// String
+    String(String),
+    /// Unbounded
+    Unbounded,
+}
+
+impl StringAffine {
+    pub fn new_key(s: &str) -> Self {
+        Self::String(s.to_string())
+    }
+
+    pub fn new_unbounded() -> Self {
+        Self::Unbounded
+    }
+}
+
+impl PartialOrd for StringAffine {
+    fn partial_cmp(&self, other: &Self) -> Option<cmp::Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+impl Ord for StringAffine {
+    fn cmp(&self, other: &Self) -> cmp::Ordering {
+        match (self, other) {
+            (StringAffine::String(x), StringAffine::String(y)) => x.cmp(y),
+            (StringAffine::String(_), StringAffine::Unbounded) => cmp::Ordering::Less,
+            (StringAffine::Unbounded, StringAffine::String(_)) => cmp::Ordering::Greater,
+            (StringAffine::Unbounded, StringAffine::Unbounded) => cmp::Ordering::Equal,
+        }
+    }
+}
+
+trait Point<T> {
+    fn new_point(x: T) -> Interval<T>;
+}
+
+impl Point<StringAffine> for Interval<StringAffine> {
+    fn new_point(x: StringAffine) -> Interval<StringAffine> {
+        match x {
+            StringAffine::String(mut x_string) => {
+                let low = x_string.clone();
+                x_string.push('\0');
+                Interval::new(
+                    StringAffine::new_key(&low),
+                    StringAffine::new_key(&x_string),
+                )
+            }
+            _ => panic!("new_point only receive StringAffine::String!"),
+        }
+    }
+}
+
+fn main() {
+    let mut interval_map = IntervalMap::<StringAffine, u32>::new();
+    interval_map.insert(
+        Interval::new(StringAffine::new_key("8"), StringAffine::Unbounded),
+        123,
+    );
+    assert!(interval_map.overlaps(&Interval::new_point(StringAffine::new_key("9"))));
+    assert!(!interval_map.overlaps(&Interval::new_point(StringAffine::new_key("7"))));
+}