Case1 . Perform a Add operation on ( i - 1 ) - copy string , Case2 . Perform a type 2 operation on ( ( i + 1 ) / 2 ) - copy string
$ dp [ $ i ] = min ( $ dp [ $ i - 1 ] + $ x , $ dp [ ( $ i + 1 ) / 2 ] + $ y + $ x ) ; } else {