$ g++ OptimalParanthesizationDP.cpp $ a.out 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
Users Online
· Guests Online: 92
· Members Online: 0
· Total Members: 188
· Newest Member: meenachowdary055
· Members Online: 0
· Total Members: 188
· Newest Member: meenachowdary055
Forum Threads
Newest Threads
No Threads created
Hottest Threads
No Threads created
Latest Articles
Articles Hierarchy
C++ Program to Perform Optimal Parenthesize using Dynamic Programming
C++ Program to Perform Optimal Parenthesize using Dynamic Programming
This is a C++ Program to perform optimal paranthesization using DP.
Here is source code of the C++ Program to Perform Optimal Paranthesization Using Dynamic Programming. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.
-
#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;
-
}
Output:
Comments
No Comments have been Posted.
Post Comment
Please Login to Post a Comment.