From aa680f79fcef30c4cf4fd71a318726f3f824daa0 Mon Sep 17 00:00:00 2001
From: Xu Shaohua <shaohua@biofan.org>
Date: Thu, 23 May 2024 10:36:59 +0800
Subject: [PATCH] sorts: Add binary heap

---
 sort/src/binary_heap.rs | 123 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 123 insertions(+)
 create mode 100644 sort/src/binary_heap.rs

diff --git a/sort/src/binary_heap.rs b/sort/src/binary_heap.rs
new file mode 100644
index 00000000..a23349ca
--- /dev/null
+++ b/sort/src/binary_heap.rs
@@ -0,0 +1,123 @@
+// Copyright (c) 2024 Xu Shaohua <shaohua@biofan.org>. All rights reserved.
+// Use of this source is governed by General Public License that can be found
+// in the LICENSE file.
+
+// Binary heap
+
+#[derive(Debug, Clone, Eq, PartialEq, Ord, PartialOrd)]
+pub struct BinaryHeap {
+    heap: Vec<i32>,
+}
+
+impl Default for BinaryHeap {
+    fn default() -> Self {
+        Self::new()
+    }
+}
+
+impl BinaryHeap {
+    #[must_use]
+    #[inline]
+    pub const fn new() -> Self {
+        Self { heap: Vec::new() }
+    }
+
+    pub fn from_slice(slice: &[i32]) -> Self {
+        Self {
+            heap: slice.to_vec(),
+        }
+    }
+
+    #[must_use]
+    #[inline]
+    pub fn len(&self) -> usize {
+        self.heap.len()
+    }
+
+    #[must_use]
+    #[inline]
+    pub fn is_empty(&self) -> bool {
+        self.heap.is_empty()
+    }
+
+    #[must_use]
+    #[inline]
+    pub fn peak(&self) -> Option<i32> {
+        self.heap.first().copied()
+    }
+
+    pub fn push(&mut self, val: i32) {
+        // 先将新的元素插入到数组尾部.
+        self.heap.push(val);
+
+        // 然后将该元素进行上移 (shift up).
+        self.shift_up(self.heap.len() - 1);
+    }
+
+    #[must_use]
+    pub fn pop(&mut self) -> Option<i32> {
+        if self.is_empty() {
+            return None;
+        }
+
+        // 将堆顶的元素交换到数组的尾部, 并弹出它.
+        let len = self.len();
+        self.heap.swap(0, len - 1);
+        let last = self.heap.pop();
+
+        // 然后调整堆顶的位置, 让它保持大顶堆的特性.
+        self.shift_down(0, len);
+
+        last
+    }
+
+    // 将该节点与父节点进行比较, 如果比父节点大, 就让它跟父节点交换,
+    // 一直重复这个过程, 直到找到合适的位置.
+    //
+    // 时间复杂度是 O(log(n)), 是树的高度.
+    fn shift_up(&mut self, mut pos: usize) {
+        if pos == 0 {
+            return;
+        }
+
+        let mut parent_pos = (pos - 1) / 2;
+        while self.heap[parent_pos] < self.heap[pos] {
+            if parent_pos == 0 {
+                break;
+            }
+            pos = parent_pos;
+            parent_pos = (pos - 1) / 2;
+        }
+    }
+
+    // 将该节点与子节点进行比较, 如果比子节点大, 就让它跟较大的那个子节点交换,
+    // 一直重复这个过 程, 直到找到合适的位置.
+    //
+    // 时间复杂度是 O(log(n)), 是树的高度.
+    fn shift_down(&mut self, mut pos: usize, len: usize) {
+        while pos * 2 + 1 < len {
+            let left = pos * 2 + 1;
+            let right = pos * 2 + 2;
+
+            let larger = if right >= len {
+                // 右子树不存在, 它超出了数组的范围.
+                left
+            } else if self.heap[left] >= self.heap[right] {
+                // 左侧子树较大
+                left
+            } else {
+                // 右侧子树较大
+                right
+            };
+
+            // 当前节点与较大的子节点进行比较, 如果比它小就进行交换.
+            if self.heap[pos] < self.heap[larger] {
+                self.heap.swap(pos, larger);
+                pos = larger;
+            } else {
+                // 当前节点比最大的子节点还大
+                break;
+            }
+        }
+    }
+}