Array Manipulation and Bit Operations Questions

Covers algorithmic problems that combine array processing with bit level techniques. Topics include traversals, subarray operations, rotation, reversing, finding missing or duplicate elements, and in place modifications under memory constraints. Also includes bit manipulation fundamentals such as bit shifting, bit masking, bitwise exclusive or and bit counting, and how these techniques are applied to solve array problems efficiently for parity checks, toggles, subset computations and low level optimizations. Emphasize time and space complexity trade offs, approaches that achieve linear time and constant or logarithmic extra space, and problem patterns common in embedded systems and systems programming.