$1.$ Fill in the blanks below.

$($a$)$ The principle followed by a queue is $($FIFO$/$LIFO$).$

$($b$)$ The data structure used for recursive calls in a program is the $($queue$/$stack$).$

$($c$)$ Given the input sequence ABCDEFG, when it can be transformed into BCAFEGD through stack operations, the sequence of stack operations is

$($Use O represents pop and I represents push, such as 'IOIOIO...$\text{'}).$

$($d$)$ Assuming the initial state of stack S is empty, and elements e$1,$ e$2,$ e$3,$ e$4,$ e$5,$ and $\backslash ($ e $6\backslash )$ are pushed onto stack $\backslash ($ S $\backslash )$ in order, If the final sequence of elements popped from the stack is e $\backslash (2,\backslash$mathrm$\{$e$\}4,\backslash$mathrm$\{$e$\}3,\backslash$mathrm$\{$e$\}6,\backslash$mathrm$\{$e$\}5,\backslash$mathrm$\{$e$\}1\backslash ),$ then the capacity of stack S must be at least

$($e$)$ A good hash function should produce outputs that are distributed across the available hash values.

$($a$$