bottom up approach to calculate score
public static double score ( int n , Vector < Integer > A , int k ) { if ( memo [ n ] [ k ] > 0 ) return memo [ n ] [ k ] ; double sum = 0 ; for ( int i = n - 1 ; i > 0 ; i -- ) { sum += A . elementAt ( i ) ; memo [ n ] [ k ] = Math . max ( memo [ n ] [ k ] , score ( i , A , k - 1 ) + sum / ( n - i ) ) ; } return memo [ n ] [ k ] ; } public static double largestSumOfAverages ( Vector < Integer > A , int K ) { int n = A . size ( ) ; double sum = 0 ; for ( int i = 0 ; i < memo . length ; i ++ ) { for ( int j = 0 ; j < memo [ i ] . length ; j ++ ) memo [ i ] [ j ] = 0.0 ; } for ( int i = 0 ; i < n ; i ++ ) { sum += A . elementAt ( i ) ;