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---
id: 587d8258367417b2b2512c82
challengeType: 1
videoUrl: ''
2020-10-01 15:54:21 +00:00
title: 在二叉搜索树中删除具有两个子节点的节点
2018-10-10 22:03:03 +00:00
---
## Description
< section id = "description" > 删除具有两个子节点的节点是最难实现的。删除这样的节点会生成两个不再连接到原始树结构的子树。我们如何重新连接它们?一种方法是在目标节点的右子树中找到最小值,并用该值替换目标节点。以这种方式选择替换确保它大于左子树中的每个节点,它成为新的父节点,但也小于右子树中的每个节点,它成为新的父节点。完成此替换后,必须从右子树中删除替换节点。即使这个操作也很棘手,因为替换可能是一个叶子,或者它本身可能是一个右子树的父亲。如果是叶子,我们必须删除其父对它的引用。否则,它必须是目标的正确子项。在这种情况下,我们必须用替换值替换目标值,并使目标引用替换的右子。说明:让我们通过处理第三种情况来完成我们的< code > remove< / code > 方法。我们为前两种情况再次提供了一些代码。现在添加一些代码来处理具有两个子节点的目标节点。任何边缘情况要注意?如果树只有三个节点怎么办?完成后,这将完成二进制搜索树的删除操作。干得好,这是一个非常难的问题! < / section >
## Instructions
< section id = "instructions" >
< / section >
## Tests
< section id = 'tests' >
```yml
tests:
- text: 存在< code > BinarySearchTree</ code > 数据结构。
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() }; return (typeof test == 'object')})());
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- text: 二叉搜索树有一个名为< code > remove</ code > 的方法。
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; return (typeof test.remove == 'function')})());
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- text: 尝试删除不存在的元素将返回< code > null</ code > 。
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testString: "assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; return (typeof test.remove == 'function') ? (test.remove(100) == null) : false})());"
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- text: 如果根节点没有子节点,则删除它会将根节点设置为< code > null</ code > 。
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testString: "assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; test.add(500); test.remove(500); return (typeof test.remove == 'function') ? (test.inorder() == null) : false})());"
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- text: < code > remove</ code > 方法从树中删除叶节点
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testString: "assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; test.add(5); test.add(3); test.add(7); test.add(6); test.add(10); test.add(12); test.remove(3); test.remove(12); test.remove(10); return (typeof test.remove == 'function') ? (test.inorder().join('') == '567') : false})());"
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- text: < code > remove</ code > 方法删除具有一个子节点的节点。
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.remove !== 'function') { return false; }; test.add(-1); test.add(3); test.add(7); test.add(16); test.remove(16); test.remove(7); test.remove(3); return (test.inorder().join('') == '-1'); })());
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- text: 删除具有两个节点的树中的根将第二个节点设置为根。
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.remove !== 'function') { return false; }; test.add(15); test.add(27); test.remove(15); return (test.inorder().join('') == '27'); })());
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- text: < code > remove</ code > 方法在保留二叉搜索树结构的同时删除具有两个子节点的节点。
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.remove !== 'function') { return false; }; test.add(1); test.add(4); test.add(3); test.add(7); test.add(9); test.add(11); test.add(14); test.add(15); test.add(19); test.add(50); test.remove(9); if (!test.isBinarySearchTree()) { return false; }; test.remove(11); if (!test.isBinarySearchTree()) { return false; }; test.remove(14); if (!test.isBinarySearchTree()) { return false; }; test.remove(19); if (!test.isBinarySearchTree()) { return false; }; test.remove(3); if (!test.isBinarySearchTree()) { return false; }; test.remove(50); if (!test.isBinarySearchTree()) { return false; }; test.remove(15); if (!test.isBinarySearchTree()) { return false; }; return (test.inorder().join('') == '147'); })());
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- text: 可以在三个节点的树上删除根。
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.remove !== 'function') { return false; }; test.add(100); test.add(50); test.add(300); test.remove(100); return (test.inorder().join('') == 50300); })());
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```
< / section >
## Challenge Seed
< section id = 'challengeSeed' >
< div id = 'js-seed' >
```js
var displayTree = (tree) => console.log(JSON.stringify(tree, null, 2));
function Node(value) {
this.value = value;
this.left = null;
this.right = null;
}
function BinarySearchTree() {
this.root = null;
this.remove = function(value) {
if (this.root === null) {
return null;
}
var target;
var parent = null;
// find the target value and its parent
(function findValue(node = this.root) {
if (value == node.value) {
target = node;
} else if (value < node.value & & node . left ! = = null ) {
parent = node;
return findValue(node.left);
} else if (value < node.value & & node . left = == null ) {
return null;
} else if (value > node.value & & node.right !== null) {
parent = node;
return findValue(node.right);
} else {
return null;
}
}).bind(this)();
if (target === null) {
return null;
}
// count the children of the target to delete
var children = (target.left !== null ? 1 : 0) + (target.right !== null ? 1 : 0);
// case 1: target has no children
if (children === 0) {
if (target == this.root) {
this.root = null;
}
else {
if (parent.left == target) {
parent.left = null;
} else {
parent.right = null;
}
}
}
// case 2: target has one child
else if (children == 1) {
var newChild = (target.left !== null) ? target.left : target.right;
if (parent === null) {
target.value = newChild.value;
target.left = null;
target.right = null;
} else if (newChild.value < parent.value ) {
parent.left = newChild;
} else {
parent.right = newChild;
}
target = null;
}
// case 3: target has two children, change code below this line
};
}
```
< / div >
### After Test
< div id = 'js-teardown' >
```js
console.info('after the test');
```
< / div >
< / section >
## Solution
< section id = 'solution' >
```js
// solution required
```
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/section>