Why vector in C++ doesn't resize automatically

Question

I've a very long factorial program which needs to find factorial up to 100. It works well up to 33 factorial but not from 34. Can someone help in identifying the problem.

#include <iostream>
#include <vector>
#include <utility>


using namespace std;

void bigFactorials(int n)
{
    vector<int> v;//If I specify the size as v(1000) it works fine but I don't 

    //want to specify the size beforehand.
    v.push_back(1);

    // Complete this function
    for(int i=2;i<=n;i++) {
        int carry = 0, mul=0;
        for(auto j=v.rbegin();j!=v.rend();j++) {
            mul=i**j + carry;
            carry=mul/10;
            *j=mul%10;
        }

        if(carry)
            v.insert(v.begin(),carry);    
    }

    for(int i:v)
        cout<<i;
}

int main()
{
    int n;

    cin >> n;
    if( n>0 && n<101 )
        bigFactorials(n);

    return 0;
}

Answer 1

Problem is when carry > 10, then you insert one integer value without splitting it into chars, it should be implemented as follows

if(carry)
{
    if (carry >= 10)
    {
        while (carry > 0)
        {
            v.insert(v.begin(),carry % 10); // put each char from carry into v
            carry = carry / 10;
        }
    }
    else
        v.insert (v.begin(),carry);
}

with this you can even keep v as vector<char> and for 50! we have 30414093201713378043612608166064768844377641568960512000000000000.

Answer 2

You are definitely overflowing, when I print out the carry values that are added to the vector:

1
5
4
3
3
3
4
6
8
13
20
35
64
121
243
510
1124
2585
6204
15511
40329
108888
304888
884176
2652528
8222838
26313083
86833176
-134263930
-134263930-639604140847618609643520000000

I switched to long long for the vector and for carry and mul and was able to get the correct answer for 34!, but 99! still overflows. Seems you need to further reduce the numbers you are adding to the vector.

Answer 3

You need to split your carry in decimal digits and insert in-front of your BigInt.

while (carry)
{
    v.insert(v.begin(), carry % 10);
    carry /= 10;
}

Here the whole function:

void bigFactorials(int n) {
    vector<int> v;//If I specify the size as v(1000) it works fine but I don't 
    //want to specify the size beforehand.
    v.push_back(1);

    // Complete this function
    for (int i = 2; i <= n; i++)
    {
        int carry = 0, mul = 0;
        for (auto j = v.rbegin(); j != v.rend(); j++)
        {
            mul = i * *j + carry;
            carry = mul / 10;
            *j = mul % 10;
        }

        while (carry)
        {
            v.insert(v.begin(), carry % 10);
            carry /= 10;
        }
    }

    for (int i : v)
        cout << i;
}

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