diff --git a/DataStructureAndAlgorithm/07 Leetcode同步练习（二）.md b/DataStructureAndAlgorithm/07 Leetcode同步练习（二）.md
index 7c887f8..91b09a6 100644
--- a/DataStructureAndAlgorithm/07 Leetcode同步练习（二）.md
+++ b/DataStructureAndAlgorithm/07 Leetcode同步练习（二）.md
@@ -30,6 +30,18 @@
: , Ϊ 01 һ
```
+**д**
+
+```c
+public class Solution
+{
+ public bool IsPalindrome(int x)
+ {
+
+ }
+}
+```
+
:
ܲתΪַ
diff --git a/DataStructureAndAlgorithm/09 栈与递归.md b/DataStructureAndAlgorithm/09 栈与递归.md
index 12df63c..d4f21d5 100644
--- a/DataStructureAndAlgorithm/09 栈与递归.md
+++ b/DataStructureAndAlgorithm/09 栈与递归.md
@@ -1,44 +1,38 @@
+# 09 ջݹ
-# Task03ջݹ飨2죩
+**֪ʶṹ**
-ջǾʹõһݽṹͼʾǹӵ˳ӵѹ뵯е˳෴ѹ뵯еӵȷ
-
-
-
-ʹõWordExcelPhotoshopϵͳеijҲջľӦãIJһȳġǾϸܡջݽṹ
+
+ջǾʹõһݽṹ磬ǹӵ˳ӵѹ뵯е˳෴ѹ뵯еӵȷֱ磬ʹõWordExcelPhotoshopϵͳеijҲջľӦãIJһȳġ
+
+Ǿϸܡջݽṹ
+
+---
## 1. ջĶ
-
-**1.1 ջĶ**
+### 1.1 ջĶ
루ջɾջֻһˣջеԱȽFirst In Last OutԱ
-1 Ա`(a0,a1,...,an)` ջջʾ
+1 Ա`$(a_0,a_1,?,a_{n-1)}$`ջջʾ
-
+
-
+
-ʾջʵһ˳ջһջʵַʽʲôأʵ˳һģ
-- ˳ջǾ̬ĵջǶ̬ģԱȽջڿռʸߡΪ˳ջ˽ϴĿռ䵫Dzûȫ洢Ԫء
-- ˳ջȻô洢ָȽջ˵Ϊʡڴռ䣬ջȴԽڴռ
-- Ҷڴ洢δ֪£ջʺϣΪջͨջ
-- ˳˵ڲɾЧʸߣ˳ڲЧʸߡǶջ˵ֻջвЧʸߡ
-**1.2 ջIJ**
+### 1.2 ջIJ
-- ջԪֵջ
+- ջԪزջ
- ջƳջԪء
- ǷΪգжջǷԪء
- õջȡջʵʰԪصĸ
- ղƳջеԪء
- ȡջԪء
-
-
-´Ϊ`C#`汾
+
```c
using System;
@@ -86,22 +80,15 @@ namespace LinearStruct
}
```
-
-
-
-
-
-## 2. ջĴ洢ʵ
-
-**2.1 ˳洢˳ջ**
+---
+## 2. ջ˳洢˳ջ
˳ջ˳ʵֵջ
ʵ֣
-
+
-´Ϊ`C#`汾
```c
using System;
@@ -196,16 +183,185 @@ namespace LinearStruct
}
```
+Ӧã
-**2.2 ʽ洢ջ**
+```c
+using System;
+using LinearStruct;
+
+namespace ExampleStack
+{
+ class Program
+ {
+ static void Main(string[] args)
+ {
+ StackTest(new SeqStack(20));
+ }
+
+ private static void StackTest(IStack stack)
+ {
+ stack.Push("a1");
+ stack.Push("a2");
+ stack.Push("a3");
+ while (stack.IsEmpty() == false)
+ {
+ Console.WriteLine(stack.StackTop);
+ stack.Pop();
+ }
+ // a3
+ // a2
+ // a1
+ }
+ }
+}
+```
+
+`SeqStack`Ȼʵ`IStack`ӿڣջͳջʱƶԪأЧʱȽϵ͡ʰջͳջŵ˳βУЧʡ
+
+
+
+- ջ`Insert(Length, data)`
+- ջ`Remove(Length - 1)`
+- ջԪأ`SeqList[Length - 1]`
+
+
+
+```c
+using System;
+
+namespace LinearStruct
+{
+ ///
+ /// ˳洢ṹʵֵջ
+ ///
+ /// ˳ջԪص
+ public class SeqStack_1 : IStack where T : IComparable
+ {
+ private readonly SeqList _lst;
+
+ ///
+ /// ʼSeqStackʵ
+ ///
+ /// SeqStackԪصĸ
+ public SeqStack_1(int max)
+ {
+ if (max <= 0)
+ throw new ArgumentOutOfRangeException();
+ _lst = new SeqList(max);
+ }
+
+ ///
+ /// ȡSeqStackʵʰԪصĸ
+ ///
+ public int Length
+ {
+ get { return _lst.Length; }
+ }
+
+ ///
+ /// ȡSeqStackԪصĸ
+ ///
+ public int MaxSize
+ {
+ get { return _lst.MaxSize; }
+ }
+
+ ///
+ /// ȡSeqStackеջԪ
+ ///
+ public T StackTop
+ {
+ get
+ {
+ if (_lst.IsEmpty())
+ throw new Exception("ջΪ.");
+ return _lst[Length - 1];
+ }
+ }
+
+ ///
+ /// Ԫջ
+ ///
+ /// ҪջԪ
+ public void Push(T data)
+ {
+ if (_lst.Length == _lst.MaxSize)
+ throw new Exception("ջѴﵽ.");
+ _lst.Insert(Length, data);
+ }
+
+ ///
+ /// Ԫسջ
+ ///
+ public void Pop()
+ {
+ if (_lst.IsEmpty())
+ throw new Exception("ջΪ.");
+ _lst.Remove(Length - 1);
+ }
+
+ ///
+ /// жSeqStackǷԪ
+ ///
+ /// Ԫطfalse,true.
+ public bool IsEmpty()
+ {
+ return _lst.IsEmpty();
+ }
+
+ ///
+ /// SeqStackƳԪ
+ ///
+ public void Clear()
+ {
+ _lst.Clear();
+ }
+ }
+}
+```
+
+Ӧã
+
+```c
+using System;
+using LinearStruct;
+
+namespace ExampleStack
+{
+ class Program
+ {
+ static void Main(string[] args)
+ {
+ StackTest(new SeqStack_1(20));
+ }
+
+ private static void StackTest(IStack stack)
+ {
+ stack.Push("a1");
+ stack.Push("a2");
+ stack.Push("a3");
+ while (stack.IsEmpty() == false)
+ {
+ Console.WriteLine(stack.StackTop);
+ stack.Pop();
+ }
+ // a3
+ // a2
+ // a1
+ }
+ }
+}
+```
+
+---
+## 3. ջʽ洢ջ
ջõʵֵջ
ʵ֣
-
+
-´Ϊ`C#`汾
```c
using System;
@@ -287,204 +443,77 @@ namespace LinearStruct
}
```
-## 3. ݹ
-
-һڲǵݹ麯
-
-Sample01nĽ׳
-
-`n! = 1 x 2 x 3 x ... x n`
-
-ѭ
-
-´Ϊ`Python`汾
-
-```python
-n = 5
-for k in range(1, 5):
- n = n * k
-print(n) # 120
-```
-
-
-ݹ飺
-
-´Ϊ`Python`汾
-
-```python
-def factorial(n):
- if n == 1:
- return 1
- return n * fact(n - 1)
-
-
-print(factorial(5)) # 120
-```
-
-Samp02쳲
-
-`f(n)=f(n-1)+f(n-2), f(0)=0 f(1)=1`
-
-ѭ
-
-´Ϊ`Python`汾
-
-```python
-i = 0
-j = 1
-lst = list([i, j])
-for k in range(2, 11):
- k = i + j
- lst.append(k)
- i = j
- j = k
-print(lst)
-# [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
-```
-
-ݹ飺
-
-´Ϊ`Python`汾
-
-```python
-def recur_fibo(n):
- if n <= 1:
- return n
- return recur_fibo(n - 1) + recur_fibo(n - 2)
-
-
-lst = list()
-for k in range(11):
- lst.append(recur_fibo(k))
-print(lst)
-# [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
-```
-
-
-ע⣺õݹIJPythonĬϵݹΪ 100
-
-```python
-import sys
-
-sys.setrecursionlimit(1000)
-```
-
-Sample03ŵ
-
-ŵԴӡһϴ˵ߡ촴ʱʯӣһϴϰմС˳ 64 ƬƽԲ̡ŰԲ̴濪ʼС˳°ڷһϡҹ涨СԲϲܷŴԲ̣֮һֻƶһԲ̡
-
-
-
-Ҫ˼ÿһôƿܻdzӣǿԽ
-
-ǿȼ a ֮⣬Ѿɹؽ a 63Ƶ b ʱֻҪٽ a ƶ c ɡ
-
-
-
-ǽ a Ƶ c b ϱµ 63 ӣa ΪաڵĿͱ˽ 63 b Ƶ c ԭȫһֻ a Ϊ b ģ 64 Ϊ 63˿ԲͬķȽ 62 b Ƶ a ٽƵ c
-
-Դƣ b Ϊ壬 a 62 Բ 61 Բƶ b һԲƵ c
-
-Ѿֹɣÿζ a b һΪ壬ȻȽԲ֮ԲƶϣٽµԲƵ c ϣظ˹̡
-
-ƶԲ̵Ĺ̾ǵݹ飬ÿ n Բ̵ƶ⣬ҪȽn-1ӽͬ⡣
-
-ǿԱдһmove(n, a, b, c)⣺move(, , , յ)
-
-1. a ֻһӵֱӰᵽ c:
-
-```python
-if n == 1:
- print(a, '-->', c)
-```
-2. a ϲֹһӵ:
-
-ȣҪ n-1 Ӱᵽ b ӻ塣ӡЧǣa --> b
-
-```python
-move(n - 1, a, c, b)
-```
-
-ٰӰᵽ c ӣҲߴһӡa-->c
-
-```python
-move(1, a, b, c)
-```
-
-ʣ b n-1 Ӱᵽ c ϣʱ㣬˻塣
-
-```python
-move(n - 1, b, a, c)
-```
-
-
- Python ʵֺŵ
-
-```python
-i = 0
-
-
-def move(n, a, b, c):
- global i
- if (n == 1):
- i += 1
- print('ƶ {0} {1} --> {2}'.format(i, a, c))
- return
- move(n - 1, a, c, b)
- move(1, a, b, c)
- move(n - 1, b, a, c)
-
-
-move(3, "a", "b", "c")
-
-# ƶ 1 a --> c
-# ƶ 2 a --> b
-# ƶ 3 c --> b
-# ƶ 4 a --> c
-# ƶ 5 b --> a
-# ƶ 6 b --> c
-# ƶ 7 a --> c
-```
-
- C# ʵֺŵ
+Ӧã
```c
-class Program
-{
- private static int i = 0;
- static void Move(int n, string a, string b, string c)
- {
- if (n == 1)
- {
- Console.WriteLine("ƶ {0} {1}-->{2}", ++i, a, c);
- return;
- }
- Move(n - 1, a, c, b);
- Move(1, a, b, c);
- Move(n - 1, b, a, c);
- }
+using System;
+using LinearStruct;
- static void Main(string[] args)
+namespace ExampleStack
+{
+ class Program
{
- Move(3, "a", "b", "c");
+ static void Main(string[] args)
+ {
+ StackTest(new LinkStack());
+ }
+
+ private static void StackTest(IStack stack)
+ {
+ stack.Push("a1");
+ stack.Push("a2");
+ stack.Push("a3");
+ while (stack.IsEmpty() == false)
+ {
+ Console.WriteLine(stack.StackTop);
+ stack.Pop();
+ }
+ // a3
+ // a2
+ // a1
+ }
}
}
-
-// ƶ 1 a --> c
-// ƶ 2 a --> b
-// ƶ 3 c --> b
-// ƶ 4 a --> c
-// ƶ 5 b --> a
-// ƶ 6 b --> c
-// ƶ 7 a --> c
```
+---
+## 4. ջӦ
+
+**4.1 **
+һлг`n`ڳᣬÿڳὫͣڲͬijվٶ`n`վıŷֱΪ1`n`гյ`n`վ`1`վĴЩվıǵĿĵͬΪ˱ڴгжӦijᣬгᣬʹǰ1`n`ĴСеijᶼִʱÿվֻжһڳἴɡ
-## 4. ϰο
-ŵij룬£`C#`汾
+һתվɳŹתվһ졢һ`k`죨λͳ֮䣩ͼ1aһתվ`k``k=3``H1``H2``H3`ʼʱ`n`ڳĻ촦תվתʱҵձ1`n`Ĵ뿪תվͨ촦ͼ1aУ`n=9`ӺǰijʼΪ581742963ͼ1b˰ҪĴкĽ
+
+
+
+
+**4.2 **
+
+ڷͼ1ΪųᣬǰμϵгᡣڼijһҪijᣬֱӰŵȥǣƶϣֱҪֵʱŽŵϡϳĽͳֻڻβСųУƶ
+
+1Դƶһβŵг
+
+2Դһβƶŵг
+
+ͼ1a3ųǰλ1ź2ųĺ棬˲3ųᣬɰ3ų뻺`H1`һڳ6ųᣬҲ뻺졣6ų`H1`ôŹ̽ɣΪ3ųλ6ųĺ棬ŵҪ3ų6ų֮ǰ˿ɰ6ų`H2`һڳ9ųᣬ`H3`Ϊ`H1``H2`ŹҲɡˣĵǰ״̬ͼ2aʾ
+
+
+
+2ųᣬԱһ죬Ϊ㻺ϳűеҪӦȰ2ų`H1`Ϊ`H3`ûпռƶ7ų8ųᡣ2ų`H2`ô4ų뱻`H3`ƶ5š7ź8ųᡣµij`u`ӦĻ죺ײij`v``v > u``v`Ļ춥Сһš**ֻʹijܵС**
+
+4ųʱ춥ijֱΪ2š6ź9ųᡣݷ4ųӦ`H2`֮7ųᱻ`H3`ͼ2b˵ǰ״̬
+
+1ųᱻ죬ʱ`H1`е2ų졣֮`H1`3ųᣬ 4ųᡣˣûпijˡ8ųᱻ`H1`Ȼ5ų촦ֱ촦֮`H2`6ųᣬ`H3`7ųᣬ`H1`8ųᣬ`H3`9ųᡣ
+
+Ϊֹ죬족ϣһ㷨˼·
+- һıǡţֱӳ졣
+- ڶıǡǻСţֱӳ졣
+- ŷ뻺졣ŵСڻջԪرջԪС档
+
+**4.3 ο**
```c
using System;
@@ -506,7 +535,6 @@ namespace TrainArrange
for (int i = 0; i < h.Length; i++)
h[i] = new LinkStack();
-
int nowOut = 1; //һҪij
int minH = int.MaxValue; //бСij
int minS = -1; //minHųӦĻ
@@ -561,7 +589,7 @@ namespace TrainArrange
}
///
- /// һз복C
+ /// һз복c
///
/// 복
/// ջŵСֵ
@@ -608,8 +636,8 @@ namespace TrainArrange
static void Main(string[] args)
{
- int[] p = new int[] {3, 6, 9, 2, 4, 7, 1, 8, 5};
- int k = 1;
+ int[] p = new int[] { 3, 6, 9, 2, 4, 7, 1, 8, 5 };
+ int k = 3;
bool result = RailRoad(p, k);
do
{
@@ -625,4 +653,205 @@ namespace TrainArrange
}
```
+**4.4 **
+
+
+
+---
+## 5. ݹ
+
+һڲǵݹ麯
+
+1nĽ׳
+
+```c
+n! = 1 x 2 x 3 x ... x n
+```
+
+ѭ
+
+```c
+static int factorial(int n)
+{
+ if (n < 1)
+ throw new ArgumentOutOfRangeException();
+
+ int result = n;
+ for (int i = 1; i < n; i++)
+ {
+ result *= i;
+ }
+ return result;
+}
+
+static void Main(string[] args)
+{
+ Console.WriteLine(factorial(5));
+ //120
+}
+```
+
+
+ݹ飺
+
+```c
+static int factorial(int n)
+{
+ if (n < 1)
+ throw new ArgumentOutOfRangeException();
+
+ if (n == 1)
+ return 1;
+ return n * factorial(n - 1);
+}
+
+static void Main(string[] args)
+{
+ Console.WriteLine(factorial(5));
+ //120
+}
+```
+
+2쳲
+
+```c
+f(n)=f(n-1)+f(n-2), f(0)=0 f(1)=1
+```
+
+
+ѭ
+
+```c
+static int[] recur_fibo(int n)
+{
+ if (n < 2)
+ throw new ArgumentOutOfRangeException();
+
+ int[] result = new int[n];
+ result[0]= 0;
+ result[1] = 1;
+ for (int i = 2; i < n; i++)
+ {
+ result[i] = result[i - 1] + result[i - 2];
+ }
+ return result;
+}
+
+static void Main(string[] args)
+{
+ int[] r = recur_fibo(11);
+ for (int i = 0; i < r.Length; i++)
+ {
+ Console.Write(r[i]+" ");
+ }
+ Console.WriteLine();
+ // 0 1 1 2 3 5 8 13 21 34 55
+}
+```
+
+ݹ飺
+
+
+```c
+static int recur_fibo(int n)
+{
+ if (n <= 1)
+ return n;
+
+ return recur_fibo(n - 1) + recur_fibo(n - 2);
+}
+
+static void Main(string[] args)
+{
+ int[] result = new int[11];
+ for (int i = 0; i < result.Length; i++)
+ {
+ result[i] = recur_fibo(i);
+ Console.Write(result[i] + " ");
+ }
+ Console.WriteLine();
+ // 0 1 1 2 3 5 8 13 21 34 55
+}
+```
+
+3ŵ
+
+ŵԴӡһϴ˵ߡ촴ʱʯӣһϴϰմС˳ 64 ƬƽԲ̡ŰԲ̴濪ʼС˳°ڷһϡҹ涨СԲϲܷŴԲ̣֮һֻƶһԲ̡
+
+
+
+Ҫ˼ÿһôƿܻdzӣǿԽ
+
+ǿȼ a ֮⣬Ѿɹؽ a 63Ƶ b ʱֻҪٽ a ƶ c ɡ
+
+
+
+ǽ a Ƶ c b ϱµ 63 ӣa ΪաڵĿͱ˽ 63 b Ƶ c ԭȫһֻ a Ϊ b ģ 64 Ϊ 63˿ԲͬķȽ 62 b Ƶ a ٽƵ c
+
+Դƣ b Ϊ壬 a 62 Բ 61 Բƶ b һԲƵ c
+
+Ѿֹɣÿζ a b һΪ壬ȻȽԲ֮ԲƶϣٽµԲƵ c ϣظ˹̡
+
+ƶԲ̵Ĺ̾ǵݹ飬ÿ n Բ̵ƶ⣬ҪȽn-1ӽͬ⡣
+
+ǿԱдһmove(n, a, b, c)⣺move(, , , յ)
+
+1. a ֻһӵֱӰᵽ c:
+
+```c
+if(n == 1)
+ Console.WriteLine(a, '-->', c)
+```
+2. a ϲֹһӵ:
+
+ȣҪ n-1 Ӱᵽ b ӻ塣ӡЧǣa --> b
+
+```python
+move(n - 1, a, c, b)
+```
+
+ٰӰᵽ c ӣҲߴһӡa-->c
+
+```python
+move(1, a, b, c)
+```
+
+ʣ b n-1 Ӱᵽ c ϣʱ㣬˻塣
+
+```python
+move(n - 1, b, a, c)
+```
+
+ C# ʵֺŵ
+
+```c
+class Program
+{
+ private static int i = 0;
+ static void Move(int n, string a, string b, string c)
+ {
+ if (n == 1)
+ {
+ Console.WriteLine("ƶ {0} {1}-->{2}", ++i, a, c);
+ return;
+ }
+ Move(n - 1, a, c, b);
+ Move(1, a, b, c);
+ Move(n - 1, b, a, c);
+ }
+
+ static void Main(string[] args)
+ {
+ Move(3, "a", "b", "c");
+ }
+}
+// ƶ 1 a --> c
+// ƶ 2 a --> b
+// ƶ 3 c --> b
+// ƶ 4 a --> c
+// ƶ 5 b --> a
+// ƶ 6 b --> c
+// ƶ 7 a --> c
+```
+