cpp-flashcards/org/study_deck_02/dsa/advanced-graphs/1584-min-cost-to-connect-all-points.org

#+PROPERTY: STUDY_DECK_02
* TODO 1584. Min Cost to Connect All Points :medium:
:PROPERTIES:
:NEETCODE: [[file:../../roadmap.org::*1584. Min Cost to Connect All Points][1584. Min Cost to Connect All Points]]
:END:

You are given an array ~points~ representing integer coordinates of some points on a 2D-plane, where ~points[i] = [x_{i}, y_{i}]~.

The cost of connecting two points ~[x_{i}, y_{i}]~ and ~[x_{j}, y_{j}]~ is the *manhattan distance* between them: ~|x_{i} - x_{j}| + |y_{i} - y_{j}|~, where ~|val|~ denotes the absolute value of ~val~.

Return /the minimum cost to make all points connected./ All points are connected if there is *exactly one* simple path between any two points.

*Example 1:*


#+begin_src
Input: points = [[0,0],[2,2],[3,10],[5,2],[7,0]]
Output: 20
Explanation: 

We can connect the points as shown above to get the minimum cost of 20.
Notice that there is a unique path between every pair of points.
#+end_src


*Example 2:*


#+begin_src
Input: points = [[3,12],[-2,5],[-4,1]]
Output: 18
#+end_src


*Constraints:*

 - ~1 <= points.length <= 1000~

 - ~-10^{6} <= x_{i}, y_{i} <= 10^{6}~

 - All pairs ~(x_{i}, y_{i})~ are distinct.

** TODO Approach
Write your approach here.

** TODO Python
#+begin_src python
class Solution:
    def minCostConnectPoints(self, points: List[List[int]]) -> int:
#+end_src

** TODO C++
#+begin_src cpp
class Solution {
public:
    int minCostConnectPoints(vector<vector<int>>& points) {
        
    }
};
#+end_src