高精度乘法，这个算法有什么问题？为什么输出是错的？

Question

#include <iostream>
#include <cstring>
#include <cstdlib>
using namespace std;
int main()
{
    int a[401], b[401], c[802], x = 0, h = 0;
    string n1, n2;
    cin >> n1;
    cin >> n2;
    int n = n1.length();
    int m = n2.length();
    memset(a, 0, sizeof(a));
    memset(b, 0, sizeof(b));
    memset(c, 0, sizeof(c));
    for (int i = 1; i <= n1.length(); i++)
        a[i] = n1[n - i ] - '0';
    for (int i = 1; i <= n2.length(); i++)
        b[i] = n2[m - i] - '0';
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++) {
            c[i + j - 1] = a[i] * b[j] + c[i + j - 1] + x;
            if (c[i + j - 1] >= 10) {
                x = c[i + j - 1] / 10;
                c[i + j - 1] %= 10;
            }
        }
    if (a[n] * b[m] + x < 10)
        h = n + m;
    else
        h = n + m - 1;
    for (int i = h; i >= 1; i--)
        cout << c[i];
    system("pause");
    return 0;
}

Answer 1

#include <iostream>
#include <string>
#include <cstring>
#include <cstdlib>
using namespace std;
int main()
{
    int a[401], b[401], c[802], x = 0, h = 0;
    string n1, n2;
    cin >> n1;
    cin >> n2;
    int n = n1.length();
    int m = n2.length();
    memset(a, 0, sizeof(a));
    memset(b, 0, sizeof(b));
    memset(c, 0, sizeof(c));
    for (int i = 1; i <= (int)n1.length(); i++)
        a[i] = n1[n - i] - '0'; //改
    for (int i = 1; i <= (int)n2.length(); i++)
        b[i] = n2[m - i] - '0'; //改
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++) {
            c[i + j - 1] = a[i] * b[j] + c[i + j - 1] + x;
            if (c[i + j - 1] >= 10) {
                x = c[i + j - 1] / 10;
                c[i + j - 1] %= 10;
            }
        }
    if (a[n] * b[m] + x < 10)
        h = n + m;
    else
        h = n + m - 1;
    //修正多余的前导0的问题
    int z;
    for (z = 800; c[z] == '0' || c[z] == 0; z--);
    if (z == -1) cout << '0';
    for (int i = z; i >= 1; i--)
        cout << c[i];
    system("pause");
    return 0;
}