Assume you have an array of numbers, where each value occurs at most twice. We consider sums of contiguous numbers in the array. But we only consider such sums whose two endpoints have the same value. The sum includes the two equal values themselves. So if the two equal numbers are at index i and index j (i < j) in array A, then we sum all the values A[i], A[i + 1], . . . , A[j].

(a) Give an algorithm that finds the maximum such sum. Make your algorithm as efficient as possible. Describe the algorithm briefly in English and in psuedo code.(b) Analyze the running time of your algorithm

:you areto design the controller for alight that functions both as an ordinary light and also as a motion activated light and alarm. a.if the manual switch s is on, then the light l is on. b.besides the manual switch, there is a motion detector, m1, which activatesthis light.c.if motion is detected but the light is on anyway because s is on, only then a secondoutput a, an alarm, is turned on. d.the disable switch, d, disables the motion activated light and alarmbut leaves manual control operation of the light using switch s.(i)read the problem statement and clearly identify the inputs and outputs for the circuit you are designing. (ii)create the truth table for this system; include the light, alarm, switch, disable, and the motion sensor.(iii)draw a schematic of this system.