# include <stdio.h>

# include <conio.h>

# include <stdlib.h>

# define sz 20

# define INF 200000

void print(unsigned long s[][sz], int i, int j)

{

if (i == j)

printf(" A%d ",i);

else

{

printf(" ( ");

print(s, i, s[i][j]);

print(s, s[i][j] + 1, j);

printf(" ) ");

}

void printm(unsigned long m[][sz], int n)

{

int i,j;

for(i=1;i<=n;i++)

{

for(j=1;j<=n;j++)

{

printf("%5d",m[i][j]);

}

printf("\n\n");

}

printf("\nThe No. of multiplication required is : %d",m[1][n]);

}

void Matrix_Chain_Order(int p[],int num)

{

unsigned long m[sz][sz] = {0};

unsigned long s[sz][sz] = {0};

unsigned int q = 0;

int i, j, k, l;

int n = num;

for(i = 1; i <= n; i++)

m[i][i] = 0;

for(l = 2; l <= n; l++)

for(i = 1; i <= (n - l + 1); i++)

{

j = i + l - 1;

m[i][j] = INF;

for(k = i; k <= j - 1; k++)

{

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;

}

print(s, i-1, j);

printf("\n\n");

printf("The Minimum No. of Multiplication Required is:\n\n");

printm(m,n);

}

void main()

{

int i,num=0,p[sz]={0};

clrscr();

printf("Enter the number of matrix : ");

scanf("%d",&num);

printf("Enter %d no. of order sequence for %d matrix :\n",num+1,num);

for(i=0;i<=num;i++)

scanf("%d",&p[i]);

printf("\n\n");

printf("MULTIPLICATION SEQUENCE IS : ");

printf("\n\n\t");

Matrix_Chain_Order(p,num);

getch();

}

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