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数据结构：稀疏矩阵的简单运算
最近专业课比较多，没怎么看数据结构了。今天有点时间写了一下数据结构中稀疏矩阵的运算。写过之后感觉代码的构思不太好。这里先发一下，
假期的时候再重新实现一下。
SpMatrix头文件
1 //The sparse matrix‘s header file
2 //the class SpMatrix
3 //Author: ‘Karllen‘
4 //Date:05/28/2014
5
6 #ifndef _SpMatrix_H_
7 #define _SPMatrix_H_
8 #include <iostream>
9 template<class T>
10 class Triple
11 {
12 public:
13 T ele; // The Triple element
14 int i,j; // The element location in the matrix
15 };
16
17 template<class T>
18 class SpMatrix
19 {
20 public:
21 SpMatrix(void);
22 SpMatrix(T **inptr,int mrow,int mcolumn); //get the matrix from inptr
23 ~SpMatrix(void);
24 void transposeSpMatrix(SpMatrix& osp); //transpose matrix
25 void addSpMatrix(const SpMatrix& lhs,const SpMatrix& rhs); //add two sparse matrix
26 void subSpMatrix(const SpMatrix& lhs,const SpMatrix& rhs); //sub two sparse matrix
27 void mulSpMatrix(const SpMatrix& lhs,const SpMatrix& rhs); //multiplication two sparse matrix
28 void divSpMatrix(const SpMatrix& lhs,const SpMatrix& rhs); //divide two sparse matrix
29 void sptoprintMatxi()const; //print the sparse matrix as matrix
30 void printMatrix()const; //print the sparse matrix
31 private:
32 Triple<T> *tri; //the pointer to sparse matrix
33 int row,column; //the sparse matrix‘s row and column
34 int count; //the total numbers of triple
35 };
36
37 template<class T>
38 SpMatrix<T>::SpMatrix(void):row(0),column(0),count(0),tri(NULL)
39 {
40
41 }
42
43 template<class T>
44 SpMatrix<T>::SpMatrix(T **inptr,int mrow,int mcolumn)
45 {
46 count = 0;
47 row = mrow;
48 column = mcolumn;
49 tri = new Triple<T>[mrow*mcolumn];
50 for (int i = 0;i<row;++i)
51 {
52 for (int j = 0;j<column;++j)
53 {
54 if (0 !=inptr[i][j])
55 {
56 tri[count].i = i;
57 tri[count].j = j;
58 tri[count].ele = inptr[i][j];
59 ++count;
60 }
61 }
62 }
63 }
64
65 template<class T>
66 SpMatrix<T>::~SpMatrix(void)
67 {
68 if (tri!=NULL)
69 {
70 delete []tri;
71 }
72 }
73
74 template<class T>
75 void SpMatrix<T>::transposeSpMatrix(SpMatrix& osp)
76 {
77 if (0!=osp.count)
78 {
79 tri = new Triple<T>[osp.count];
80 row = osp.column;
81 column = osp.row;
82 int k = 0;
83 for (int i = 0;i<osp.column;++i)
84 {
85 for (int j = 0;j<osp.count;++j)
86 {
87 if (i == osp.tri[j].j)
88 {
89 tri[k].i = osp.tri[j].j;
90 tri[k].j = osp.tri[j].i;
91 tri[k].ele = osp.tri[j].ele;
92 ++k;
93 ++count;
94 }
95 }
96 }
97 }
98 else
99 {
100 std::cout<<"三元组个数为0，不能转置"<<std::endl;
101 }
102 }
103
104 template<class T>
105 void SpMatrix<T>::addSpMatrix(const SpMatrix& lhs,const SpMatrix& rhs)
106 {
107 if (lhs.row==lhs.column&&rhs.row==rhs.column&&lhs.row==rhs.row)
108 {
109 row = lhs.row;
110 column = lhs.column;
111 tri = new Triple<T>[lhs.count+rhs.count];
112 int li=0,lj=0,i=0;
113 while(li<lhs.count&&lj<rhs.count)
114 {
115 if (lhs.tri[li].i==rhs.tri[lj].i)
116 {
117 if (lhs.tri[li].j==rhs.tri[lj].j)
118 {
119 if (lhs.tri[li].ele+rhs.tri[lj].ele!=0)
120 {
121 tri[i].i = lhs.tri[li].i;
122 tri[i].j = lhs.tri[li].j;
123 tri[i].ele = lhs.tri[li].ele+rhs.tri[lj].ele;
124 ++i;
125 ++count;
126 }
127 ++li;
128 ++lj;
129 }
130 else
131 {
132 if (lhs.tri[li].j<rhs.tri[lj].j)
133 {
134 tri[i].ele = lhs.tri[li].ele;
135 tri[i].i = lhs.tri[li].i;
136 tri[i].j = lhs.tri[li].j;
137 ++i;
138 ++count;
139 ++li;
140 }
141 else
142 {
143 tri[i].ele = rhs.tri[lj].ele;
144 tri[i].i = rhs.tri[lj].i;
145 tri[i].j = rhs.tri[lj].j;
146 ++i;
147 ++count;
148 ++lj;
149 }
150 }
151 }
152 else
153 {
154 if (lhs.tri[li].i<rhs.tri[lj].i)
155 {
156 tri[i].ele = lhs.tri[li].ele;
157 tri[i].i = lhs.tri[li].i;
158 tri[i].j = lhs.tri[li].j;
159 ++i;
160 ++count;
161 ++li;
162 }
163 else
164 {
165 tri[i].ele = rhs.tri[lj].ele;
166 tri[i].i = rhs.tri[lj].i;
167 tri[i].j = rhs.tri[lj].j;
168 ++i;
169 ++count;
170 ++lj;
171 }
172 }
173
174 }
175 if (li==lhs.count)
176 {
177 while (lj<rhs.count)
178 {
179 tri[i].ele = rhs.tri[lj].ele;
180 tri[i].i = rhs.tri[lj].i;
181 tri[i].j = rhs.tri[lj].j;
182 ++i;
183 ++count;
184 ++lj;
185 }
186 }
187 if(lj==rhs.count&&lhs.count!=li)
188 {
189 while (li<lhs.count)
190 {
191 tri[i].ele = lhs.tri[li].ele;
192 tri[i].i = lhs.tri[li].i;
193 tri[i].j = lhs.tri[li].j;
194 ++i;
195 ++count;
196 ++li;
197 }
198 }
199 }
200 else
201 {
202 std::cout<<"Two matrix is different type and aren‘t to add!"<<std::endl;
203 }
204 }
205
206 template<class T>
207 void SpMatrix<T>::subSpMatrix(const SpMatrix& lhs,const SpMatrix& rhs)
208 {
209 if (lhs.row==lhs.column&&rhs.row==rhs.column&&lhs.row==rhs.row)
210 {
211 row = lhs.row;
212 column = lhs.column;
213 tri = new Triple<T>[lhs.count+rhs.count];
214 int li=0,lj=0,i=0;
215 while(li<lhs.count&&lj<rhs.count)
216 {
217 if (lhs.tri[li].i==rhs.tri[lj].i)
218 {
219 if (lhs.tri[li].j==rhs.tri[lj].j)
220 {
221 if (lhs.tri[li].ele-rhs.tri[lj].ele!=0)
222 {
223 tri[i].i = lhs.tri[li].i;
224 tri[i].j = lhs.tri[li].j;
225 tri[i].ele = lhs.tri[li].ele-rhs.tri[lj].ele;
226 ++i;
227 ++count;
228 }
229 ++li;
230 ++lj;
231 }
232 else
233 {
234 if (lhs.tri[li].j<rhs.tri[lj].j)
235 {
236 tri[i].ele = lhs.tri[li].ele;
237 tri[i].i = lhs.tri[li].i;
238 tri[i].j = lhs.tri[li].j;
239 ++i;
240 ++count;
241 ++li;
242 }
243 else
244 {
245 tri[i].ele = -rhs.tri[lj].ele;
246 tri[i].i = rhs.tri[lj].i;
247 tri[i].j = rhs.tri[lj].j;
248 ++i;
249 ++count;
250 ++lj;
251 }
252 }
253 }
254 else
255 {
256 if (lhs.tri[li].i<rhs.tri[lj].i)
257 {
258 tri[i].ele = lhs.tri[li].ele;
259 tri[i].i = lhs.tri[li].i;
260 tri[i].j = lhs.tri[li].j;
261 ++i;
262 ++count;
263 ++li;
264 }
265 else
266 {
267 tri[i].ele = -rhs.tri[lj].ele;
268 tri[i].i = rhs.tri[lj].i;
269 tri[i].j = rhs.tri[lj].j;
270 ++i;
271 ++count;
272 ++lj;
273 }
274 }
275
276 }
277 if (li==lhs.count)
278 {
279 while (lj<rhs.count)
280 {
281 tri[i].ele = -rhs.tri[lj].ele;
282 tri[i].i = rhs.tri[lj].i;
283 tri[i].j = rhs.tri[lj].j;
284 ++i;
285 ++count;
286 ++lj;
287 }
288 }
289 if(lj==rhs.count&&lhs.count!=li)
290 {
291 while (li<lhs.count)
292 {
293 tri[i].ele = lhs.tri[li].ele;
294 tri[i].i = lhs.tri[li].i;
295 tri[i].j = lhs.tri[li].j;
296 ++i;
297 ++count;
298 ++li;
299 }
300 }
301 }
302 else
303 {
304 std::cout<<"Two matrix is different type and aren‘t to sub!"<<std::endl;
305 }
306 }
307
308
309 template<class T>
310 void SpMatrix<T>::mulSpMatrix(const SpMatrix& lhs,const SpMatrix& rhs)
311 {
312 if (lhs.column==rhs.row&&0!=lhs.count||0!=rhs.count)
313 {
314 row = lhs.row;
315 column = rhs.column;
316 int _alN = row*column;
317 tri = new Triple<T>[_alN];
318
319 int *rhsRowSize = new int[rhs.row]; //save the rhs the element that‘s not zero int the row
320 int *rhsRowStart = new int[rhs.row]; //save the first element‘s location int the sparse matrix
321 int *rhsSzele = new int[rhs.column];
322 for (int i=0;i<rhs.row;++i)
323 {
324 rhsRowSize[i] = 0;
325 }
326 for (int i=0; i<rhs.count;++i) //calculate the numbers of every row in the rhs
327 {
328 ++rhsRowSize[rhs.tri[i].i];
329 }
330
331 rhsRowStart[0] = 0; //calculate the location of first row in the rhs
332 for (int i=1;i<rhs.row;++i)
333 {
334 rhsRowStart[i] = rhsRowStart[i-1]+rhsRowSize[i-1];
335 }
336
337 int k = 0;
338 for (int i = 0;i<lhs.row;++i) //calculate the every row of lhs
339 {
340 for (int j = 0;j<rhs.column;j++) //make the all 0
341 {
342 rhsSzele[j] = 0;
343 }
344 while (k<lhs.count && i==lhs.tri[k].i)
345 {
346 int cRlF = lhs.tri[k].j;
347 for (int i = rhsRowStart[cRlF]; cRlF == rhs.tri[i].i ; ++i)
348 {
349 rhsSzele[rhs.tri[i].j]+=lhs.tri[k].ele * rhs.tri[i].ele;
350 }
351 ++k;
352 }
353
354 for (int j = 0 ; j<rhs.column;++j) //deal the result every i row value
355 {
356 if (0!=rhsSzele[j])
357 {
358 tri[count].i = i;
359 tri[count].j = j;
360 tri[count].ele = rhsSzele[j];
361 ++count;
362 }
363 }
364 }
365 delete [] rhsRowSize;
366 delete [] rhsRowStart;
367 delete [] rhsSzele;
368 }
369 else
370 {
371 std::cout<<"两矩阵不满足相成的条件"<<std::endl;
372 }
373 }
374
375 template<class T>
376 void SpMatrix<T>::sptoprintMatxi()const
377 {
378 if (0!=count)
379 {
380 int k = 0,i = 0;
381 int rcm = row*column;
382 while(i<rcm)
383 {
384
385 if (i == tri[k].i*column+tri[k].j)
386 {
387 std::cout<<tri[k].ele<<" ";
388 ++k;
389 }
390 else
391 {
392 std::cout<<0<<" ";
393 }
394 if (0 == (i+1)%column )
395 {
396 std::cout<<::std::endl;
397 }
398 ++i;
399 }
400 std::cout<<std::endl;
401 }
402 std::cout<<std::endl;
403 }
404
405 template<class T>
406 void SpMatrix<T>::printMatrix()const
407 {
408 for (int i = 0;i<count;++i)
409 {
410 std::cout<<tri[i].i<<" "<<tri[i].j<<" "<<tri[i].ele<<std::endl;
411 }
412 std::cout<<"三元组的个数为："<<count<<std::endl;
413 std::cout<<std::endl;
414 }
415
416
417 #endif //_SpMatrix_H_
menu.h测试头文件代码
1 #ifndef _KARMENU_H_
2 #define _KARMENU_H_
3 #include "SpMatrix.h"
4 #include<stdlib.h>
5 void transMatrix()
6 {
7 int **mptr1 = NULL;
8 int row1,column1;
9 std::cout<<"Enter the matrix‘s row ";
10 std::cin>>row1;
11 std::cout<<"Enter the matrix‘s column ";
12 std::cin>>column1;
13
14 mptr1 = new int *[row1];
15 for (int i=0;i<row1;++i)
16 {
17 mptr1[i]= new int[column1];
18 for (int j=0;j<column1;++j)
19 {
20 std::cin>>mptr1[i][j];
21 }
22 }
23 SpMatrix<int> spmat1(mptr1,row1,column1);
24 SpMatrix<int> spmat2;
25 spmat2.transposeSpMatrix(spmat1);
26 std::cout<<std::endl;
27 std::cout<<"转置矩阵为："<<std::endl;
28 spmat2.sptoprintMatxi();
29 std::cout<<"转置矩阵的三元组表示为："<<std::endl;
30 spmat2.printMatrix();
31 }
32 void addMatrixM()
33 {
34 int **mptr1 = NULL;
35 int row1,column1;
36 std::cout<<"Enter the matrix‘s row ";
37 std::cin>>row1;
38 std::cout<<"Enter the matrix‘s column ";
39 std::cin>>column1;
40
41 mptr1 = new int *[row1];
42 for (int i=0;i<row1;++i)
43 {
44 mptr1[i]= new int[column1];
45 for (int j=0;j<column1;++j)
46 {
47 std::cin>>mptr1[i][j];
48 }
49 }
50 int **mptr2 = NULL;
51 int row2,column2;
52 std::cout<<"Enter the matrix‘s row ";
53 std::cin>>row2;
54 std::cout<<"Enter the matrix‘s column ";
55 std::cin>>column2;
56
57 mptr2 = new int *[row2];
58 for (int i=0;i<row2;++i)
59 {
60 mptr2[i]= new int[column2];
61 for (int j=0;j<column2;++j)
62 {
63 std::cin>>mptr2[i][j];
64 }
65 }
66 if (row1==column1&&row2==column2&&row1==row2)
67 {
68 SpMatrix<int> spmat1(mptr1,row1,column1);
69 SpMatrix<int> spmat2(mptr2,row2,column2);
70 SpMatrix<int> spmat3;
71 spmat3.addSpMatrix(spmat1,spmat2);
72 std::cout<<std::endl;
73 std::cout<<"被加矩阵的三元组表示："<<std::endl;
74 spmat1.printMatrix();
75 std::cout<<"加数矩阵的三元组表示："<<std::endl;
76 spmat2.printMatrix();
77
78 std::cout<<"所求和矩阵的普通表示："<<std::endl;
79 spmat3.sptoprintMatxi();
80 std::cout<<"所求和矩阵的三元组表示："<<std::endl;
81 spmat3.printMatrix();
82 }
83 else
84 {
85 std::cout<<"输入矩阵的阶数不符合要求，请输入等阶矩阵操作"<<std::endl;
86 }
87
88 for (int i = 0;i<row1;++i)
89 {
90 delete [] mptr1[i];
91 }
92 delete []mptr1;
93
94 for (int i = 0;i<row2;++i)
95 {
96 delete [] mptr2[i];
97 }
98 delete []mptr2;
99 mptr2 = NULL;
100 }
101
102 void subMatrixM()
103 {
104 int **mptr1 = NULL;
105 int row1,column1;
106 std::cout<<"Enter the matrix‘s row ";
107 std::cin>>row1;
108 std::cout<<"Enter the matrix‘s column ";
109 std::cin>>column1;
110
111 mptr1 = new int *[row1];
112 for (int i=0;i<row1;++i)
113 {
114 mptr1[i]= new int[column1];
115 for (int j=0;j<column1;++j)
116 {
117 std::cin>>mptr1[i][j];
118 }
119 }
120 int **mptr2 = NULL;
121 int row2,column2;
122 std::cout<<"Enter the matrix‘s row ";
123 std::cin>>row2;
124 std::cout<<"Enter the matrix‘s column ";
125 std::cin>>column2;
126
127 mptr2 = new int *[row2];
128 for (int i=0;i<row2;++i)
129 {
130 mptr2[i]= new int[column2];
131 for (int j=0;j<column2;++j)
132 {
133 std::cin>>mptr2[i][j];
134 }
135 }
136 if(row1==column1&&row2==column2&&row1==row2)
137 {
138 SpMatrix<int> spmat1(mptr1,row1,column1);
139 SpMatrix<int> spmat2(mptr2,row2,column2);
140 SpMatrix<int> spmat3;
141 spmat3.subSpMatrix(spmat1,spmat2);
142 std::cout<<std::endl;
143 std::cout<<"被减矩阵的三元组表示："<<std::endl;
144 spmat1.printMatrix();
145 std::cout<<"减数矩阵的三元组表示："<<std::endl;
146 spmat2.printMatrix();
147
148 std::cout<<"所求差矩阵的普通表示："<<std::endl;
149 spmat3.sptoprintMatxi();
150 std::cout<<"所求差矩阵的三元组表示："<<std::endl;
151 spmat3.printMatrix();
152 }
153 else
154 {
155 std::cout<<"您输入的矩阵不符合要求，求输入等阶矩阵"<<std::endl;
156 }
157 for (int i = 0;i<row1;++i)
158 {
159 delete [] mptr1[i];
160 }
161 delete []mptr1;
162
163 for (int i = 0;i<row2;++i)
164 {
165 delete [] mptr2[i];
166 }
167 delete []mptr2;
168 }
169
170 void mulMatrixM()
171 {
172 int **mptr1 = NULL;
173 int row1,column1;
174 std::cout<<"Enter the matrix‘s row ";
175 std::cin>>row1;
176 std::cout<<"Enter the matrix‘s column ";
177 std::cin>>column1;
178
179 mptr1 = new int *[row1];
180 for (int i=0;i<row1;++i)
181 {
182 mptr1[i]= new int[column1];
183 for (int j=0;j<column1;++j)
184 {
185 std::cin>>mptr1[i][j];
186 }
187 }
188 int **mptr2 = NULL;
189 int row2,column2;
190 std::cout<<"Enter the matrix‘s row ";
191 std::cin>>row2;
192 std::cout<<"Enter the matrix‘s column ";
193 std::cin>>column2;
194
195 mptr2 = new int *[row2];
196 for (int i=0;i<row2;++i)
197 {
198 mptr2[i]= new int[column2];
199 for (int j=0;j<column2;++j)
200 {
201 std::cin>>mptr2[i][j];
202 }
203 }
204 if(column1 == row2)
205 {
206 SpMatrix<int> spmat1(mptr1,row1,column1);
207 SpMatrix<int> spmat2(mptr2,row2,column2);
208 SpMatrix<int> spmat3;
209 spmat3.mulSpMatrix(spmat1,spmat2);
210 std::cout<<std::endl;
211 std::cout<<"被乘矩阵的三元组表示："<<std::endl;
212 spmat1.printMatrix();
213 std::cout<<"乘数矩阵的三元组表示："<<std::endl;
214 spmat2.printMatrix();
215
216 std::cout<<"所求积矩阵的普通表示："<<std::endl;
217 spmat3.sptoprintMatxi();
218 std::cout<<"所求积矩阵的三元组表示："<<std::endl;
219 spmat3.printMatrix();
220 }
221 else
222 {
223 std::cout<<"您输入的矩阵不符合要求，请输入符合符合阶数要求的矩阵"<<std::endl;
224
225 }
226 for (int i = 0;i<row1;++i)
227 {
228 delete [] mptr1[i];
229 }
230 delete []mptr1;
231
232 for (int i = 0;i<row2;++i)
233 {
234 delete [] mptr2[i];
235 }
236 delete []mptr2;
237
238 }
239
240 void divMatrixM()
241 {
242
243 }
244
245 int menu()
246 {
247 int zmyn;
248 int choose = 0 ;
249 char a[10]={0};
250 do
251 {
252 std::cout<<"测试矩阵的运算"<<std::endl;
253 std::cout<<"1: 矩阵转置"<<std::endl;
254 std::cout<<"2: 矩阵求和"<<std::endl;
255 std::cout<<"3： 矩阵求差"<<std::endl;
256 std::cout<<"4: 矩阵求积"<<std::endl;
257 std::cout<<"5: 退出运算"<<std::endl;
258 std::cout<<"请输入1--5的选项!"<<std::endl;
259 std::cin>>a;
260 choose = atoi(a);
261 while (choose<1||choose>5)
262 {
263 std::cout<<"您输入的选项不和要求，请输入1--5之间的数字进行操作"<<std::endl;
264 std::cin>>a;
265 choose = atoi(a);
266 }
267 switch(choose)
268 {
269 case 1:
270 transMatrix();break;
271 case 2:
272 addMatrixM();break;
273 case 3:
274 subMatrixM();break;
275 case 4:
276 mulMatrixM();break;
277 case 5:
278 return 0;
279 default: ;
280 }
281 std::cout<<"输入1继续操作，输入0或者其他停止操作" <<std::endl;
282 std::cin>>a;
283 zmyn = atoi(a);
284 while (zmyn<0||zmyn>9)
285 {
286 std::cout<<"请正确输入"<<std::endl;
287 std::cin>>a;
288 zmyn = atoi(a);
289 }
290 system("cls");
291 }while(1 == zmyn);
292
293 return 0;
294 }
295 #endif //end _KARMENU_H_
main函数入口：
1 #include "KarMenu.h"
2 //static const int ROW = 10;
3 //static const int COLUMN = 10;
4 int main(void)
5 {
6 return menu();
7 }
测试：
矩阵转置：
矩阵求和：
矩阵求差：
矩阵求积：
测试均正确通过
数据结构：稀疏矩阵的简单运算
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