## Wednesday, December 31, 2014

### UVa Problem 186 - Trip Routing

Problem:

Solution:

We could have solve the problem by running the single source shortest path algorithm on all queries, but it could be much faster if we just run all pair shortest path once and answer the queries right away.

For all pair shortest paths, we used Floyd Warshall's algorithm for its simplicity.

The problem is quite complicated and tricky, be careful with a few things:

1. All highways are assumed to be bidirectional.
2. The input contain multiple edges.

Lots of coding work is devoted to the parsing of the inputs, mapping of names to numbers and so on. I had a bug with edge lookup because these complicated work are not done properly.

Code:

#include "stdafx.h"

// http://uva.onlinejudge.org/index.php?option=onlinejudge&page=show_problem&problem=122

#include "UVa186.h"

#include <iostream>
#include <iomanip>
#include <string>
#include <map>
#include <vector>
#include <algorithm>

using namespace std;

void UVa186_split(string line, string* parts);
int UVa186_assign_city_number(map<string, int>& city_numbers, map<int, string>& city_namings, string city_name);

int UVa186()
{
map<string, int> city_numbers;
map<int, string> city_namings;
map<pair<int, int>, string> edge_namings;
vector<pair<pair<int, int>, int> > edges;
vector<pair<int, int> > queries;

string line;
getline(cin, line);
do
{
string parts[4];
UVa186_split(line, parts);

string src = parts[0];
string dst = parts[1];
string route = parts[2];
int cost = stoi(parts[3]);

int src_id = UVa186_assign_city_number(city_numbers, city_namings, src);
int dst_id = UVa186_assign_city_number(city_numbers, city_namings, dst);

if (dst_id < src_id)
{
int temp = src_id;
src_id = dst_id;
dst_id = temp;
}

pair<int, int> edge(src_id, dst_id);
edge_namings.insert(pair<pair<int, int>, string>(edge, route));
edges.push_back(pair<pair<int, int>, int>(edge, cost));

getline(cin, line);
}
while (line != "");

getline(cin, line);
while (true)
{
string parts[2];
UVa186_split(line, parts);
queries.push_back(pair<int, int>(city_numbers[parts[0]], city_numbers[parts[1]]));

if (cin.eof())
{
break;
}

getline(cin, line);

if (line == "")
{
break;
}
}

// Step 2: Produce the data structures for Floyd Warshall
int number_of_nodes = city_numbers.size();

vector<vector<int> > distances;
vector<vector<bool> > reachable;
vector<vector<int> > path;
distances.resize(number_of_nodes);
reachable.resize(number_of_nodes);
path.resize(number_of_nodes);
for (int src = 0; src < number_of_nodes; src++)
{
distances[src].resize(number_of_nodes);
reachable[src].resize(number_of_nodes);
path[src].resize(number_of_nodes);

for (int dst = 0; dst < number_of_nodes; dst++)
{
distances[src][dst] = -1;
reachable[src][dst] = false;
path[src][dst] = -1;
}
}

for (unsigned int e = 0; e < edges.size(); e++)
{
pair<pair<int, int>, int> edge = edges[e];
int src = edge.first.first;
int dst = edge.first.second;
int cost = edge.second;

// The input has multiple edges!
{
distances[src][dst] = cost;
reachable[src][dst] = true;
path[src][dst] = dst;

distances[dst][src] = cost;
reachable[dst][src] = true;
path[dst][src] = src;
}
}

for (int k = 0; k < number_of_nodes; k++)
{
for (int src = 0; src < number_of_nodes; src++)
{
for (int dst = 0; dst < number_of_nodes; dst++)
{
if (reachable[src][k] && reachable[k][dst]) // relaxation is possible if the proposal is valid
{
int current_distance = distances[src][dst];
int propose_distance = distances[src][k] + distances[k][dst];
if (!reachable[src][dst] || propose_distance < current_distance)
{
distances[src][dst] = propose_distance;
reachable[src][dst] = true;
path[src][dst] = path[src][k];
}
}
}
}
}

for (unsigned int q = 0; q < queries.size(); q++)
{
pair<int, int> query = queries[q];
int src = query.first;
int dst = query.second;

cout << endl;
cout << endl;

cout << "From                 To                   Route      Miles" << endl;
cout << "-------------------- -------------------- ---------- -----" << endl;

int cur = src;
while (true)
{
int path_src_id = cur;
int path_dst_id = path[cur][dst];
string path_src_name = city_namings[path_src_id];
string path_dst_name = city_namings[path_dst_id];

int edge_src_id = min(path_src_id, path_dst_id);
int edge_dst_id = max(path_src_id, path_dst_id);

string route = edge_namings[pair<int, int>(edge_src_id, edge_dst_id)];
while (path_src_name.length() < 20)
{
path_src_name += ' ';
}
while (path_dst_name.length() < 20)
{
path_dst_name += ' ';
}
while (route.length() < 10)
{
route += ' ';
}

cout << path_src_name << " " << path_dst_name << " " << route << " ";
cout << right << setw(5) << adjacency_matrix[path_src_id][path_dst_id] << endl;

cur = path_dst_id;
if (cur == dst)
{
break;
}
}
cout << "                                                     -----" << endl;
cout << "                                          Total      ";
cout << right << setw(5) << distances[src][dst] << endl;
}

return 0;
}

void UVa186_split(string line, string* parts)
{
string* current_part = parts;
for (unsigned int i = 0; i < line.length(); i++)
{
if (line[i] != ',')
{
(*current_part) += line[i];
}
else
{
current_part++;
}
}
}

int UVa186_assign_city_number(map<string, int>& city_numbers, map<int, string>& city_namings, string city_name)
{
int city_number;
map<string, int>::iterator probe = city_numbers.find(city_name);
if (probe == city_numbers.end())
{
city_number = city_numbers.size();
city_numbers.insert(pair<string, int>(city_name, city_number));
city_namings.insert(pair<int, string>(city_number, city_name));
}
else
{
city_number = probe->second;
}

return city_number;
}