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Line Reflection

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Description

Given n points on a 2D plane, find if there is such a line parallel to y-axis that reflect the given points.

Example 1:

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Input: [[1,1],[-1,1]]
Output: true

Example 2:

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Input: [[1,1],[-1,-1]]
Output: false

Solution

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class Solution {
public:
    bool isReflected(vector<pair<int, int>>& points) {
        if (points.size() == 0) return true;
        
        unordered_map<int, set<int>> mapping;
        for (auto& point : points) mapping[point.second].insert(point.first);
        
        auto iter = mapping.begin();
        auto left = iter->second.begin();
        auto right = iter->second.rbegin();
        int target = *left + *right;
        
        while(iter != mapping.end()) {
            auto& lis = iter->second;
            left = lis.begin();
            right = lis.rbegin();
            while (left != lis.end() && right != lis.rend() && *left <= *right) {
                if (*left + *right != target) return false;
                ++left; ++right;
            }
            ++iter;
        }
        return true;
    }
};