You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
65 lines
2.1 KiB
C++
65 lines
2.1 KiB
C++
#include<stdio.h>
|
|
#include<limits.h>
|
|
#include<iostream>
|
|
|
|
using namespace std;
|
|
|
|
// Matrix Ai has dimension p[i-1] x p[i] for i = 1..n
|
|
|
|
int MatrixChainOrder(int p[], int n)
|
|
{
|
|
/* For simplicity of the program, one extra row and one extra column are
|
|
allocated in m[][]. 0th row and 0th column of m[][] are not used */
|
|
int m[n][n];
|
|
int s[n][n];
|
|
int i, j, k, L, q;
|
|
/* m[i,j] = Minimum number of scalar multiplications needed to compute
|
|
the matrix A[i]A[i+1]...A[j] = A[i..j] where dimention of A[i] is
|
|
p[i-1] x p[i] */
|
|
// cost is zero when multiplying one matrix.
|
|
for (i = 1; i < n; i++)
|
|
m[i][i] = 0;
|
|
// L is chain length.
|
|
for (L = 2; L < n; L++)
|
|
{
|
|
for (i = 1; i <= n - L + 1; i++)
|
|
{
|
|
j = i + L - 1;
|
|
m[i][j] = INT_MAX;
|
|
for (k = i; k <= j - 1; k++)
|
|
{
|
|
// q = cost/scalar multiplications
|
|
q = m[i][k] + m[k + 1][j] + p[i - 1] * p[k] * p[j];
|
|
if (q < m[i][j])
|
|
{
|
|
m[i][j] = q;
|
|
s[i][j] = k;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return m[1][n - 1];
|
|
}
|
|
int main()
|
|
{
|
|
cout
|
|
<< "Enter the array p[], which represents the chain of matrices such that the ith matrix Ai is of dimension p[i-1] x p[i]";
|
|
cout << "Enter the total length:";
|
|
int n;
|
|
cin >> n;
|
|
int array[n];
|
|
cout << "Enter the dimensions: ";
|
|
for (int var = 0; var < n; ++var)
|
|
{
|
|
cin >> array[var];
|
|
}
|
|
cout << "Minimum number of multiplications is: " << MatrixChainOrder(array,
|
|
n);
|
|
return 0;
|
|
}
|
|
|
|
/*
|
|
|
|
Enter the array p[], which represents the chain of matrices such that the ith matrix Ai is of dimension p[i-1] x p[i]Enter the total length:4
|
|
Enter the dimensions: 2 4 3 5
|
|
Minimum number of multiplications is: 54
|