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| 1 | +#include <climits> |
| 2 | +#include <iostream> |
| 3 | +using namespace std; |
| 4 | + |
| 5 | +#define MAX 10 |
| 6 | + |
| 7 | +// dp table to store the solution for already computed sub problems |
| 8 | +int dp[MAX][MAX]; |
| 9 | + |
| 10 | +// Function to find the most efficient way to multiply the given sequence of |
| 11 | +// matrices |
| 12 | +int MatrixChainMultiplication(int dim[], int i, int j) { |
| 13 | + // base case: one matrix |
| 14 | + if (j <= i + 1) |
| 15 | + return 0; |
| 16 | + |
| 17 | + // stores minimum number of scalar multiplications (i.e., cost) |
| 18 | + // needed to compute the matrix M[i+1]...M[j] = M[i..j] |
| 19 | + int min = INT_MAX; |
| 20 | + |
| 21 | + // if dp[i][j] is not calculated (calculate it!!) |
| 22 | + |
| 23 | + if (dp[i][j] == 0) { |
| 24 | + // take the minimum over each possible position at which the |
| 25 | + // sequence of matrices can be split |
| 26 | + |
| 27 | + for (int k = i + 1; k <= j - 1; k++) { |
| 28 | + // recur for M[i+1]..M[k] to get a i x k matrix |
| 29 | + int cost = MatrixChainMultiplication(dim, i, k); |
| 30 | + |
| 31 | + // recur for M[k+1]..M[j] to get a k x j matrix |
| 32 | + cost += MatrixChainMultiplication(dim, k, j); |
| 33 | + |
| 34 | + // cost to multiply two (i x k) and (k x j) matrix |
| 35 | + cost += dim[i] * dim[k] * dim[j]; |
| 36 | + |
| 37 | + if (cost < min) |
| 38 | + min = cost; // store the minimum cost |
| 39 | + } |
| 40 | + dp[i][j] = min; |
| 41 | + } |
| 42 | + |
| 43 | + // return min cost to multiply M[j+1]..M[j] |
| 44 | + return dp[i][j]; |
| 45 | +} |
| 46 | + |
| 47 | +// main function |
| 48 | +int main() { |
| 49 | + // Matrix i has Dimensions dim[i-1] & dim[i] for i=1..n |
| 50 | + // input is 10 x 30 matrix, 30 x 5 matrix, 5 x 60 matrix |
| 51 | + int dim[] = {10, 30, 5, 60}; |
| 52 | + int n = sizeof(dim) / sizeof(dim[0]); |
| 53 | + |
| 54 | + // Function Calling: MatrixChainMultiplications(dimensions_array, starting, |
| 55 | + // ending); |
| 56 | + |
| 57 | + cout << "Minimum cost is " << MatrixChainMultiplication(dim, 0, n - 1) |
| 58 | + << "\n"; |
| 59 | + |
| 60 | + return 0; |
| 61 | +} |
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