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Suppose we have n different points in K dimension space, the value of n is in range (2, 105), and value of k in range (1 to 5). We have to determine the point such that the sum of Manhattan distance from resultant point to n points is minimized.

The Manhattan distance between two points P1(x1, y1) and P2(x2, y2), is |x1 – x2| + |y1 – y2|. Suppose dimension is 3, and there are three points like (1, 1, 1), (2, 2, 2), (3, 3, 3), then the output will be (2, 2, 2).

To solve this problem, we have to sort the points in all K dimensions and get the output from the middle elements of each of the k dimensions.

#include<iostream> #include<vector> #include<cmath> #include<algorithm> using namespace std; void minimizeHanhattan(int n, int k, vector<vector<int> >& pointList) { for (int i = 0; i < k; ++i) //sort in all k dimension sort(pointList[i].begin(), pointList[i].end()); for (int i = 0; i < k; ++i) cout << pointList[i][(ceil((double)n / 2) - 1)] << " "; } int main() { int n = 4, k = 4; vector<vector<int> > point = { { 1, 5, 2, 4 }, { 6, 2, 0, 6 }, { 9, 5, 1, 3 }, { 6, 7, 5, 9 } }; minimizeHanhattan(n, k, point); }

2 2 3 6

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