What is the final value of "count" after the pseudocode fragment shown below?

count = 0
For i = 1 to 3
For j = i + 1 to 4
count := count + (j - i)
End-for
End-for

Question

What is the final value of "count" after the pseudocode fragment shown below?

count = 0 
For i = 1 to 3
    For j = i + 1 to 4 
        count := count + (j - i) 
    End-for 
End-for

BlackTom AI · Accepted Answer

The loops compute the sum of (j − i) for all ordered pairs with 1 ≤ i < j ≤ 4.

1. Relevant knowledge points and concepts
- Nested loops iterate over i and j; j runs from i+1 to 4 inclusive.
- count accumulates positive integers (j − i) for each pair (i, j) with i < j.
- You can evaluate by explicit enumeration or by using a small combinatorial summation.

2. Complete step-by-step reasoning
Start with count = 0. Run i from 1 to 3.

- For i = 1: j runs 2, 3, 4.
  - j=2: add (2−1) = 1 → count = 0 + 1 = 1
  - j=3: add (3−1) = 2 → count = 1 + 2 = 3
  - j=4: add (4−1) = 3 → count = 3 + 3 = 6
  After i=1, count = 6.

- For i = 2: j runs 3, 4.
  - j=3: add (3−2) = 1 → count = 6 + 1 = 7
  - j=4: add (4−2) = 2 → count = 7 + 2 = 9
  After i=2, count = 9.

- For i = 3: j runs 4.
  - j=4: add (4−3) = 1 → count = 9 + 1 = 10
  After i=3, count = 10.

3. Intermediate calculations shown above for each (i, j) pair lead to a final count of 10.

4. Why the correct answer is correct
Every pair with i < j from 1..4 contributes the positive difference j−i. Summing those contributions (1+2+3 from i=1, then 1+2 from i=2, then 1 from i=3) gives 6+3+1 = 10.

5. Why the other options are incorrect
- 0: impossible because positive increments occur for each valid pair.
- 20: twice the correct result; no step in the loop doubles contributions.
- 35: unrelated large value (for example, 35 is 1+...+7) and does not match the actual pairwise differences computed above.

6. Conclusion
The final value of count after the loops is 10, which matches the provided correct answer.

What is the final value of "count" after the pseudocode fragment shown below? count = 0 For i = 1 to 3 For j = i + 1 to 4 count := count + (j - i) End-for End-for 单项选择题

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