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Problem solution · C++

Minimum Runes to Add to Cast Spell

Minimum Runes to Add to Cast Spell: a C++ solution using depth-first search. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Depth-first search
Source
walkccc LeetCode Solutions
Length
77 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

Depth-first search

For Minimum Runes to Add to Cast Spell, the implementation follows one branch at a time, making it suitable for components, trees, backtracking, or dependency exploration.

  1. Define the state carried into one recursive or stack frame.
  2. Mark or choose the current state before exploring children.
  3. Combine child results or undo the choice when the branch finishes.

Code notes

  • 77 lines of C++ from the credited upstream file 3383.cpp.
  • The implementation visibly relies on sequence storage.
  • 8 loop blocks detected, together with recursive traversal.

Complexity

Count unique states for graph traversal; for backtracking, count the branching factor and maximum depth.

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 Runes to Add to Cast Spell · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  int minRunesToAdd(int n, vector<int>& crystals, vector<int>& flowFrom,                    vector<int>& flowTo) {    vector<vector<int>> graph(n);    vector<vector<int>> reversedGraph(n);     for (int i = 0; i < flowFrom.size(); ++i) {      const int u = flowFrom[i];      const int v = flowTo[i];      graph[u].push_back(v);      reversedGraph[v].push_back(u);    }     // Identify Strongly Connected Components (SCC) using Kosaraju's Algorithm    vector<bool> seen(n);    vector<int> orderStack;    vector<int> componentIds(n, -1);    int componentCount = 0;     for (int i = 0; i < n; ++i)      if (!seen[i])        kosaraju(graph, i, seen, orderStack);     for (int i = n - 1; i >= 0; --i) {      const int u = orderStack[i];      if (componentIds[u] == -1)        identifySCC(reversedGraph, u, componentIds, componentCount++);    }     // Track crystal-containing components and inter-component edges.    vector<bool> hasCrystal(componentCount);    vector<bool> hasInterComponentEdge(componentCount);     for (const int u : crystals)      hasCrystal[componentIds[u]] = true;     for (int i = 0; i < flowFrom.size(); ++i) {      const int id1 = componentIds[flowFrom[i]];      const int id2 = componentIds[flowTo[i]];      if (id1 != id2)  // Edge is inter-component.        hasInterComponentEdge[id2] = true;    }     // Count components requiring additional runes.    int ans = 0;     for (int i = 0; i < componentCount; ++i)      if (!hasCrystal[i] && !hasInterComponentEdge[i])        ++ans;     return ans;  }  private:  // Creates a topological order stack using Kosaraju's Algorithm.  void kosaraju(const vector<vector<int>>& graph, int u, vector<bool>& seen,                vector<int>& orderStack) {    seen[u] = true;    for (const int v : graph[u])      if (!seen[v])        kosaraju(graph, v, seen, orderStack);    orderStack.push_back(u);  }   // Assigns component IDs during SCC identification in the second DFS.  void identifySCC(const vector<vector<int>>& reversedGraph, int u,                   vector<int>& componentIds, int componentId) {    if (componentIds[u] != -1)      return;    componentIds[u] = componentId;    for (const int v : reversedGraph[u])      if (componentIds[v] < 0)        identifySCC(reversedGraph, v, componentIds, componentId);  }};

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