Chris recently received an array p as his birthday gift from Joseph, whose elements are either 0 or 1. He wants to use it to generate an infinite long superarray. Here is his strategy: each time, he inverts his array by bits, changing all 0 to 1 and all 1 to 0 to get another array, then concatenate the original array and the inverted array together. For example, if the original array is [0, 1, 1, 0], then the inverted array will be [1, 0, 0, 1] and the new array will be [0, 1, 1, 0, 1, 0, 0, 1]. He wonders what the array will look like after he repeat this many many times. He ask you to help him sort this out. Given the original array pp of length n and two indices ,a, b (≪≪,≪(n≪a≪b,≪ means much less than) Design an algorithm to calculate the sum of elements between a and b of the generated infinite array p^, specifically, ∑≤≤p^∑a≤i≤bpi^. He also wants you to do it real fast, so make sure your algorithm runs less than ()O(b) time.

Required:
Explain your algorithm and analyze its complexity.

Alook-up table used to convert pixel values to output values on a monitor. essentially, all pixels with a value of 190 or above are shown as white (i.e. 255), and all values with a value of 63 or less are shown as black (i.e. 0). in between the pixels are scaled so that a pixel with a value p is converted to a pixel of value 2/127 −+3969). if a pixel has a value of 170 originally, what value will be used to display the pixel on the monitor? if a value of 110 is used to display the pixel on the monitor, what was the original value of the pixel?

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Write a program that displays the following menu: geometry calculator 1. calculate the area of a circle 2. calculate the area of a rectangle 3. calculate the area of a triangle 4. quit enter your choice (1-4): if the user enters 1, the program should ask for the radius of the circle and then display its area. use the following formula: area = ď€(the square of r) use 3.14159 for ď€ and the radius of the circle for r. if the user enters 2, the program should ask for the length and width of the rectangle and then display the rectangle’s area. use the following formula: area = length * width if the user enters 3, the program should ask for the length of the triangle’s base and its height, and then display its area. use the following formula: area = base * height * .5 if the user enters 4, the program should end. input validation: display an error message if the user enters a number outside the range of 1 through 4 when selecting an item from the menu. do not accept negative values for the circle’s radius, the rectangle’s length or width, or the triangle’s base or height. note: if the user enters an improper menu choice (1-4), the program prints "the valid choices are 1 through 4. run the program again and select one of those." if the user enters a negative radius, the program prints "the radius can not be less than zero." if the user enters a negative value for height or base, the program prints "only enter positive values for base and height."