英文:
Why the x is 5050?
问题
for(i = 1; i <= 100; i++)
for(j = i; j <= 100; j++)
x++;
System.out.println(x);
一开始我以为结果会是 10,000，但实际上是 5050。为什么？i 发生了什么变化？
英文:
for(i = 1;i <= 100;i++)
for(j = i; j <= 100; j++)
x++;
System.out.println(x);
First I thought that the result would be 10.000, but it was 5050. Why? What does the i changes?
答案1
得分: 8
5050这个答案是正确的，假设x为0（根据你的结果推断出来的）。之所以不是10000，是因为代码中的这行：j = i，而不是例如j = 1，这使得结果为100 + 99 + 98 + ... + 1 = 5050。
英文:
The answer 5050 is correct, given the assumption that x is 0 (as it appears based on your results). The reason it is not 10,000 is the line j = i instead of e.g. j = 1, which makes it 100 + 99 + 98 + ... + 1 = 5050.
答案2
得分: 2
起初，i 为 1，因此 j 也从 1 变化到 100，内部循环执行了 100 次迭代，这意味着 x 被增加了 100 次。
接下来，i 变为 2，所以 j 从 2 变化到 100。这意味着进行了 99 次迭代，x 被增加了 99 次，依此类推...
这是从 1 累加到 100 所有数字的和，即 (100 * (100 + 1)) / 2 == 5050。
英文:
At first i is 1, so j goes from 1 too 100 and the inner loop does 100 iterations, which means x is incremented 100 times.
The next time, i becomes 2, so j goes from 2 to 100. That means 99 iterations and x is incremented 99 times and so on and so forth...
That's the sum of all numbers from 100 to 1, which is (100 * (100 + 1)) / 2 == 5050
答案3
得分: 0
内部循环在外部循环的每次迭代中执行(100 - i)次。即当外部循环中的i的值为0时，内部循环执行100次；当外部循环中的i的值为1时，内部循环执行99次，依此类推。将所有这些值相加得到100 + 99 + 98 + ... + 1 = 5050。
英文:
The inner loop executes (100 - i) times on each iteration of the outer loop. i.e. when the value of i = 0 in the outer loop, the inner loop executes 100 times, when the value of i = 1 in the outer loop, the inner loop executes 99 times and so on and so forth. When adding all these values 100 + 99 + 98 + ... + 1 = 5050
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