Why vector<int> is faster than vector<bool> in the following case

Question

This phenomenon is found when I programmed for the LeetCode problem N-Queens.

I have two versions of accepted code, the only difference between which is the way I stored the hash table, one is using vector<int> and the other is using vector<bool>. To be specific, the two versions of code are as follows:

Version 1, vector<int>, Running Time: 4 ms

class Solution {
public:
void dfs(vector<string>& crtrst, vector<vector<string>>& finalrsts, int row, vector<int>& mup, vector<int>& m45dgr, vector<int>& m135dgr)
{
    int n = crtrst.size();
    
    if (row == n)
    {
        finalrsts.push_back(crtrst);
        return;
    }
    
    for (int j=0; j<n; j++)
    {
        if (mup[j] && m45dgr[j-row+n-1] && m135dgr[row+j])
        {
            crtrst[row][j] = 'Q';
            mup[j] = m45dgr[j-row+n-1] = m135dgr[row+j] = 0;
        
            dfs(crtrst,finalrsts,row+1,mup,m45dgr,m135dgr);
        
            crtrst[row][j] = '.';
            mup[j] = m45dgr[j-row+n-1] = m135dgr[row+j] = 1;
        }
    }
}

vector<vector<string>> solveNQueens(int n) 
{
    vector<vector<string>> finalrsts;
    vector<string> crtrst(n,string(n,'.'));
    vector<int> mup(n,1);
    vector<int> m45dgr(2*n-1,1); // degree 45: '\'
    vector<int> m135dgr(2*n-1,1); // degree 135: '/';
    int row = 0;
    dfs(crtrst,finalrsts,row,mup,m45dgr,m135dgr);
    return finalrsts;
}
};

Version 2, vector<bool>, Running time: 12 ms

class Solution {
public:
void dfs(vector<string>& crtrst, vector<vector<string>>& finalrsts, int row, 
    vector<bool>& mup, vector<bool>& m45dgr, vector<bool>& m135dgr)
{
    int n = crtrst.size();
    
    if (row == n)
    {
        finalrsts.push_back(crtrst);
        return;
    }
    
    for (int j=0; j<n; j++)
    {
        if (mup[j] && m45dgr[j-row+n-1] && m135dgr[row+j])
        {
            crtrst[row][j] = 'Q';
            mup[j] = m45dgr[j-row+n-1] = m135dgr[row+j] = false;
        
            dfs(crtrst,finalrsts,row+1,mup,m45dgr,m135dgr);
        
            crtrst[row][j] = '.';
            mup[j] = m45dgr[j-row+n-1] = m135dgr[row+j] = true;
        }
    }
}

vector<vector<string>> solveNQueens(int n) 
{
    vector<vector<string>> finalrsts;
    vector<string> crtrst(n,string(n,'.'));
    vector<bool> mup(n,true);
    vector<bool> m45dgr(2*n-1,true); // degree 45: '\'
    vector<bool> m135dgr(2*n-1,true); // degree 135: '/';
    int row = 0;
    dfs(crtrst,finalrsts,row,mup,m45dgr,m135dgr);
    return finalrsts;
}
};

As I know that, vector<bool> stores each element using 1 bit rather than a bool variable (may be 2 Bytes), and vector<int> stores each element using 4 Bytes. So vector<bool> seems tinier than vector<int>. However, why it is slower than vector<int>?

Answer 1

Access to single bits is usually slower than to complete addressable units (bytes in the lingo of C++). For example, to write a byte, you just issue a write instruction (mov on x86). To write a bit, you need to load the byte containing it, use bitwise operators to set the right bit within the byte, and then store the resulting byte.

The compact size of a bit vector is nice for storage requirements, but it will result in a slowdown except when your data becomes large enough that caching issues play a role.

If you want to have speed and still be more efficient than 4 bytes per value, try a vector<unsigned char>.