c++ - 增量工作非常奇怪

Question

这个程序应该给出任何大小的阶乘的最后 100 位。然而，main() 中的 counter2++ 发生了一些奇怪的事情。每次循环在 main() 函数中运行(即 99 次)，counter2 都会增加 +1。然而，这是显示的内容:

2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
71
86
90
123
164
196
207
254
300
362
432
471
551
620
630
708
761
772
857
896
985
1036
1100
1116
1207
1209
1280
1356
1417
1452
1512

Counter2 最终是 1512 而不是 100，但如果我从 main() 中删除 mult(i) 或 carry()，那么它会显示 100。为什么 counter2 最终是 1512 而不是 100？

#include <iostream>

using namespace std;

int numbers[100];
int counter2 = 0;

void init(){
//sets elements 1-99 of numbers[] to 0, increments counter2 by 1, sets numbers[0] = 1
    for (int i = 1; i < 100; i++){
        numbers[i] = 0;
    }
    numbers[0] = 1;
    counter2++;
}

void mult(int x){
//multiplies each element by 1 through n to calculate for !n
//this is used to represent a very large number without using a BigInt library
//the nth element is a placeholder for the n+1 position of the number
//e.g 2nd element represents 100-900 of the number, 4th represents 1000-9000, etc
//carry() is used to take care of overflow, so that it's only 1 digit per element
    for (int i = 0; i < 100; i++){
        numbers[i] *= x;
    }
}

void carry(){
//in order to make previous function work, this adds any overflow to the next
//element. e.g: 8 * 4 = 32, 3 is added to numbers[i+1], sets numbers[i] to 2
    int counter = 0;
    for (int i = 0; i < 100; i++){
        if (numbers[i] >= 10){
            counter = numbers[i] / 10;
            numbers[i+1] += counter;
            numbers[i] = numbers[i] % (counter * 10);
        }
    }
}

int main()
{
    init();
    for (int i = 2; i < 101; i++){
    //calculates the last 100 digits of !100, but counter2 ends up being 1512
        mult(i);
        carry();
        counter2++;
        cout << counter2 << endl;
    }
}

Answer 1

您正在写超过 carry() 中 numbers 数组的末尾:

        numbers[i+1] += counter;

这里，i 可以是 99，在这种情况下 numbers[i+1] 超出范围。

从技术上讲，这是 undefined behaviour .在实践中发生的情况是您覆盖了 count2 变量，该变量恰好位于数组之后的内存中。

关于内存错误的一个令人讨厌的事情是，它们可以长时间无症状，然后在最坏的情况下浮出水面。 valgrind是检测此类问题的绝佳工具。