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# 12 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ϡ<EFBFBD><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
**֪ʶ<D6AA>ṹ<EFBFBD><E1B9B9>**
![ͼ1 ֪ʶ<D6AA>ṹ](https://img-blog.csdnimg.cn/20201019145851727.png)
## 1. <20><><EFBFBD><EFBFBD>
### 1.1 <20><><EFBFBD><EFBFBD><EFBFBD>Ķ<EFBFBD><C4B6><EFBFBD>
<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ǿ<EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><EFBFBD>˳<EFBFBD><EFBFBD><EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɶ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɵļ<EFBFBD><EFBFBD>ϣ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ķ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD>ء<EFBFBD>
<EFBFBD><EFBFBD><EFBFBD>磺
- <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ӧһά<D2BB><CEAC><EFBFBD><EFBFBD>
```math
A=(a_0,a_1,\cdots,a_{n-1})
```
- <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ӧ<EFBFBD><D3A6>ά<EFBFBD><CEAC><EFBFBD><EFBFBD>
```math
A_{m \times n} =\begin{bmatrix}
a_{00}&a_{01} &\cdots &a_{0n-1}\\
a_{10}&a_{11} &\cdots &a_{1n-1}\\
\cdots& \cdots &\cdots &\cdots\\
a_{m-10}&a_{m-11}& \cdots &a_{m-1n-1}\\
\end{bmatrix}
```
<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʾȺ<EFBFBD><EFBFBD><EFBFBD>Ĺ<EFBFBD><EFBFBD>ԣ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ͬһ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ͣ<EFBFBD>
<EFBFBD>±<EFBFBD><EFBFBD><EFBFBD>ʾ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ĸ<EFBFBD><EFBFBD>ԣ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ռ<EFBFBD>ж<EFBFBD><EFBFBD><EFBFBD><EFBFBD>ĵ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
### 1.2 <20><><EFBFBD><EFBFBD><EFBFBD>Ĵ洢
**<EFBFBD><EFBFBD>1<EFBFBD><EFBFBD>`$n$`ά<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ķ<EFBFBD><EFBFBD><EFBFBD>**
<EFBFBD>±<EFBFBD><EFBFBD><EFBFBD>`$n$`<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ`$n$`ά<EFBFBD><EFBFBD><EFBFBD>顣
<EFBFBD><EFBFBD><EFBFBD>磺
```c
//һά<D2BB><CEAC><EFBFBD>飨<EFBFBD>ߣ<EFBFBD>
int[] a = new int[10];
//<2F><>ά<EFBFBD><CEAC><EFBFBD><EFBFBD> <20><><EFBFBD>棩
int[ , ] a = new int[2,3];
//<2F><>ά<EFBFBD><CEAC><EFBFBD><EFBFBD> <20><><EFBFBD>壩<EFBFBD><E5A3A9><EFBFBD><EFBFBD><EFBFBD>ȣ<EFBFBD><C8A3>飨<EFBFBD>壩<EFBFBD><E5A3A9>2.ҳ<><D2B3> 3.<2E><> 4.<2E>С<EFBFBD>
int[ , , ] a = new int[2,3,4];
```
**<EFBFBD><EFBFBD>2<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>洢<EFBFBD><EFBFBD><EFBFBD>ص<EFBFBD>**
- <20><><EFBFBD><EFBFBD>Ԫ<EFBFBD><D4AA><EFBFBD><EFBFBD><EFBFBD>ڴ<EFBFBD><DAB4>а<EFBFBD>˳<EFBFBD><CBB3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>洢<EFBFBD><E6B4A2>
- <20><><EFBFBD><EFBFBD><EFBFBD>Ĵ洢<C4B4><E6B4A2><EFBFBD>䰴<EFBFBD><E4B0B4><EFBFBD>У<EFBFBD>C<EFBFBD><43>C++<2B><>C#<23>ȣ<EFBFBD><C8A3><EFBFBD><EFBFBD>У<EFBFBD>Forturn<72>ȣ<EFBFBD><C8A3><EFBFBD><EFBFBD>С<EFBFBD>
- <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʾ<EFBFBD><CABE><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>׵<EFBFBD>ַ<EFBFBD><D6B7><EFBFBD>dz<EFBFBD><C7B3><EFBFBD><EFBFBD><EFBFBD>
**<EFBFBD><EFBFBD>3<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ĵ洢**
<u>һά<D2BB><CEAC><EFBFBD><EFBFBD>`a[n]`</u>
<EFBFBD><EFBFBD>Ԫ<EFBFBD>ذ<EFBFBD><EFBFBD>½DZ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>δ<EFBFBD><EFBFBD>š<EFBFBD>
<EFBFBD><EFBFBD><EFBFBD><EFBFBD>`int[] a = new int[5];`
![ͼ2 һά<D2BB><CEAC><EFBFBD><EFBFBD><EFBFBD>洢](https://img-blog.csdnimg.cn/20191218195949938.png)
<u><3E><>ά<EFBFBD><CEAC><EFBFBD><EFBFBD>`a[m,n]`</u>
<EFBFBD><EFBFBD><EFBFBD><EFBFBD>`int[ , ] a = new int[2,3];`
![ͼ3 <20><>ά<EFBFBD><CEAC><EFBFBD><EFBFBD><EFBFBD>洢](https://img-blog.csdnimg.cn/20191218200106993.png)
<u><3E><>ά<EFBFBD><CEAC><EFBFBD><EFBFBD>`a[m,n,l]`</u>
<EFBFBD><EFBFBD>һά<EFBFBD>±<EFBFBD><EFBFBD>仯<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ά<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һά<EFBFBD><EFBFBD><EFBFBD>±<EFBFBD><EFBFBD>仯<EFBFBD><EFBFBD><EFBFBD>졣
<EFBFBD><EFBFBD><EFBFBD><EFBFBD>`int[ , , ] a = new int[2,3,4];`
![ͼ4 <20><>ά<EFBFBD><CEAC><EFBFBD><EFBFBD><EFBFBD>Ĵ洢](https://img-blog.csdnimg.cn/20191218200209131.png)
**ע<>⣺**
C#<23><>`int[,]`<EFBFBD><EFBFBD>`int[][]`<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
- `int[,]` <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȷ<EFBFBD><C8B7>
```c
static void Main(string[] args)
{
int[,] Arr = new int[2, 5] { { 1, 2, 3, 5, 6 }, { 1, 2, 3, 4, 5 } };
for (int i = 0; i < 2; ++i)
{
for (int j = 0; j < 5; ++j)
{
Console.Write(Convert.ToString(Arr[i, j]) + " ");
}
Console.WriteLine();
}
// 1 2 3 5 6
// 1 2 3 4 5
}
```
- `int[][]` <20><><EFBFBD><EFBFBD>ȷ<EFBFBD><C8B7><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
```c
static void Main(string[] args)
{
int[][] Arr = new int[3][]; //<2F><>ʾ<EFBFBD><CABE><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һά<D2BB><CEAC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Arr[0] = new int[5] { 1, 2, 3, 4, 5 };
Arr[1] = new int[2] { 0, 1 };
Arr[2] = new int[0] { };
for (int i = 0; i < Arr.Length; ++i)
{
foreach (int j in Arr[i])
{
Console.Write(j + " ");
}
Console.WriteLine();
}
// 1 2 3 4 5
// 0 1
//
}
```
### 1.3 <20><><EFBFBD><EFBFBD><EFBFBD>ķ<EFBFBD><C4B7><EFBFBD>
<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɷ<EFBFBD>Ϊ<EFBFBD><EFBFBD>̬<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ͷ<EFBFBD>̬<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ࡣ
**<EFBFBD><EFBFBD>1<EFBFBD><EFBFBD><EFBFBD><EFBFBD>̬<EFBFBD><EFBFBD><EFBFBD><EFBFBD>**
<EFBFBD>ڳ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʱ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ռ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>顣
<EFBFBD><EFBFBD><EFBFBD><EFBFBD>
```
//<2F><>̬<EFBFBD><CCAC><EFBFBD>飨<EFBFBD><E9A3A8><EFBFBD><EFBFBD>֮<EFBFBD><D6AE><EFBFBD><EFBFBD><EFBFBD>鳤<EFBFBD>Ȳ<EFBFBD><C8B2>ɸı䣩
int[] a = new int[10];
```
**<EFBFBD><EFBFBD>2<EFBFBD><EFBFBD><EFBFBD><EFBFBD>̬<EFBFBD><EFBFBD><EFBFBD><EFBFBD>**
<EFBFBD>ڳ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʱ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ռ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>飨<EFBFBD><EFBFBD><EFBFBD><EFBFBD>֮<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>鳤<EFBFBD>ȿɸ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
![ͼ5 <20><>̬<EFBFBD><CCAC><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ͼ](https://img-blog.csdnimg.cn/20201019105328214.png)
```c
using System;
namespace LinearStruct
{
/// <summary>
/// <20><>̬<EFBFBD><CCAC><EFBFBD><EFBFBD><EFBFBD>ij<EFBFBD><C4B3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʵ<EFBFBD><CAB5>
/// </summary>
/// <typeparam name="T"><3E><>̬<EFBFBD><CCAC><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD>ص<EFBFBD><D8B5><EFBFBD><EFBFBD><EFBFBD></typeparam>
public class DArray<T> where T : IComparable<T>
{
private T[] _array;
/// <summary>
/// <20><>ȡ<EFBFBD><C8A1>̬<EFBFBD><CCAC><EFBFBD><EFBFBD><EFBFBD>ĵ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>
/// </summary>
public int Size { get; private set; }
/// <summary>
/// <20><>ʼ<EFBFBD><CABC>DArray<61><79><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʵ<EFBFBD><CAB5>
/// </summary>
/// <param name="size"><3E><>̬<EFBFBD><CCAC><EFBFBD><EFBFBD><EFBFBD>ij<EFBFBD>ʼ<EFBFBD><CABC><EFBFBD><EFBFBD></param>
public DArray(int size)
{
if (size <= 0)
throw new ArgumentOutOfRangeException();
Size = size;
_array = new T[Size];
}
/// <summary>
/// <20>ı䶯̬<E4B6AF><CCAC><EFBFBD><EFBFBD><EFBFBD>ij<EFBFBD><C4B3><EFBFBD>
/// </summary>
/// <param name="newSize"><3E><>̬<EFBFBD><CCAC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>³<EFBFBD><C2B3><EFBFBD></param>
public void ReSize(int newSize)
{
if (newSize <= 0)
throw new ArgumentOutOfRangeException();
if (Size != newSize)
{
T[] newArray = new T[newSize];
int n = newSize < Size ? newSize : Size;
for (int i = 0; i < n; i++)
{
newArray[i] = _array[i];
}
_array = newArray;
Size = newSize;
}
}
/// <summary>
/// <20><>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ָ<EFBFBD><D6B8><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD><D4AA>
/// </summary>
/// <param name="index">Ҫ<><D2AA><EFBFBD>û<EFBFBD><C3BB><EFBFBD><EFBFBD>õ<EFBFBD>Ԫ<EFBFBD>ش<EFBFBD><D8B4>㿪ʼ<E3BFAA><CABC><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <returns>ָ<><D6B8><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD><D4AA></returns>
public T this[int index]
{
get
{
if (index < 0 || index > Size - 1)
throw new IndexOutOfRangeException();
return _array[index];
}
set
{
if (index < 0 || index > Size - 1)
throw new IndexOutOfRangeException();
_array[index] = value;
}
}
}
}
```
### 1.4 <20><>̬<EFBFBD><CCAC><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ӧ<EFBFBD><D3A6>
<EFBFBD><EFBFBD>дһ<EFBFBD>δ<EFBFBD><EFBFBD>룬Ҫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>`N`<EFBFBD><EFBFBD><EFBFBD>ö<EFBFBD>̬<EFBFBD><EFBFBD><EFBFBD><EFBFBD>`A`<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>`2~N`֮<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>5<EFBFBD><EFBFBD>7<EFBFBD>ı<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>顣
<EFBFBD><EFBFBD><EFBFBD>磺`N=100`
<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>5 7 10 14 15 20 21 25 28 30 35 40 42 45 49 50 55 56 60 63 65 70 75 77 80 84 85 90 91 95 98 100
<EFBFBD>ο<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>£<EFBFBD>
![ͼ6 <20><>̬<EFBFBD><CCAC><EFBFBD><EFBFBD>ʵ<EFBFBD><CAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>](https://img-blog.csdnimg.cn/20201019105841792.png#pic_center)
```c
static void Main(string[] args)
{
Console.WriteLine("N=");
string s = Console.ReadLine();
int n;
if (int.TryParse(s, out n))
{
DArray<int> arr = new DArray<int>(10);
int j = 0;
for (int i = 2; i <= n; i++)
{
if (i % 5 == 0 || i % 7 == 0)
{
if (j == arr.Size)
arr.ReSize(arr.Size + 10);
arr[j] = i;
j++;
}
}
for (int i = 0; i < j; i++)
{
Console.Write(arr[i] + " ");
}
}
}
```
---
## 2. ϡ<><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
### 2.1 ϡ<><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ķ<EFBFBD><C4B6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
**<EFBFBD><EFBFBD>1<EFBFBD><EFBFBD>ϡ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ķ<EFBFBD><EFBFBD><EFBFBD>**
<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>`$A$`<EFBFBD>з<EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD>صĸ<EFBFBD><EFBFBD><EFBFBD>ԶԶС<EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD>صĸ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>`$A$`Ϊϡ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
<EFBFBD><EFBFBD><EFBFBD><EFBFBD>
```math
A = \begin {bmatrix}
50 & 0 & 0 & 0\\
10 & 0 & 20 & 0\\
0 & 0 & 0 & 0\\
-30 & 0 & -60 & 5
\end{bmatrix}
```
<EFBFBD><EFBFBD><EFBFBD>ö<EFBFBD>ά<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>洢<EFBFBD><EFBFBD><EFBFBD><EFBFBD>̫<EFBFBD>˷Ѵ洢<EFBFBD>ռ䡣
**<EFBFBD><EFBFBD>2<EFBFBD><EFBFBD>ϡ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>IJ<EFBFBD><EFBFBD><EFBFBD>**
- <20><>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
- <20><>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
- <20><>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ָ<EFBFBD><D6B8><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD><D4AA>
- <20><><EFBFBD><EFBFBD><EFBFBD>ӷ<EFBFBD>
- <20><><EFBFBD><EFBFBD>ת<EFBFBD><D7AA>
- <20><><EFBFBD><EFBFBD><EFBFBD>˷<EFBFBD>
![ͼ7 <20><><EFBFBD><EFBFBD><EFBFBD>ӿ<EFBFBD>](https://img-blog.csdnimg.cn/20201019111305663.png)
```c
namespace LinearStruct
{
/// <summary>
/// <20><><EFBFBD><EFBFBD><EFBFBD>ij<EFBFBD><C4B3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
/// </summary>
public interface IMatrix<T>
{
/// <summary>
/// <20><>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
/// </summary>
int Rows { get; }
/// <summary>
/// <20><>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
/// </summary>
int Cols { get; }
/// <summary>
/// <20><>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ָ<EFBFBD><D6B8><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD><D4AA>
/// </summary>
/// <param name="i">Ҫ<><D2AA>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD>õ<EFBFBD>Ԫ<EFBFBD>ش<EFBFBD><D8B4>㿪ʼ<E3BFAA><CABC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <param name="j">Ҫ<><D2AA>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD>õ<EFBFBD>Ԫ<EFBFBD>ش<EFBFBD><D8B4>㿪ʼ<E3BFAA><CABC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <returns></returns>
T this[int i, int j] { get; set; }
/// <summary>
/// <20><><EFBFBD><EFBFBD><EFBFBD>ӷ<EFBFBD>
/// </summary>
/// <param name="b"><3E><>֮<EFBFBD><D6AE><EFBFBD>ӵ<EFBFBD><D3B5><EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <returns><3E><><EFBFBD>Ӻ<EFBFBD><D3BA><EFBFBD><EFBFBD>¾<EFBFBD><C2BE><EFBFBD></returns>
IMatrix<T> Add(IMatrix<T> b);
/// <summary>
/// <20><><EFBFBD><EFBFBD>ת<EFBFBD><D7AA>
/// </summary>
/// <returns>ת<>ú<EFBFBD><C3BA><EFBFBD><EFBFBD>¾<EFBFBD><C2BE><EFBFBD></returns>
IMatrix<T> Transpose();
/// <summary>
/// <20><><EFBFBD><EFBFBD><EFBFBD>˷<EFBFBD>
/// </summary>
/// <param name="b"><3E><>֮<EFBFBD>ҳ˵<D2B3><CBB5><EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <returns><3E><><EFBFBD>˺<EFBFBD><CBBA><EFBFBD><EFBFBD>¾<EFBFBD><C2BE><EFBFBD></returns>
IMatrix<T> Multiply(IMatrix<T> b);
}
}
```
### 2.2 ϡ<><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ĵ洢<C4B4><E6B4A2>ʵ<EFBFBD><CAB5>
<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>`<60><>Row<6F><77>Col<6F><6C>Value<75><65>`<EFBFBD>ķ<EFBFBD>ʽ<EFBFBD>洢<EFBFBD>Ͷ<EFBFBD>λϡ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>еķ<EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD>أ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>ִ洢ϡ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ķ<EFBFBD>ʽ<EFBFBD><EFBFBD>Ϊ<EFBFBD><EFBFBD>Ԫ<EFBFBD>飨Triple<EFBFBD><EFBFBD><EFBFBD><EFBFBD>
![ͼ8 ϡ<><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ĵ洢](https://img-blog.csdnimg.cn/20201019111609268.png)
<EFBFBD><EFBFBD><EFBFBD><EFBFBD>˳<EFBFBD><EFBFBD><EFBFBD>ķ<EFBFBD>ʽ<EFBFBD><EFBFBD><EFBFBD>д洢<EFBFBD><EFBFBD>
![ͼ9 ˳<><CBB3><EFBFBD><EFBFBD>ʽ<EFBFBD>洢ϡ<E6B4A2><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>](https://img-blog.csdnimg.cn/20201019111704277.png)
<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʽ<EFBFBD>ķ<EFBFBD>ʽ<EFBFBD><EFBFBD><EFBFBD>д洢<EFBFBD><EFBFBD>
![ͼ10 <20><>ʽ<EFBFBD><CABD>ʽ<EFBFBD>洢ϡ<E6B4A2><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>](https://img-blog.csdnimg.cn/20201019111738648.png)
**<EFBFBD><EFBFBD>1<EFBFBD><EFBFBD><EFBFBD>Խ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>ķ<EFBFBD>װ**
![ͼ11 ϡ<><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ͼ](https://img-blog.csdnimg.cn/20201019143656996.png)
```c
using System;
namespace LinearStruct
{
/// <summary>
/// ϡ<><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
/// </summary>
public class Triple : IComparable<Triple>
{
/// <summary>
/// <20><>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ھ<EFBFBD><DABE><EFBFBD><EFBFBD>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
/// </summary>
public int Row { get; }
/// <summary>
/// <20><>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ھ<EFBFBD><DABE><EFBFBD><EFBFBD>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
/// </summary>
public int Col { get; }
/// <summary>
/// <20><>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD>ý<EFBFBD><C3BD><EFBFBD><EFBFBD>ھ<EFBFBD><DABE><EFBFBD><EFBFBD>е<EFBFBD>ֵ
/// </summary>
public double Value { get; set; }
/// <summary>
/// <20><>ʼ<EFBFBD><CABC>Triple<6C><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʵ<EFBFBD><CAB5>
/// </summary>
/// <param name="i"><3E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ھ<EFBFBD><DABE><EFBFBD><EFBFBD>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <param name="j"><3E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ھ<EFBFBD><DABE><EFBFBD><EFBFBD>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <param name="value"><3E><><EFBFBD><EFBFBD><EFBFBD>ھ<EFBFBD><DABE><EFBFBD><EFBFBD>е<EFBFBD>ֵ</param>
public Triple(int i, int j, double value)
{
if (i < 0 || j < 0)
throw new Exception("<EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD><EFBFBD>λ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ч.");
Row = i;
Col = j;
Value = value;
}
/// <summary>
/// Triple<6C><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD>
/// </summary>
/// <returns>Triple<6C><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD></returns>
public override string ToString()
{
return string.Format("({0},{1},{2})", Row, Col, Value);
}
/// <summary>
/// <20>Ƚ<EFBFBD><C8BD><EFBFBD>Ԫ<EFBFBD><D4AA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ݵĴ<DDB5>С
/// </summary>
/// <param name="other"><3E><><EFBFBD>Ƚϵ<C8BD><CFB5><EFBFBD>Ԫ<EFBFBD><D4AA></param>
/// <returns></returns>
public int CompareTo(Triple other)
{
if (Value < other.Value) return -1;
if (Value > other.Value) return 1;
return 0;
}
}
}
```
**<EFBFBD><EFBFBD>2<EFBFBD><EFBFBD><EFBFBD><EFBFBD>ϡ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ķ<EFBFBD>װ**
![ͼ12 ϡ<><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ͼ](https://img-blog.csdnimg.cn/20201019114927840.png)
```c
using System;
namespace LinearStruct
{
/// <summary>
/// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>͵<EFBFBD>ʵ<EFBFBD><CAB5>--ϡ<><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
/// </summary>
public class SparseMatrix : IMatrix<double>
{
private readonly DLinkList<Triple> _lst;
/// <summary>
/// <20><>ȡϡ<C8A1><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
/// </summary>
public int Rows { get; }
/// <summary>
/// <20><>ȡϡ<C8A1><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
/// </summary>
public int Cols { get; }
/// <summary>
/// <20><>ʼ<EFBFBD><CABC>SparseMatrix<69><78><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʵ<EFBFBD><CAB5>
/// </summary>
/// <param name="rows">ϡ<><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <param name="cols">ϡ<><CFA1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
public SparseMatrix(int rows, int cols)
{
if (rows <= 0 || cols <= 0)
throw new ArgumentOutOfRangeException();
Rows = rows;
Cols = cols;
_lst = new DLinkList<Triple>();
}
private DNode<Triple> GetIndex(int i, int j)
{
DNode<Triple> temp = _lst.PHead;
while (temp != null)
{
if (temp.Data.Row == i && temp.Data.Col == j)
break;
temp = temp.Next;
}
return temp;
}
private void RemoveNode(DNode<Triple> node)
{
if (node.Next == null)
{
_lst.Remove(_lst.Length - 1);
}
else if (node.Prior == null)
{
_lst.Remove(0);
}
else
{
node.Prior.Next = node.Next;
node.Next.Prior = node.Prior;
}
}
/// <summary>
/// <20><>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ָ<EFBFBD><D6B8><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD><D4AA>
/// </summary>
/// <param name="i">Ҫ<><D2AA>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD>õ<EFBFBD>Ԫ<EFBFBD>ش<EFBFBD><D8B4>㿪ʼ<E3BFAA><CABC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <param name="j">Ҫ<><D2AA>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD>õ<EFBFBD>Ԫ<EFBFBD>ش<EFBFBD><D8B4>㿪ʼ<E3BFAA><CABC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <returns></returns>
public double this[int i, int j]
{
get
{
if (i < 0 || i > Rows - 1 || j < 0 || j > Cols - 1)
throw new IndexOutOfRangeException();
DNode<Triple> node = GetIndex(i, j);
return node == null ? 0.0 : node.Data.Value;
}
set
{
if (i < 0 || i > Rows - 1 || j < 0 || j > Cols - 1)
throw new IndexOutOfRangeException();
DNode<Triple> node = GetIndex(i, j);
if (node == null)
{
if (value != 0.0)
{
_lst.InsertAtRear(new Triple(i, j, value));
}
}
else
{
if (value != 0.0)
{
node.Data.Value = value;
}
else
{
RemoveNode(node);
}
}
}
}
/// <summary>
/// <20><><EFBFBD><EFBFBD><EFBFBD>ӷ<EFBFBD>
/// </summary>
/// <param name="b"><3E><>֮<EFBFBD><D6AE><EFBFBD>ӵ<EFBFBD><D3B5><EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <returns><3E><><EFBFBD>Ӻ<EFBFBD><D3BA><EFBFBD><EFBFBD>¾<EFBFBD><C2BE><EFBFBD></returns>
public SparseMatrix Add(SparseMatrix b)
{
if (b == null)
throw new ArgumentNullException();
if (b.Rows != Rows || b.Cols != Cols)
throw new Exception("<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>.");
SparseMatrix temp = new SparseMatrix(Rows, Cols);
for (int i = 0; i < Rows; i++)
for (int j = 0; j < Cols; j++)
temp[i, j] = this[i, j] + b[i, j];
return temp;
}
/// <summary>
/// <20><><EFBFBD><EFBFBD>ת<EFBFBD><D7AA>
/// </summary>
/// <returns>ת<>ú<EFBFBD><C3BA><EFBFBD><EFBFBD>¾<EFBFBD><C2BE><EFBFBD></returns>
public SparseMatrix Transpose()
{
SparseMatrix temp = new SparseMatrix(Cols, Rows);
for (int i = 0; i < temp.Rows; i++)
for (int j = 0; j < temp.Cols; j++)
temp[i, j] = this[j, i];
return temp;
}
/// <summary>
/// <20><><EFBFBD><EFBFBD><EFBFBD>˷<EFBFBD>
/// </summary>
/// <param name="b"><3E><>֮<EFBFBD>ҳ˵<D2B3><CBB5><EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <returns><3E><><EFBFBD>˺<EFBFBD><CBBA><EFBFBD><EFBFBD>¾<EFBFBD><C2BE><EFBFBD></returns>
public SparseMatrix Multiply(SparseMatrix b)
{
if (b == null)
throw new ArgumentNullException();
if (Cols != b.Rows)
throw new Exception("<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>.");
SparseMatrix temp = new SparseMatrix(Rows, b.Cols);
for (int i = 0; i < Rows; i++)
{
for (int j = 0; j < b.Cols; j++)
{
double value = 0.0;
for (int k = 0; k < Cols; k++)
value += this[i, k] * b[k, j];
temp[i, j] = value;
}
}
return temp;
}
/// <summary>
/// <20><><EFBFBD><EFBFBD><EFBFBD>ӷ<EFBFBD><D3B7><EFBFBD><EFBFBD><EFBFBD>
/// </summary>
/// <param name="a"><3E><>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <param name="b"><3E>ڶ<EFBFBD><DAB6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD></param>
/// <returns><3E><><EFBFBD>Ӻ<EFBFBD><D3BA><EFBFBD><EFBFBD>¾<EFBFBD><C2BE><EFBFBD></returns>
public static SparseMatrix operator +(SparseMatrix a, SparseMatrix b)
{
if (a == null || b == null)
throw new ArgumentNullException();
return a.Add(b);
}
/// <summary>
/// <20><><EFBFBD><EFBFBD><EFBFBD>˷<EFBFBD><CBB7><EFBFBD><EFBFBD><EFBFBD>
/// </summary>
/// <param name="a"><3E><><EFBFBD>ߵľ<DFB5><C4BE><EFBFBD></param>
/// <param name="b"><3E>ұߵľ<DFB5><C4BE><EFBFBD></param>
/// <returns><3E><><EFBFBD>˺<EFBFBD><CBBA><EFBFBD><EFBFBD>¾<EFBFBD><C2BE><EFBFBD></returns>
public static SparseMatrix operator *(SparseMatrix a, SparseMatrix b)
{
if (a == null || b == null)
throw new ArgumentNullException();
return a.Multiply(b);
}
/// <summary>
/// SparseMatrix<69><78><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD>
/// </summary>
/// <returns>SparseMatrix<69><78><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD></returns>
public override string ToString()
{
string str = string.Empty;
DNode<Triple> temp = _lst.PHead;
while (temp != null)
{
str += temp.Data + "\n";
temp = temp.Next;
}
return str;
}
IMatrix<double> IMatrix<double>.Add(IMatrix<double> b)
{
return Add((SparseMatrix)b);
}
IMatrix<double> IMatrix<double>.Transpose()
{
return Transpose();
}
IMatrix<double> IMatrix<double>.Multiply(IMatrix<double> b)
{
return Multiply((SparseMatrix)b);
}
}
}
```
<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
```c
static void Main(string[] args)
{
IMatrix<double> a = new SparseMatrix(2, 3);
IMatrix<double> b = new SparseMatrix(3, 2);
SparseMatrix c = new SparseMatrix(2, 2);
a[0, 2] = 1;
a[1, 0] = 1;
b[1, 1] = 4;
b[2, 0] = 1;
c[0, 1] = 1;
c[1, 0] = 1;
SparseMatrix d = (SparseMatrix)a * (SparseMatrix)b + c;
IMatrix<double> e = a.Multiply(b).Add(c);
Console.WriteLine("D:\n{0}", d);
Console.WriteLine("E:\n{0}", e);
// D:
// (0, 0, 1)
// (0, 1, 1)
// (1, 0, 1)
// E:
// (0, 0, 1)
// (0, 1, 1)
// (1, 0, 1)
}
```

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DataStructureAndAlgorithm/12 字符串.md → DataStructureAndAlgorithm/13 字符串.md
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