## Monday, May 16, 2016

### LinkedIn – Interview – Find colinear points in O(n^2) | Yaozong's Blog

LinkedIn – Interview – Find colinear points in O(n^2) | Yaozong's Blog
Strictly speaking, the following code is not O(n^2), because insert points into map takes O(logn). However, if we define hash functions for pair, it could be reduced to O(n^2).

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vector<vector<pair<int,int>>> find_colinear_points(vector<pair<int,int>>& pts)
{
vector<vector<pair<int,int>>> res;

map<pair<double, double>, set<pair<int,int>>> ht;
map<double, set<pair<int,int>>> vert;

for (int i = 0; i < pts.size(); ++i)
{
for (int j = i + 1; j < pts.size(); ++j)
{
if (pts[i].first == pts[j].first) {
vert[pts[i].first].insert(pts[i]);
vert[pts[i].first].insert(pts[j]);
}
else {
int dx = pts[i].first - pts[j].first;
int dy = pts[i].second - pts[j].second;
double s = dy * 1.0 / dx;
double d = pts[i].second - s * pts[i].first;
ht[make_pair(s, d)].insert(pts[i]);
ht[make_pair(s, d)].insert(pts[j]);
}
}
}

for (auto elem : vert) {
if (elem.second.size() > 2) {
vector<pair<int, int>> tmp(elem.second.begin(), elem.second.end());
res.push_back(tmp);
}
}

for (auto elem : ht) {
if (elem.second.size() > 2) {
vector<pair<int, int>> tmp(elem.second.begin(), elem.second.end());
res.push_back(tmp);
}
}

return res;
}
Read full article from LinkedIn – Interview – Find colinear points in O(n^2) | Yaozong's Blog