GATE CS 2025 Set 1 Q53 — Programming in C

Let's trace the execution of the function gate(14362) step-by-step:

Step 1: Determine the initial value of $t$
The first while (n >= t) loop finds the smallest power of $10$ greater than $n$. For $n = 14362$, the loop terminates when $t = 100000$.
After the loop, t /= 10; sets $t = 10000$.

Step 2: Extract digits and construct newnum
The second while (t > 0) loop extracts the digits of $n$ from left to right (most significant to least significant) and alternates selecting them using the turn flag:

• Iteration 1:
  • $d = 14362 / 10000 = 1$, $n = 14362 \% 10000 = 4362$, $t = 1000$.
  • Since turn == 0, newnum remains $0$.
  • turn becomes $(0 + 1) \% 2 = 1$.
• Iteration 2:
  • $d = 4362 / 1000 = 4$, $n = 4362 \% 1000 = 362$, $t = 100$.
  • Since turn == 1, newnum = 10 * 0 + 4 = 4.
  • turn becomes $(1 + 1) \% 2 = 0$.
• Iteration 3:
  • $d = 362 / 100 = 3$, $n = 362 \% 100 = 62$, $t = 10$.
  • Since turn == 0, newnum remains $4$.
  • turn becomes $(0 + 1) \% 2 = 1$.
• Iteration 4:
  • $d = 62 / 10 = 6$, $n = 62 \% 10 = 2$, $t = 1$.
  • Since turn == 1, newnum = 10 * 4 + 6 = 46.
  • turn becomes $(1 + 1) \% 2 = 0$.
• Iteration 5:
  • $d = 2 / 1 = 2$, $n = 2 \% 1 = 0$, $t = 0$.
  • Since turn == 0, newnum remains $46$.
  • turn becomes $(0 + 1) \% 2 = 1$.

The loop terminates because $t = 0$. The function returns newnum, which is 46.