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    Dynamic Programming and Sequence Processing PYQs for GATE DA

    Solve 1+ Dynamic Programming and Sequence Processing previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

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    Question 1
    2024 PYQ
    Level 3: Exam Standard
    Consider the function computeS(X) whose pseudocode is given below:

    computeS(X)

    for to

    if

    end if
    end for
    return S

    Which ONE of the following values is returned by the function computeS(X)
    for X = [6, 3, 5, 4, 10]?
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    Dynamic Programming and Sequence Processing PYQs for GATE DA

    Solve 1+ Dynamic Programming and Sequence Processing previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

    Chapter Roadmap: Dynamic Programming and Sequence Processing

    Chapter Roadmap

    Your journey to mastering sequence-based dynamic programming.

    1. Consecutive Sequence Lengths

    Finding the longest contiguous subarray satisfying a condition.

    2. Subsequence Lengths

    Tackling non-contiguous sequences like LIS and LCS.

    3. Advanced Variations

    Matrix chain multiplication, edit distance, and complex states.

    What you will master

    • Defining precise DP states for sequence problems.
    • Formulating correct recurrence relations.
    • Optimizing space complexity from to .
    • Avoiding common traps in boundary conditions.

    Topic Hero: Dynamic Programming for Consecutive Sequence Lengths

    Topic Hero: Consecutive Sequence Lengths

    Focuses on finding the longest contiguous segment that satisfies a specific condition.

    Extend

    If condition met with previous element, add to previous segment.

    Reset

    If condition broken, start a new segment of length .

    This local decision builds a global solution in time.

    Dynamic Programming and Sequence Processing: Solved Questions with Step-by-Step Explanations (1 Problems)

    Question 1 · Programming, Data Structures and Algorithms · 2024 MCQ
    Consider the function computeS(X) whose pseudocode is given below:

    computeS(X)

    for to

    if

    end if
    end for
    return S

    Which ONE of the following values is returned by the function computeS(X)
    for X = [6, 3, 5, 4, 10]?
    1. A.

      [1, 1, 2, 3, 4]

    2. B.

      [1, 1, 2, 3, 3]

    3. C.

      [1, 1, 2, 1, 2]

    4. D.

      [1, 1, 2, 1, 5]

    Correct Answer:

    C

    Step-by-Step Solution

    Insight: This is a consecutive sequence DP question where S[i] represents the length of the longest non-decreasing contiguous subarray ending at index i. The pseudocode implements the standard "extend or reset" pattern.

    Exam route: Trace the pseudocode step by step for the given array X = [6, 3, 5, 4, 10].

    Learning route:

    • i=1: S[1] = 1 (base case, single element is always valid).
    • i=2: X[1]=6, X[2]=3. Check 6 <= 3: false. So S[2] remains 1 (reset).
    • i=3: X[2]=3, X[3]=5. Check 3 <= 5: true. So S[3] = 1 + S[2] = 1 + 1 = 2 (extend).
    • i=4: X[3]=5, X[4]=4. Check 5 <= 4: false. So S[4] remains 1 (reset).
    • i=5: X[4]=4, X[5]=10. Check 4 <= 10: true. So S[5] = 1 + S[4] = 1 + 1 = 2 (extend).

    Final array: S = [1, 1, 2, 1, 2].

    Verification: The longest non-decreasing contiguous subarrays ending at each index are: [6] (length 1), [3] (length 1), [3, 5] (length 2), [4] (length 1), [4, 10] (length 2). This matches S = [1, 1, 2, 1, 2].

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