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1584. Min Cost to Connect All Points 👍

  • Time: $O(n^2)$
  • Space: $O(1)$
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class Solution {
 public:
  int minCostConnectPoints(vector<vector<int>>& points) {
    // dist[i] := the minimum distance to connect the points[i]
    vector<int> dist(points.size(), INT_MAX);
    int ans = 0;

    for (int i = 0; i < points.size() - 1; ++i) {
      for (int j = i + 1; j < points.size(); ++j) {
        // Try to connect the points[i] with the points[j].
        dist[j] = min(dist[j], abs(points[i][0] - points[j][0]) +
                                   abs(points[i][1] - points[j][1]));
        // Swap the points[j] (the point with the mnimum distance) with the
        // points[i + 1].
        if (dist[j] < dist[i + 1]) {
          swap(points[j], points[i + 1]);
          swap(dist[j], dist[i + 1]);
        }
      }
      ans += dist[i + 1];
    }

    return ans;
  }
};

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class Solution {
  public int minCostConnectPoints(int[][] points) {
    // dist[i] := the minimum distance to connect the points[i]
    int[] dist = new int[points.length];
    Arrays.fill(dist, Integer.MAX_VALUE);
    int ans = 0;

    for (int i = 0; i < points.length - 1; ++i) {
      for (int j = i + 1; j < points.length; ++j) {
        // Try to connect the points[i] with the points[j].
        dist[j] = Math.min(dist[j], Math.abs(points[i][0] - points[j][0]) +
                                        Math.abs(points[i][1] - points[j][1]));
        // Swap the points[j] (the point with the minimum distance) with the
        // points[i + 1].
        if (dist[j] < dist[i + 1]) {
          final int[] tempPoint = points[j];
          points[j] = points[i + 1];
          points[i + 1] = tempPoint;
          final int tempDist = dist[j];
          dist[j] = dist[i + 1];
          dist[i + 1] = tempDist;
        }
      }
      ans += dist[i + 1];
    }

    return ans;
  }
}

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class Solution:
  def minCostConnectPoints(self, points: list[int]) -> int:
    # dist[i] := the minimum distance to connect the points[i]
    dist = [math.inf] * len(points)
    ans = 0

    for i in range(len(points) - 1):
      for j in range(i + 1, len(points)):
        # Try to connect the points[i] with the points[j].
        dist[j] = min(dist[j], abs(points[i][0] - points[j][0]) +
                      abs(points[i][1] - points[j][1]))
        # Swap the points[j] (the point with the mnimum distance) with the
        # points[i + 1].
        if dist[j] < dist[i + 1]:
          points[j], points[i + 1] = points[i + 1], points[j]
          dist[j], dist[i + 1] = dist[i + 1], dist[j]
      ans += dist[i + 1]

    return ans