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Problem solution · C++

Minimum Total Distance Traveled

Minimum Total Distance Traveled: a C++ solution using sorting and greedy selection. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Sorting and greedy selection
Source
walkccc LeetCode Solutions
Length
36 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Sorting and greedy selection

For Minimum Total Distance Traveled, the implementation first exposes a useful order, then scans that order while making locally justified choices.

  1. Choose the key that reveals the greedy or grouping structure.
  2. Sort the relevant records by that key.
  3. Scan in order, maintaining the invariant that makes each local choice safe.

Code notes

  • 36 lines of C++ from the credited upstream file 2463.cpp.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected.

Complexity

Sorting is typically the dominant term unless the subsequent scan uses a more expensive nested operation.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeMinimum Total Distance Traveled · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  long long minimumTotalDistance(vector<int>& robot,                                 vector<vector<int>>& factory) {    ranges::sort(robot);    ranges::sort(factory);    vector<vector<vector<long>>> mem(        robot.size(),        vector<vector<long>>(factory.size(), vector<long>(robot.size())));    return minimumTotalDistance(robot, factory, 0, 0, 0, mem);  }  private:  // Returns the minimum distance to fix robot[i..n) with factory[j..n), where  // factory[j] already fixed k robots.  long minimumTotalDistance(const vector<int>& robot,                            const vector<vector<int>>& factory, int i, int j,                            int k, vector<vector<vector<long>>>& mem) {    if (i == robot.size())      return 0;    if (j == factory.size())      return LONG_MAX;    if (mem[i][j][k] > 0)      return mem[i][j][k];    const long skipFactory =        minimumTotalDistance(robot, factory, i, j + 1, 0, mem);    const int position = factory[j][0];    const int limit = factory[j][1];    const long useFactory =        limit > k ? minimumTotalDistance(robot, factory, i + 1, j, k + 1, mem) +                        abs(robot[i] - position)                  : LONG_MAX / 2;    return mem[i][j][k] = min(skipFactory, useFactory);  }};

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