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- Algorithms Question Three points P, Q, and R are said to be collinear if they are on a single line. To check whether the 3 points lie on the same line, we use the distance formula. If P, Q and R are three collinear points, then: Distance from P to Q + Distance from Q to R = Distance from P to R PQ + QR = PR The distance between two points (x1, y1) and (x2, y2) is given by Hence, we can easily find the distance between the points P, Q and R, with the help of this formula. Design an algorithm (pseudocode) to check whether three points are collinear. In your solution include the input and the output.Note: Numbers greater then 3,999 require symbols with lines over letters. We can't use these, so use lower case v for 5000 and x for 10000. The first 10 numbers are I II (1+1=2) III (1+1+1=3) IV (5-1=4) V VI (5+1=6) VII (5+2=7) VIII (5+3=8) IX (10-1=9) X This pattern repeats for larger numbers. For example to create 47, we need to figure out 40 first. 4 was IV, there are equivalent 1, 5, and 10 symbols for the tens place. We can determine that 40 is XL since X is 10 and L is 50. We then combine this with 7 from above to get XLVII. Every value can be broken down into this basic 1-9 pattern just using different symbols. (1) Create a function roman(num, one, five, ten) that takes a number between 1 and 9. The function returns a string with the roman representation using the strings given for the one, five, and ten symbols. If a number outside the range is given return the empty string "". For example, Executing roman(4,"X","L","C") should return "XL" (2) Create a function roman_num(num)…We would like to find the minimum number of steps required to get 0 from any number, when you can only subtract a digit present in that number in a single step. For example, if you are given 25. Then you can either subtract 2 or 5 from 25. Let's subtract 5 then we will get 20. Then we can subtract 2 and get 18 and so on. The minimum number of steps to get from 25 to 0 is shown below: 25→20→18→10→9→0. Now you need to write a DP program to find the minimum number of steps to solve the problem for any input. Input range will be from 0 to 999. [Python Implementation]
- Complete the following: p ∨ (q ∧ ¨ r) ≡ p ∨ (¨ r ∧ q) by: _______________________________ ≡ (p ∨ ¨ r) ∧ (p ∨ q) by: _______________________________ ≡ (¨ r ∨ p) ∧ (p ∨ q) by: _______________________________ ≡ (r → p) ∧ (p ∨ q) by: _______________________________To represent an integer value of n in decimal, we need to use ⌈log10(n + 1)⌉ digits . Verify this using n = 35, 1290. Note that for any real number x, ⌈x⌉ is the smallest integer that is greater than x, this means we always round up. For example, ⌈10.3⌉ = 11, ⌈−5.2⌉ = −5. To represent an intege value of n in binary, we need to use ⌈log2(n + 1)⌉ binary digits . Verify this using n = 35, 1290. Use the definition of logarithmic function to show that log2n / log10n = log2102. In this problem, you will write different programs to x n , where x ∈ R, n ∈ N. a) Devise an iterative algorithm to compute x n using only multiplications.
- IN STO a IN STO b test LDA a SUB b BRP count LDA c OUT LDA d OUT HLT count STO a LDA c ADD one STO c LDA d SUB b STO d BR test a DAT b DAT c DAT 0 one DAT 1 d DAT 0 Using this LMC program to solve a÷b=cRd where a = 20 b = 4 what is c and remainder d. IF a = 20 b = 4 c should be 5 and d should be 0. IS there reason to why i keep getting the remainder as 980In the example below, the sum of the fourth powers of each digit that forms the 4-digit numbers gives the number itself: 1634 = 14 + 64 + 34 + 44 8208 = 84 + 24 + 04 + 84 9474 = 94 + 44 + 74 + 44 And sum of these numbers is 1634 + 8208 + 9474 = 19316. Find the sum of all numbers that can be written as the sum of the fifth forces of their numbers. (P.s.: You have to done it by C++)Write a program that calculate the values of (X + Y) x (X – Y) where X, Y = 0, 1, 2, …, 9and prints the following table:X|Y 0 1 2 3 4 5 6 7 8 90| 0 -1 -4 -9 -16 -25 -36 -49 -64 -811| 1 0 -3 -8 -15 -24 -35 -48 -63 -802| 4 3 0 -5 -12 -21 -32 -45 -60 -773| 9 8 5 0 -7 -16 -27 -40 -55 -724| 16 15 12 7 0 -9 -20 -33 -48 -655| 25 24 21 16 9 0 -11 -24 -39 -566| 36 35 32 27 20 11 0 -13 -28 -457| 49 48 45 40 33 24 13 0 -15 -328| 64 63 60 55 48 39 28 15 0 -179| 81 80 77 72 65 56 45 32 17 0
- Q Sum For parts (a)-(e), decide if it is true or false. If the statement is true, then prove it (to prove it you will either need to use the definition and find constants or use the limit laws). If the statement is false, then give a reason or a counterexample a. 10n2 = O(n3). b. n2 ∈ Ω(n3) c. 2n ∈ O(2n+1) d. n! ∈ Θ((n + 1)!) e.√n = O(nsin(n)) Full explain this question very fast solution sent me step by stepPlease solve the running time of the problem below. Please show your solution. See attached photo for the example. int exam_2(int n) { int i, j, sum = 0; if(n==1) { return 1; } for(i=1; i<=n/2; i++) { for(j=1; j<=n; j+=3) { sun += j; } } return sum + exam_2(n/3);}The following function f uses recursion: def f(n): if n <= 1 return n else return f(n-1) + f(n-2) 5 Let n be a valid input, i.e., a natural number. Which of the following functions returns the same result but without recursion? a) def f(n): a <- 0 b <- 1 if n = 0 return a elsif n = 1 return b else for i in 1..n c <- a + b a <- b b <- c return b f(n): a <- 0 i <- n while i > 0 a <- a + i + (i-1) return a f(n): arr[0] <- 0 arr[1] <- 1 if n <= 1 return arr[n] else for i in 2..n arr[i] <- arr[i-1] + arr[i-2] return arr[n] f(n): arr[0..n] <- [0, ..., n] if n <= 1 return arr[n] else a <- 0 for i in 0..n a <- a + arr[i] return a