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Merge pull request #37 from vAporInside/master
Added Strassen’s Algorithm: CPP
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  • Divide and Conquer/Strassen’s Matrix Multiplication Algorithm/CPP

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‎Divide and Conquer/Strassen’s Matrix Multiplication Algorithm/CPP/Strassen.cpp

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// CPP program to implement Strassen’s Matrix
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// Multiplication Algorithm
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#include <bits/stdc++.h>
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using namespace std;
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typedef long long lld;
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/* Strassen's Algorithm for matrix multiplication
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Complexity: O(n^2.808) */
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inline lld** MatrixMultiply(lld** a, lld** b, int n, int l, int m)
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{
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lld** c = new lld*[n];
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for (int i = 0; i < n; i++)
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c[i] = new lld[m];
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < m; j++) {
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c[i][j] = 0;
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for (int k = 0; k < l; k++) {
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c[i][j] += a[i][k] * b[k][j];
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}
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}
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}
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return c;
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}
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inline lld** Strassen(lld** a, lld** b, int n, int l, int m)
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{
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if (n == 1 || l == 1 || m == 1)
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return MatrixMultiply(a, b, n, l, m);
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lld** c = new lld*[n];
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for (int i = 0; i < n; i++)
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c[i] = new lld[m];
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int adjN = (n >> 1) + (n & 1);
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int adjL = (l >> 1) + (l & 1);
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int adjM = (m >> 1) + (m & 1);
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lld**** As = new lld***[2];
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for (int x = 0; x < 2; x++) {
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As[x] = new lld**[2];
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for (int y = 0; y < 2; y++) {
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As[x][y] = new lld*[adjN];
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for (int i = 0; i < adjN; i++) {
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As[x][y][i] = new lld[adjL];
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for (int j = 0; j < adjL; j++) {
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int I = i + (x & 1) * adjN;
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int J = j + (y & 1) * adjL;
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As[x][y][i][j] = (I < n && J < l) ? a[I][J] : 0;
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}
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}
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}
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}
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lld**** Bs = new lld***[2];
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for (int x = 0; x < 2; x++) {
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Bs[x] = new lld**[2];
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for (int y = 0; y < 2; y++) {
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Bs[x][y] = new lld*[adjN];
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for (int i = 0; i < adjL; i++) {
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Bs[x][y][i] = new lld[adjM];
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for (int j = 0; j < adjM; j++) {
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int I = i + (x & 1) * adjL;
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int J = j + (y & 1) * adjM;
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Bs[x][y][i][j] = (I < l && J < m) ? b[I][J] : 0;
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}
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}
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}
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}
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lld*** s = new lld**[10];
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for (int i = 0; i < 10; i++) {
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switch (i) {
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case 0:
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s[i] = new lld*[adjL];
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for (int j = 0; j < adjL; j++) {
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s[i][j] = new lld[adjM];
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for (int k = 0; k < adjM; k++) {
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s[i][j][k] = Bs[0][1][j][k] - Bs[1][1][j][k];
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}
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}
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break;
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case 1:
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s[i] = new lld*[adjN];
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for (int j = 0; j < adjN; j++) {
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s[i][j] = new lld[adjL];
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for (int k = 0; k < adjL; k++) {
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s[i][j][k] = As[0][0][j][k] + As[0][1][j][k];
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}
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}
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break;
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case 2:
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s[i] = new lld*[adjN];
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for (int j = 0; j < adjN; j++) {
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s[i][j] = new lld[adjL];
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for (int k = 0; k < adjL; k++) {
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s[i][j][k] = As[1][0][j][k] + As[1][1][j][k];
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}
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}
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break;
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case 3:
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s[i] = new lld*[adjL];
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for (int j = 0; j < adjL; j++) {
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s[i][j] = new lld[adjM];
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for (int k = 0; k < adjM; k++) {
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s[i][j][k] = Bs[1][0][j][k] - Bs[0][0][j][k];
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}
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}
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break;
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case 4:
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s[i] = new lld*[adjN];
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for (int j = 0; j < adjN; j++) {
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s[i][j] = new lld[adjL];
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for (int k = 0; k < adjL; k++) {
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s[i][j][k] = As[0][0][j][k] + As[1][1][j][k];
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}
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}
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break;
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case 5:
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s[i] = new lld*[adjL];
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for (int j = 0; j < adjL; j++) {
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s[i][j] = new lld[adjM];
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for (int k = 0; k < adjM; k++) {
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s[i][j][k] = Bs[0][0][j][k] + Bs[1][1][j][k];
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}
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}
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break;
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case 6:
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s[i] = new lld*[adjN];
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for (int j = 0; j < adjN; j++) {
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s[i][j] = new lld[adjL];
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for (int k = 0; k < adjL; k++) {
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s[i][j][k] = As[0][1][j][k] - As[1][1][j][k];
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}
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}
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break;
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case 7:
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s[i] = new lld*[adjL];
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for (int j = 0; j < adjL; j++) {
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s[i][j] = new lld[adjM];
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for (int k = 0; k < adjM; k++) {
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s[i][j][k] = Bs[1][0][j][k] + Bs[1][1][j][k];
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}
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}
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break;
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case 8:
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s[i] = new lld*[adjN];
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for (int j = 0; j < adjN; j++) {
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s[i][j] = new lld[adjL];
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for (int k = 0; k < adjL; k++) {
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s[i][j][k] = As[0][0][j][k] - As[1][0][j][k];
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}
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}
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break;
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case 9:
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s[i] = new lld*[adjL];
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for (int j = 0; j < adjL; j++) {
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s[i][j] = new lld[adjM];
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for (int k = 0; k < adjM; k++) {
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s[i][j][k] = Bs[0][0][j][k] + Bs[0][1][j][k];
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}
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}
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break;
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}
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}
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lld*** p = new lld**[7];
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p[0] = Strassen(As[0][0], s[0], adjN, adjL, adjM);
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p[1] = Strassen(s[1], Bs[1][1], adjN, adjL, adjM);
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p[2] = Strassen(s[2], Bs[0][0], adjN, adjL, adjM);
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p[3] = Strassen(As[1][1], s[3], adjN, adjL, adjM);
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p[4] = Strassen(s[4], s[5], adjN, adjL, adjM);
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p[5] = Strassen(s[6], s[7], adjN, adjL, adjM);
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p[6] = Strassen(s[8], s[9], adjN, adjL, adjM);
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for (int i = 0; i < adjN; i++) {
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for (int j = 0; j < adjM; j++) {
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c[i][j] = p[4][i][j] + p[3][i][j] - p[1][i][j] + p[5][i][j];
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if (j + adjM < m)
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c[i][j + adjM] = p[0][i][j] + p[1][i][j];
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if (i + adjN < n)
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c[i + adjN][j] = p[2][i][j] + p[3][i][j];
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if (i + adjN < n && j + adjM < m)
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c[i + adjN][j + adjM] = p[4][i][j] + p[0][i][j] - p[2][i][j] - p[6][i][j];
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}
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}
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for (int x = 0; x < 2; x++) {
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for (int y = 0; y < 2; y++) {
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for (int i = 0; i < adjN; i++) {
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delete[] As[x][y][i];
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}
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delete[] As[x][y];
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}
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delete[] As[x];
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}
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delete[] As;
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for (int x = 0; x < 2; x++) {
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for (int y = 0; y < 2; y++) {
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for (int i = 0; i < adjL; i++) {
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delete[] Bs[x][y][i];
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}
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delete[] Bs[x][y];
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}
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delete[] Bs[x];
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}
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delete[] Bs;
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for (int i = 0; i < 10; i++) {
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switch (i) {
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case 0:
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case 3:
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case 5:
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case 7:
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case 9:
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for (int j = 0; j < adjL; j++) {
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delete[] s[i][j];
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}
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break;
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case 1:
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case 2:
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case 4:
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case 6:
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case 8:
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for (int j = 0; j < adjN; j++) {
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delete[] s[i][j];
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}
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break;
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}
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delete[] s[i];
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}
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delete[] s;
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for (int i = 0; i < 7; i++) {
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for (int j = 0; j < (n >> 1); j++) {
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delete[] p[i][j];
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}
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delete[] p[i];
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}
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delete[] p;
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return c;
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}
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int main()
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{
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lld** matA;
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matA = new lld*[2];
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for (int i = 0; i < 2; i++)
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matA[i] = new lld[3];
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matA[0][0] = 1;
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matA[0][1] = 2;
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matA[0][2] = 3;
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matA[1][0] = 4;
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matA[1][1] = 5;
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matA[1][2] = 6;
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lld** matB;
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matB = new lld*[3];
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for (int i = 0; i < 3; i++)
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matB[i] = new lld[2];
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matB[0][0] = 7;
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matB[0][1] = 8;
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matB[1][0] = 9;
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matB[1][1] = 10;
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matB[2][0] = 11;
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matB[2][1] = 12;
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lld** matC = Strassen(matA, matB, 2, 3, 2);
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for (int i = 0; i < 2; i++) {
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for (int j = 0; j < 2; j++) {
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printf("%lld ", matC[i][j]);
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}
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printf("\n");
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}
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return 0;
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}

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