fastest way to get the maximal difference between 2 vectors

Question

I would like to get ideas for finding a fast way to get the maximal difference between 2 vectors as if they're accumulated .

For example, (not accumulated yet)

vector<int> vec1 = {10, 30, 20, 40 };
vector<int> vec2 = {5, 10, 5, 8 };

the naive way to get the result, is to accumulate them first into new vectors so:

vector<int> accumulated_vec1 = {10, 10+30, 10+30+20, 10+30+20+40};
vector<int> accumulated_vec2 = {5, 5+10, 5+10+5, 5+10+5+8};

ie:

accumulated_vec1 = {10,40,60,100};
accumulated_vec2 = {5,15,20,28};

Then, the result is the max between abs(accumulated_vec1[i]-accumulated_vec2[i]) while 0 <= i <= 3.

so result = 72 (when i==3)

a faster way can be by representing the vectors by 1 number(even 0.10302040)... but I can't find it helpful :\\ Think that I have millions pairs of the 2 vectors vec1 and vec2, and I am trying to avoid calculating the accumulated vectors for each of pair.. sorry if it's not clear but if I find a solution, I'll answer this annoying question.

Answer 1

Fastest way...

int maxDiff(const vector<int> &v1, const vector<int> &v2) {
    int maxDiff(0), diff(0);

    for (auto it1 = v1.begin(), it2 = v2.begin(); it1 != v1.end() && it2 != v2.end(); ++it1, ++it2) {
        diff += *it1-*it2;
        maxDiff = max(abs(diff), maxDiff);
    }

    return maxDiff;
}

No other vector construction, just moving pointers that are even faster than getting elements per their index each time.

Live Demo

Answer 2

Take a look at the code below. Does this do what you are asking?

vector<int> accumulated_vec;
accumulated_vec.resize(vec1.size());
accumulated_vec[0] = vec1[0] - vec2[0];

for(int i = 1; i < accumulated_vec.size(); i++)
{
    accumulated_vec[i] = accumulated_vec[i-1] + (vec1[i] - vec2[i]);
    cout << accumulated_vec[i] << endl;
}

Answer 3

Here is my version for your problem

int getAccumulatedForIndex(int index, vector<int> &vec) {
    if (index == 0) {
        return vec.at(index);
    }
    return vec.at(index) + getAccumulatedForIndex(index - 1, vec);
}

and than

int getAccumulatedMax(vector<int> vec1, vector<int> vec2) {
    if (vec1.size() != vec2.size()) { // don't much each other
        return -1;
    }

    int max = -1;
    for (int i = 0; i < vec1.size(); ++i) {
        int currentMax = abs(getAccumulatedForIndex(i, vec1) - getAccumulatedForIndex(i, vec2));
        if (currentMax > max) {
            max = currentMax;
        }
    }

    return max;
}

hope that's it what you want