Matric chain multiplication

// matrix chain multiplication
// dimensions of matrix are given  [40 ,20 ,30,10,30] // find min cost of multiplication
// 2 X 3 : 3 X6 multiple kara to new matrix  2 X 6 ki bani
// iski cost 2 X3 X6 hogi
// so move a partition and choose them solve them apply a condn
// [40, 20, 30 ,10,30] to Array 1 is 40 X 20 ... array 2 is 20 X 30
// so arr1 X (rest) gives diff result than (arr1 X arr2 ) *(rest)
int dp[100][100];

int mcm(vector<int>arr ,int i, int j){
    if(i>=j) return 0;
    if(dp[i][j]!= -1) return dp[i][j];
    int mn = INT_MAX;
    // arr_i = i-1 X i;
    for(int a=i;a<j;a++){
        int cost = mcm(arr,i,a) + mcm(arr,a+1,j) + arr[i-1]*arr[a]*arr[j] ;
        mn = min(mn,cost);
    }
    dp[i][j] = mn;
    return dp[i][j];
}


int main(){
    int n = arr.size();
    memset(dp,-1,sizeof(dp));
  int ans =   mcm(arr , 1,n-1);
    return ans;
}