How many times is the variable "count" updated inside the loop in the pseudocode fragment below?

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

Question

How many times is the variable "count" updated inside the loop in the pseudocode fragment 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

Each execution of the inner loop performs one update "count := count + (j - i)". So the problem reduces to counting how many distinct (i, j) pairs the nested loops generate.

1) Relevant knowledge points and concepts
- Nested loop iteration: For i from 1 to 3 (inclusive) and for each i, j runs from i+1 to 4 (inclusive).
- Each (i, j) pair triggers one update of count.
- Counting pairs can be done by direct enumeration, summing per i, or recognizing combinations: number of unordered pairs chosen from {1,2,3,4} equals C(4,2) = 6.

2) Complete reasoning step by step
- For i = 1: j runs from 2 to 4, so j = 2, 3, 4 → 3 updates.
- For i = 2: j runs from 3 to 4, so j = 3, 4 → 2 updates.
- For i = 3: j runs from 4 to 4, so j = 4 → 1 update.
- Sum updates across all i: 3 + 2 + 1 = 6.

3) Intermediate calculations shown
- i = 1: updates = { (1,2), (1,3), (1,4) } → 3
- i = 2: updates = { (2,3), (2,4) } → 2
- i = 3: updates = { (3,4) } → 1
- Total = 3 + 2 + 1 = 6

4) Why the correct answer is correct
Each inner-loop execution increments count exactly once. Counting the valid (i, j) combinations as shown yields six such executions, so count is updated six times.

5) Why other options are incorrect
- 0: impossible because the loops produce iterations and the inner statement executes.
- 10: this equals the sum of the values (j - i) over all pairs (1+2+3+1+2+1 = 10), not the number of updates. The question asks how many times count is updated, not by how much in total.
- 12: might be mistaken by multiplying loop bounds (3 × 4), but j does not run from 1 to 4 for every i; j starts at i+1, so 12 is incorrect.

6) Conclusion
The count variable is updated 6 times. This matches the provided correct answer: 6.

How many times is the variable "count" updated inside the loop in the pseudocode fragment 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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