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Bracket_in_MCM
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Bracket_in_MCM
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long long dp[501][501];
int bracket[501][501];
void printString(int i,int j,string &ans)
{
if(i>j)
return;
if(i==j-1 or i==j)
{
ans+='A'+j-1;
return;
}
ans+='(';
printString(i,bracket[i][j],ans);
printString(bracket[i][j],j,ans);
ans+=')';
}
long long recurse(int i,int j,int arr[])
{
if(i==j-1 or i==j)
{
bracket[i][j]=j;
return 0;
}
if(dp[i][j]!=-1)
return dp[i][j];
long long mn=1e18;
int brkpt=0;
for(int k=i+1;k<j;k++)
{
long long val=recurse(i,k,arr)+recurse(k,j,arr)+arr[i]*arr[k]*arr[j];
if(val<=mn)
{
mn=val;
brkpt=k;
}
}
bracket[i][j]=brkpt;
return dp[i][j]=mn;
}
string matrixChainOrder(int p[], int n)
{
memset(dp,-1,sizeof(dp));
long long x=recurse(0,n-1,p);
string ans="";
printString(0,n-1,ans);
return ans;
}