Consider the following 3-PARTITION problem. Given integers a1; : : : ; an, we want to determine whether it is possible to partition of f1; : : : ; ng into three disjoint subsets I; J;K such that X i2I ai = X j2J aj = X k2K ak = 1 3 Xn i=1 ai For example, for input (1; 2; 3; 4; 4; 5; 8) the answer is yes, because there is the partition (1; 8), (4; 5), (2; 3; 4). On the other hand, for input (2; 2; 3; 5) the answer is no. Devise and analyze a dynamic programming algorithm for 3-PARTITION that runs in time polynomial in n and in P i ai.

Write a new lc-3 trap subroutine (i.e. a subroutine that will be invoked via the trap instruction) that will receive a numeric digit entered at the keyboard (i.e. an ascii character), echo it to the screen, and return in r0 the corresponding numeric value: so if the user types the digit '7', the character '7' will appear on the screen, but the value returned in r0 will be b0000 0000 0000 0111 (#7) you may not use any trap calls in your code - you must implement the "polling" code that interrogates the keyboard status and data registers. ; getnum_tsr ; a subroutine for obtaining a numeric value ; given ascii numeric digit input to keyboard. ; the numeric digit is echoed to the console (e.g. '7' = b0000 0000 0011 0111), ; but the value returned in r0 is the actual numeric value ; corresponding to the digit (e.g. b0000 0000 0000 0111 =