# C++ Program to Implement Strassen’s Algorithm

This is a C++ Program to implement Strassen’s algorithm for matrix multiplication. In the mathematical discipline of linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm used for matrix multiplication. It is faster than the standard matrix multiplication algorithm and is useful in practice for large matrices, but would be slower than the fastest known algorithms for extremely large matrices.

Here is source code of the C++ Program to Implement Strassen’s Algorithm. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

1. `#include <assert.h>`
2. `#include <stdio.h>`
3. `#include <stdlib.h>`
4. `#include <time.h>`
5. ` `
6. `#define M 2`
7. `#define N (1<<M)`
8. ` `
9. `typedef double datatype;`
10. `#define DATATYPE_FORMAT "%4.2g"`
11. `typedef datatype mat[N][N]; // mat[2**M,2**M]  for divide and conquer mult.`
12. `typedef struct`
13. `{`
14. `        int ra, rb, ca, cb;`
15. `} corners; // for tracking rows and columns.`
16. `// A[ra..rb][ca..cb] .. the 4 corners of a matrix.`
17. ` `
18. `// set A[a] = I`
19. `void identity(mat A, corners a)`
20. `{`
21. `    int i, j;`
22. `    for (i = a.ra; i < a.rb; i++)`
23. `        for (j = a.ca; j < a.cb; j++)`
24. `            A[i][j] = (datatype) (i == j);`
25. `}`
26. ` `
27. `// set A[a] = k`
28. `void set(mat A, corners a, datatype k)`
29. `{`
30. `    int i, j;`
31. `    for (i = a.ra; i < a.rb; i++)`
32. `        for (j = a.ca; j < a.cb; j++)`
33. `            A[i][j] = k;`
34. `}`
35. ` `
36. `// set A[a] = [random(l..h)].`
37. `void randk(mat A, corners a, double l, double h)`
38. `{`
39. `    int i, j;`
40. `    for (i = a.ra; i < a.rb; i++)`
41. `        for (j = a.ca; j < a.cb; j++)`
42. `            A[i][j] = (datatype) (l + (h - l) * (rand() / (double) RAND_MAX));`
43. `}`
44. ` `
45. `// Print A[a]`
46. `void print(mat A, corners a, char *name)`
47. `{`
48. `    int i, j;`
49. `    printf("%s = {\n", name);`
50. `    for (i = a.ra; i < a.rb; i++)`
51. `    {`
52. `        for (j = a.ca; j < a.cb; j++)`
53. `            printf(DATATYPE_FORMAT ", ", A[i][j]);`
54. `        printf("\n");`
55. `    }`
56. `    printf("}\n");`
57. `}`
58. ` `
59. `// C[c] = A[a] + B[b]`
60. `void add(mat A, mat B, mat C, corners a, corners b, corners c)`
61. `{`
62. `    int rd = a.rb - a.ra;`
63. `    int cd = a.cb - a.ca;`
64. `    int i, j;`
65. `    for (i = 0; i < rd; i++)`
66. `    {`
67. `        for (j = 0; j < cd; j++)`
68. `        {`
69. `            C[i + c.ra][j + c.ca] = A[i + a.ra][j + a.ca] + B[i + b.ra][j`
70. `                    + b.ca];`
71. `        }`
72. `    }`
73. `}`
74. ` `
75. `// C[c] = A[a] - B[b]`
76. `void sub(mat A, mat B, mat C, corners a, corners b, corners c)`
77. `{`
78. `    int rd = a.rb - a.ra;`
79. `    int cd = a.cb - a.ca;`
80. `    int i, j;`
81. `    for (i = 0; i < rd; i++)`
82. `    {`
83. `        for (j = 0; j < cd; j++)`
84. `        {`
85. `            C[i + c.ra][j + c.ca] = A[i + a.ra][j + a.ca] - B[i + b.ra][j`
86. `                    + b.ca];`
87. `        }`
88. `    }`
89. `}`
90. ` `
91. `// Return 1/4 of the matrix: top/bottom , left/right.`
92. `void find_corner(corners a, int i, int j, corners *b)`
93. `{`
94. `    int rm = a.ra + (a.rb - a.ra) / 2;`
95. `    int cm = a.ca + (a.cb - a.ca) / 2;`
96. `    *b = a;`
97. `    if (i == 0)`
98. `        b->rb = rm; // top rows`
99. `    else`
100. `        b->ra = rm; // bot rows`
101. `    if (j == 0)`
102. `        b->cb = cm; // left cols`
103. `    else`
104. `        b->ca = cm; // right cols`
105. `}`
106. ` `
107. `// Multiply: A[a] * B[b] => C[c], recursively.`
108. `void mul(mat A, mat B, mat C, corners a, corners b, corners c)`
109. `{`
110. `    corners aii[2][2], bii[2][2], cii[2][2], p;`
111. `    mat P[7], S, T;`
112. `    int i, j, m, n, k;`
113. ` `
114. `    // Check: A[m n] * B[n k] = C[m k]`
115. `    m = a.rb - a.ra;`
116. `    assert(m==(c.rb-c.ra));`
117. `    n = a.cb - a.ca;`
118. `    assert(n==(b.rb-b.ra));`
119. `    k = b.cb - b.ca;`
120. `    assert(k==(c.cb-c.ca));`
121. `    assert(m>0);`
122. ` `
123. `    if (n == 1)`
124. `    {`
125. `        C[c.ra][c.ca] += A[a.ra][a.ca] * B[b.ra][b.ca];`
126. `        return;`
127. `    }`
128. ` `
129. `    // Create the 12 smaller matrix indexes:`
130. `    //  A00 A01   B00 B01   C00 C01`
131. `    //  A10 A11   B10 B11   C10 C11`
132. `    for (i = 0; i < 2; i++)`
133. `    {`
134. `        for (j = 0; j < 2; j++)`
135. `        {`
136. `            find_corner(a, i, j, &aii[i][j]);`
137. `            find_corner(b, i, j, &bii[i][j]);`
138. `            find_corner(c, i, j, &cii[i][j]);`
139. `        }`
140. `    }`
141. ` `
142. `    p.ra = p.ca = 0;`
143. `    p.rb = p.cb = m / 2;`
144. ` `
145. `#define LEN(A) (sizeof(A)/sizeof(A[0]))`
146. `    for (i = 0; i < LEN(P); i++)`
147. `        set(P[i], p, 0);`
148. ` `
149. `#define ST0 set(S,p,0); set(T,p,0)`
150. ` `
151. `    // (A00 + A11) * (B00+B11) = S * T = P0`
152. `    ST0;`
153. `    add(A, A, S, aii[0][0], aii[1][1], p);`
154. `    add(B, B, T, bii[0][0], bii[1][1], p);`
155. `    mul(S, T, P[0], p, p, p);`
156. ` `
157. `    // (A10 + A11) * B00 = S * B00 = P1`
158. `    ST0;`
159. `    add(A, A, S, aii[1][0], aii[1][1], p);`
160. `    mul(S, B, P[1], p, bii[0][0], p);`
161. ` `
162. `    // A00 * (B01 - B11) = A00 * T = P2`
163. `    ST0;`
164. `    sub(B, B, T, bii[0][1], bii[1][1], p);`
165. `    mul(A, T, P[2], aii[0][0], p, p);`
166. ` `
167. `    // A11 * (B10 - B00) = A11 * T = P3`
168. `    ST0;`
169. `    sub(B, B, T, bii[1][0], bii[0][0], p);`
170. `    mul(A, T, P[3], aii[1][1], p, p);`
171. ` `
172. `    // (A00 + A01) * B11 = S * B11 = P4`
173. `    ST0;`
174. `    add(A, A, S, aii[0][0], aii[0][1], p);`
175. `    mul(S, B, P[4], p, bii[1][1], p);`
176. ` `
177. `    // (A10 - A00) * (B00 + B01) = S * T = P5`
178. `    ST0;`
179. `    sub(A, A, S, aii[1][0], aii[0][0], p);`
180. `    add(B, B, T, bii[0][0], bii[0][1], p);`
181. `    mul(S, T, P[5], p, p, p);`
182. ` `
183. `    // (A01 - A11) * (B10 + B11) = S * T = P6`
184. `    ST0;`
185. `    sub(A, A, S, aii[0][1], aii[1][1], p);`
186. `    add(B, B, T, bii[1][0], bii[1][1], p);`
187. `    mul(S, T, P[6], p, p, p);`
188. ` `
189. `    // P0 + P3 - P4 + P6 = S - P4 + P6 = T + P6 = C00`
190. `    add(P[0], P[3], S, p, p, p);`
191. `    sub(S, P[4], T, p, p, p);`
192. `    add(T, P[6], C, p, p, cii[0][0]);`
193. ` `
194. `    // P2 + P4 = C01`
195. `    add(P[2], P[4], C, p, p, cii[0][1]);`
196. ` `
197. `    // P1 + P3 = C10`
198. `    add(P[1], P[3], C, p, p, cii[1][0]);`
199. ` `
200. `    // P0 + P2 - P1 + P5 = S - P1 + P5 = T + P5 = C11`
201. `    add(P[0], P[2], S, p, p, p);`
202. `    sub(S, P[1], T, p, p, p);`
203. `    add(T, P[5], C, p, p, cii[1][1]);`
204. ` `
205. `}`
206. `int main()`
207. `{`
208. `    mat A, B, C;`
209. `    corners ai = { 0, N, 0, N };`
210. `    corners bi = { 0, N, 0, N };`
211. `    corners ci = { 0, N, 0, N };`
212. `    srand(time(0));`
213. `    // identity(A,bi); identity(B,bi);`
214. `    // set(A,ai,2); set(B,bi,2);`
215. `    randk(A, ai, 0, 2);`
216. `    randk(B, bi, 0, 2);`
217. `    print(A, ai, "A");`
218. `    print(B, bi, "B");`
219. `    set(C, ci, 0);`
220. `    // add(A,B,C, ai, bi, ci);`
221. `    mul(A, B, C, ai, bi, ci);`
222. `    print(C, ci, "C");`
223. `    return 0;`
224. `}`

Output:

```\$ g++ StrassenMulitplication.cpp
\$ a.out

A = {
1.2, 0.83, 0.39, 0.41,
1.8,  1.9, 0.49, 0.23,
0.38, 0.72,  1.8,  1.9,
0.13,  1.8, 0.48, 0.82,
}
B = {
1.2,  1.6,  1.4,  1.6,
0.27, 0.63,  0.3, 0.79,
0.58,  1.2,  1.1, 0.07,
2,  1.9, 0.47, 0.47,
}
C = {
2.7,  3.7,  2.6,  2.9,
3.4,    5,  3.7,  4.5,
5.3,  6.7,  3.6,  2.2,
2.5,  3.5,  1.6,  2.1,
}```

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