Question
In a common backtracking approach to generate
permutations of a string, elements are swapped to explore different arrangements. Complete the line that swaps characters s[index] and s[i] def recurPermute(index, s, ans):   if index == len(s):     ans.append("".join(s))     return   for i in range(index, len(s)):     s[index], s[i] = _________ # Line to complete (swap)     recurPermute(index + 1, s, ans)     s[index], s[i] = _________ # Line to complete (backtrack swap)Solution
• Concept: Generating permutations using backtracking often involves swapping elements to explore different arrangements. After a recursive call returns, the swap needs to be undone (backtracked) to restore the array to its previous state for other branches of the recursion. • Code Analysis: o The for loop iterates from index to len(s)-1. o Inside the loop, s[index] is swapped with s[i] to place a different character at the current index position. o After the recursive call recurPermute(index + 1, s, ans), the swap needs to be reversed. • Explanation of Correct Answer (A): s[i], s[index] (for both lines) o The Pythonic way to swap two variables a and b is a, b = b, a. o To swap s[index] and s[i], the correct syntax is s[index], s[i] = s[i], s[index]. This line is used both for the initial swap before the recursive call and for the backtracking swap after the recursive call to restore the array.
I. 6y2 – 23y + 20 = 0
II. 4x2 – 24 x + 35 = 0
The quadratic equation (p + 1)x 2 - 8(p + 1)x + 8(p + 16) = 0 (where p ≠-1) has equal roots. find the value of p.
I. 56x² - 99x + 40 = 0
II. 8y² - 30y + 25 = 0
I. 2x² - 7x + 3 = 0
II. 8y² - 14y + 5 = 0
I. x2Â - 9x - 52 = 0
II. y2Â - 16y + 63 = 0
I. y² + y – 56 = 0
II. 2x² + 11 x – 40 = 0
I. 2p2 + 25p – 13 = 0
II. 2q2 – 19q = 2q + 23
I. 2x² - 9x + 10 = 0
II. 3y² + 11y + 6 = 0
I. x2 + 24x + 143 = 0
II. y2 + 12y + 35 = 0
I. x2 – 13x + 36 = 0
II. 3y2 – 29y + 18 = 0