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Problem solution · C++

Maximum Cost of Trip With K Highways

Maximum Cost of Trip With K Highways: a C++ solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Direct simulation
Source
walkccc LeetCode Solutions
Length
47 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

Direct simulation

For Maximum Cost of Trip With K Highways, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 47 lines of C++ from the credited upstream file 2247.cpp.
  • The implementation visibly relies on sequence storage.
  • 3 loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

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 codeMaximum Cost of Trip With K Highways · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  int maximumCost(int n, vector<vector<int>>& highways, int k) {    if (k + 1 > n)      return -1;     int ans = -1;    vector<vector<int>> mem(n, vector<int>(1 << n, -1));    vector<vector<pair<int, int>>> graph(n);     for (const vector<int>& h : highways) {      const int u = h[0];      const int v = h[1];      const int w = h[2];      graph[u].emplace_back(v, w);      graph[v].emplace_back(u, w);    }     for (int i = 0; i < n; ++i)      ans = max(ans, maximumCost(graph, i, 1 << i, k, mem));     return ans;  }  private:  // Returns the maximum cost of trip starting from u, where `mask` is the  // bitmask of the visited cities.  int maximumCost(const vector<vector<pair<int, int>>>& graph, int u,                  unsigned mask, int k, vector<vector<int>>& mem) {    if (popcount(mask) == k + 1)      return 0;    if (mem[u][mask] != -1)      return mem[u][mask];     int res = -1;    for (const auto& [v, w] : graph[u]) {      if (mask >> v & 1)        continue;      const int nextCost = maximumCost(graph, v, mask | 1 << v, k, mem);      if (nextCost != -1)        res = max(res, w + nextCost);    }     return mem[u][mask] = res;  }};

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