📄 matrix_multiplication.cpp
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#include<string.h>
#include<stdio.h>
#define MAX 21
int p[MAX],ptr;
int m[MAX][MAX];
int s[MAX][MAX];
void prnt(int i, int j)
{
if (i == j) {
printf("A%d",i);
return;
}
else if (i < j) {
printf("(");
prnt(i,s[i][j]);
printf(" x ");
prnt(s[i][j]+1,j);
printf(")");
}
return;
}
int main()
{
int N,temp_N,T;
int hang,lie;
int i,j,k,r,t;
T = 0;
while (scanf("\n%d",&N) !=EOF) {
if (N == 0)
break;
T ++;
temp_N = N; ptr = 0;
while (temp_N--) {
scanf("\n%d %d",&hang,&lie);
if (N-1 == temp_N) {
p[ptr++] = hang;p[ptr++] = lie;
}
else p[ptr++] = lie;
}
for (i = 1;i <= N;i ++)
m[i][i] = 0;
for (r = 2;r <= N; r++) {
for (i = 1;i <= N - r+1;i ++) {
j = i + r - 1;
m[i][j] = m[i+1][j] + p[i-1]*p[i]*p[j];
s[i][j] = i;
for (k = i + 1; k < j; k++) {
t = m[i][k] + m[k+1][j] + p[i-1] * p[k] * p[j];
if (t < m[i][j]) {
m[i][j] = t;
s[i][j] = k;
}
}
}
}
printf("Case %d: ",T);
prnt(1,N);
printf("\n");
}
return 0;
}
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