Solve the first order linear recurrence relation: $F_n=5F_{n-1}+4$ with the initial value

$F_0=0$

Solution:

Given $8$ elements: $\{x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8\},$ with the last element as the pivot,

we do a standard partition operation. What is the maximum number of swap op$-$

erations we may have?

Ans:

Given a heap with $n$ nodes, if we know that there are $72$ nodes with height $2$ in this

heap, what are the possible values you can take for $n?$

Ans:

Given a max$-$heap whose values correspond to the array indices from $1$ through

$2024,$ what is the smallest possible index for a node with height $2$ in the heap?

Ans: