In a complete binary tree in height =5 what will be th minimum number of nodes at level 5 ? What will be the index of leaf node in a right-skewd binary tree with height =7,where every parent has at most one child?​

)a grad student comes up with the following algorithm to sort an array a[1..n] that works by first sorting the first 2/3rds of the array, then sorting the last 2/3rds of the (resulting) array, and finally sorting the first 2/3rds of the new array. 1: function g-sort(a, n) . takes as input an array of n numbers, a[1..n] 2: g-sort-recurse(a, 1, n) 3: end function 4: function g-sort-recurse(a, `, u) 5: if u ⒠` ≤ 0 then 6: return . 1 or fewer elements already sorted 7: else if u ⒠` = 1 then . 2 elements 8: if a[u] < a[`] then . swap values 9: temp ↠a[u] 10: a[u] ↠a[`] 11: a[`] ↠temp 12: end if 13: else . 3 or more elements 14: size ↠u ⒠` + 1 15: twothirds ↠d(2 ◠size)/3e 16: g-sort-recurse(a, `, ` + twothirds ⒠1) 17: g-sort-recurse(a, u ⒠twothirds + 1, u) 18: g-sort-recurse(a, `, ` + twothirds ⒠1) 19: end if 20: end function first (5 pts), prove that the algorithm correctly sorts the numbers in the array (in increasing order). after showing that it correctly sorts 1 and 2 element intervals, you may make the (incorrect) assumption that the number of elements being passed to g-sort-recurse is always a multiple of 3 to simplify the notation (and drop the floors/ceilings).

Which component acts as a platform on which application software runs

Jason, samantha, ravi, sheila, and ankit are preparing for an upcoming marathon. each day of the week, they run a certain number of miles and write them into a notebook. at the end of the week, they would like to know the number of miles run each day, the total miles for the week, and average miles run each day. write a program to them analyze their data. your program must contain parallel arrays: an array to store the names of the runners and a two-dimensional array of five rows and seven columns to store the number of miles run by each runner each day. furthermore, your program must contain at least the following functions: a function to read and store the runners’ names and the numbers of miles run each day; a function to find the total miles run by each runner and the average number of miles run each day; and a function to output the results. (you may assume that the input data is stored in a file and each line of data is in the following form: runnername milesday1 milesday2 milesday3 milesday4 milesday5 milesday6 milesday7.)