GATE 2024 DA Q.39: solution and answer

Official answer: CSource: Official answer key, GATE 2024 DA (IISc Bengaluru)

1. The pseudo-code is:

   computeS(X)
   S[1] ← 1
   for i ← 2 to length(X)
      S[i] ← 1
      if X[i-1] ≤ X[i]
            S[i] ← S[i] + S[i-1]
      end if
   end for
   return S

   For each position $i\ge 2$, S[i] is first set to 1. It grows by S[i-1] only when X[i-1] <= X[i]. So S[i] is the length of the run of non-decreasing consecutive elements that ends at position $i$. It restarts at 1 whenever X[i-1] > X[i].

2. Input: $X=[6,3,5,4,10]$ (1-indexed), so length(X) = 5. Start with $S[1]=1$.

3. $i=2$: S[2] = 1. The test X[1] <= X[2] is $6\le 3$, which is false. So $S[2]=1$.

4. $i=3$: S[3] = 1. The test X[2] <= X[3] is $3\le 5$, which is true. So $S[3]=1+S[2]=1+1=2$.

5. $i=4$: S[4] = 1. The test X[3] <= X[4] is $5\le 4$, which is false. So $S[4]=1$.

6. $i=5$: S[5] = 1. The test X[4] <= X[5] is $4\le 10$, which is true. So $S[5]=1+S[4]=1+1=2$.

7. The function returns $S=[1,1,2,1,2]$, which is option (C).