TopCoder SRM 144 Division 2 1100 pts problem. It took me a while to figure this out, but once you notice that the technician must traverse each junction twice except for the largest path the solution comes quite straightforward.

SRM_144_Div2_1100.cpp

#include <vector>

using std::vector;

class PowerOutage {
 public:
  int estimateTimeOut(vector<int> fromJunction, vector<int> toJunction, vector<int> ductLength) {
    int max_minutes = 0;
    
    for(auto p : ductLength) {
      max_minutes += p * 2;
    }
    
    return max_minutes - longestPath(0, fromJunction, toJunction, ductLength);
  }
  
  int longestPath(int origin, vector<int>& fromJunction, vector<int>& toJunction, vector<int>& ductLength) {
    int max_path = 0;
    
    for(int i = 0; i < fromJunction.size(); ++i) {
      if( fromJunction[i] == origin ) {
        int path_size = ductLength[i] + longestPath( toJunction[i], fromJunction, toJunction, ductLength );
        max_path = (path_size > max_path) ? path_size : max_path;
      }
    }
  
    return max_path;
  }
};