Suppose that we want to multiply 500 matrices and we use the optimal parenthesization computed by the MATRIX-CHAIN-ORDER function discussed in class. After finding the optimal parenthesization, how many pairs of round brackets ( ) are printed by the procedure PRINT-OPTIMAL-PARENS(s, 1, 500)? a. 249
b. 501
c. 251
d. 250
e. 499
f. 500

)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).

Terri needs to insert a cover page into her document. where should she go to access the commands to do so? o insert tab, objects group o insert tab, illustrations group o insert tab, pages group o insert tab, media group submit

The average cost of one year at a private college in 2012-2013 is $43,289. the average grant aid received by a student at a private college in 2012-2013 is $15,680.   what is the average student contribution for one year at a private college in 2012-2013?