Practice Question (Gate 1994)

AI Summary

An AI-generated summary of this video lecture.

The video features a lecture on data structures, specifically focusing on a GATE 1994 problem about stack permutations. The problem asks which of the given output sequences can be generated from the input sequence 1, 2, 3, 4, 5 using a single stack. The instructor systematically evaluates four options: (a) 3, 4, 5, 1, 2; (b) 3, 4, 5, 2, 1; (c) 1, 5, 2, 3, 4; and (d) 5, 4, 3, 1, 2. He uses a visual representation of a stack to trace the necessary push and pop operations for each case, demonstrating the Last In First Out (LIFO) property.

Chapters

1. 0:00 – 2:00 00:00-02:00

   The instructor starts by reading the question and drawing a stack diagram. He analyzes option (a) 3, 4, 5, 1, 2. To output 3, he pushes 1, 2, 3 and pops 3. To output 4, he pushes 4 and pops 4. To output 5, he pushes 5 and pops 5. At this point, the stack contains 1 and 2, with 2 at the top. Since the next required output is 1, but 2 is blocking it, he marks option (a) as incorrect. He then analyzes option (b) 3, 4, 5, 2, 1. He performs the same pushes for 3, 4, and 5. After popping 5, the stack has 1 and 2. He pops 2, then pops 1, successfully matching the sequence. He marks option (b) as correct. He briefly checks option (c) 1, 5, 2, 3, 4, showing that after popping 5, the stack has 2, 3, 4, making it impossible to pop 2 next.

2. 2:00 – 2:35 02:00-02:35

   The instructor concludes the analysis by checking option (d) 5, 4, 3, 1, 2. He pushes 1 through 5, pops 5, 4, 3. The stack now contains 1 and 2. The next required output is 1, but 2 is on top. He crosses out option (d). He confirms that option (b) is the only valid permutation. He reiterates the core concept that a stack follows the Last In First Out (LIFO) principle, meaning elements must be popped in reverse order of their insertion if they are waiting in the stack.

The lecture effectively demonstrates how to validate stack permutations by simulating the push and pop operations. The key takeaway is that for any valid stack permutation, if an element is pushed onto the stack, it must be popped before any elements pushed after it can be popped. This LIFO constraint is the primary filter used to eliminate invalid options like (a), (c), and (d), leaving (b) as the correct answer.