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Added Strassen's Algorithm for matrix multiplication #132

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Added Strassen's Algorithm for matrix multiplication #132

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182 changes: 182 additions & 0 deletions C++/Strassen's_Algorithm.cpp
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Original file line number Diff line number Diff line change
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#include <bits/stdc++.h>
using namespace std;

#define ROW_1 4
#define COL_1 4

#define ROW_2 4
#define COL_2 4

void print(string display, vector<vector<int> > matrix,
int start_row, int start_column, int end_row,
int end_column)
{
cout << endl << display << " =>" << endl;
for (int i = start_row; i <= end_row; i++) {
for (int j = start_column; j <= end_column; j++) {
cout << setw(10);
cout << matrix[i][j];
}
cout << endl;
}
cout << endl;
return;
}

vector<vector<int> >
add_matrix(vector<vector<int> > matrix_A,
vector<vector<int> > matrix_B, int split_index,
int multiplier = 1)
{
for (auto i = 0; i < split_index; i++)
for (auto j = 0; j < split_index; j++)
matrix_A[i][j]
= matrix_A[i][j]
+ (multiplier * matrix_B[i][j]);
return matrix_A;
}

vector<vector<int> >
multiply_matrix(vector<vector<int> > matrix_A,
vector<vector<int> > matrix_B)
{
int col_1 = matrix_A[0].size();
int row_1 = matrix_A.size();
int col_2 = matrix_B[0].size();
int row_2 = matrix_B.size();

if (col_1 != row_2) {
cout << "\nError: The number of columns in Matrix "
"A must be equal to the number of rows in "
"Matrix B\n";
return {};
}

vector<int> result_matrix_row(col_2, 0);
vector<vector<int> > result_matrix(row_1,
result_matrix_row);

if (col_1 == 1)
result_matrix[0][0]
= matrix_A[0][0] * matrix_B[0][0];
else {
int split_index = col_1 / 2;

vector<int> row_vector(split_index, 0);

vector<vector<int> > a00(split_index, row_vector);
vector<vector<int> > a01(split_index, row_vector);
vector<vector<int> > a10(split_index, row_vector);
vector<vector<int> > a11(split_index, row_vector);
vector<vector<int> > b00(split_index, row_vector);
vector<vector<int> > b01(split_index, row_vector);
vector<vector<int> > b10(split_index, row_vector);
vector<vector<int> > b11(split_index, row_vector);

for (auto i = 0; i < split_index; i++)
for (auto j = 0; j < split_index; j++) {
a00[i][j] = matrix_A[i][j];
a01[i][j] = matrix_A[i][j + split_index];
a10[i][j] = matrix_A[split_index + i][j];
a11[i][j] = matrix_A[i + split_index]
[j + split_index];
b00[i][j] = matrix_B[i][j];
b01[i][j] = matrix_B[i][j + split_index];
b10[i][j] = matrix_B[split_index + i][j];
b11[i][j] = matrix_B[i + split_index]
[j + split_index];
}

vector<vector<int> > p(multiply_matrix(
a00, add_matrix(b01, b11, split_index, -1)));
vector<vector<int> > q(multiply_matrix(
add_matrix(a00, a01, split_index), b11));
vector<vector<int> > r(multiply_matrix(
add_matrix(a10, a11, split_index), b00));
vector<vector<int> > s(multiply_matrix(
a11, add_matrix(b10, b00, split_index, -1)));
vector<vector<int> > t(multiply_matrix(
add_matrix(a00, a11, split_index),
add_matrix(b00, b11, split_index)));
vector<vector<int> > u(multiply_matrix(
add_matrix(a01, a11, split_index, -1),
add_matrix(b10, b11, split_index)));
vector<vector<int> > v(multiply_matrix(
add_matrix(a00, a10, split_index, -1),
add_matrix(b00, b01, split_index)));

vector<vector<int> > result_matrix_00(add_matrix(
add_matrix(add_matrix(t, s, split_index), u,
split_index),
q, split_index, -1));
vector<vector<int> > result_matrix_01(
add_matrix(p, q, split_index));
vector<vector<int> > result_matrix_10(
add_matrix(r, s, split_index));
vector<vector<int> > result_matrix_11(add_matrix(
add_matrix(add_matrix(t, p, split_index), r,
split_index, -1),
v, split_index, -1));

for (auto i = 0; i < split_index; i++)
for (auto j = 0; j < split_index; j++) {
result_matrix[i][j]
= result_matrix_00[i][j];
result_matrix[i][j + split_index]
= result_matrix_01[i][j];
result_matrix[split_index + i][j]
= result_matrix_10[i][j];
result_matrix[i + split_index]
[j + split_index]
= result_matrix_11[i][j];
}

a00.clear();
a01.clear();
a10.clear();
a11.clear();
b00.clear();
b01.clear();
b10.clear();
b11.clear();
p.clear();
q.clear();
r.clear();
s.clear();
t.clear();
u.clear();
v.clear();
result_matrix_00.clear();
result_matrix_01.clear();
result_matrix_10.clear();
result_matrix_11.clear();
}
return result_matrix;
}

int main()
{
vector<vector<int> > matrix_A = { { 1, 1, 1, 1 },
{ 2, 2, 2, 2 },
{ 3, 3, 3, 3 },
{ 2, 2, 2, 2 } };

print("Array A", matrix_A, 0, 0, ROW_1 - 1, COL_1 - 1);

vector<vector<int> > matrix_B = { { 1, 1, 1, 1 },
{ 2, 2, 2, 2 },
{ 3, 3, 3, 3 },
{ 2, 2, 2, 2 } };

print("Array B", matrix_B, 0, 0, ROW_2 - 1, COL_2 - 1);

vector<vector<int> > result_matrix(
multiply_matrix(matrix_A, matrix_B));

print("Result Array", result_matrix, 0, 0, ROW_1 - 1,
COL_2 - 1);
}

// Time Complexity: T(N) = 7T(N/2) + O(N^2) => O(N^Log7)
// which is approximately O(N^2.8074)
// Code Contributed By:Heeba Khan