(20 points) Let A[1::n] be an array of distinct positive integers, and let t be a positive integer. (a) (10 points) Assuming that A is sorted, show that in O(n) time it can be decided if A contains two distinct elements x and y such that x + y = t. (b) (10 points) Use part (a) to show that the following problem, re- ferred to as the 3-Sum problem, can be solved in O(n2) time: 3-Sum Given an array A[1::n] of distinct positive integers, and a positive integer t, determine whether or not there are three distinct elements x, y, z in A such that x+y+z = t.

3. (6 pts) internally in the computer, with few exceptions, all numerical computation is done using binary numbers. output, however, often uses ascii, which is formed by appending 011 to the left of a bcd code. thus, an algorithm that directly converts a binary integer to a bcd integer is very useful. here is one such algorithm 1) draw lines to the left of the binary number to bound the expected bcd decades. (each decade is a group of 4 bits.) move the binary number one bit to the left. add 0011 to each bcd decade containing a binary value> 0100 repeat steps 2-3 until the last bit in the binary number has been moved into the least significant decade position. (note that when the last bit has been shifted into bcd decade, step 3 is not repeated.) read the bcd result. 2) 3) 4) 5) a) execute the algorithm for the binary number 1101101 b) execute the algorithm for the binary number 01110101110 4. (4 pts) represent the decimal number 3568 in bcd; excess-3 code; ascil; and hex.

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What is the primary difference between the header section of a document and the body? a. the body is displayed on the webpage and the header is not. b. the header is displayed on the webpage and the body is not. c. the tag for the body is self-closing, but the tags for the headers must be closed. d. the tag for the header is self closing, but the tag for the body must be closed.