This problem pertains to Merkle trees in blockchain systems. Let there be a bitcoin full node

which wants to efficiently verify whether a transaction is there in any of the blocks. The steps

progress as shown below. Note that B is a new block with block header H and transactions T$,$ the

hash value is denoted as h and t is any transaction in the set T$.$ Complete the algorithm. Use the

exact hash algorithm name wherever applicable.

$1.$ Compute h $=\_\_\_\_,$ verifies the proof$-$of$-$work in $\_\_\_\_$ and checks the timestamp in $\_\_\_\_$

$2.$ For each transaction t $\backslash$in $\_\_\_\_,$ verifies t$$s signature$($s$),$ verifies that $\_\_\_\_$ does not double

spend, and appends t as the rightmost leaf of the current block$$s $\_\_\_\_$

$3.$ After all t have been verified and appended, computes and stores the interior node hashes

and the root hash r in the form of a $\_\_\_\_\_$

$4.$ Verify that the computed root hash equals the root hash in the block header $\_\_\_\_$