## Sunday, November 9, 2014

### UVa Problem 166 - Making Change

Problem:

Solution:

I thought about dynamic programming. The shopper keeper's problem is easy to solve with infinite number of coins, but the buyer's is not because coin supply is limited. Going to six dimensional DP just isn't the way to go. So I think something else.

I reused the idea I had my solution in UVa 10440 Ferry Loading II. Model the state space as a graph and find the shortest path.

This time life is much easier because the edge weight is just 1. All I have to do is to do a BFS.

Coin change isn't always have to go through dynamic programming, greedy work just fine this time around.

The code is not optimized, for example, some times it allocates memory without using it because the node is already visited. The search go through stupid path like give shop keeper 2 dollars and shop keeper gives it back. But it is good enough to get it accepted, so I won't bother fixing them.

Code:

#include "stdafx.h"

// http://uva.onlinejudge.org/index.php?option=onlinejudge&page=show_problem&problem=102

#include "UVa166.h"

#include <iostream>
#include <iomanip>
#include <set>
#include <queue>

using namespace std;

struct UVa166_State
{
int num_5_cents;
int num_10_cents;
int num_20_cents;
int num_50_cents;
int num_1_dollar;
int num_2_dollars;
int value_in_cents;
int used_coin;
};

class UVa166_State_less
{
public:
bool operator()(UVa166_State* first, UVa166_State* second)
{
if (first->value_in_cents < second->value_in_cents)
{
return true;
}
else if (first->value_in_cents > second->value_in_cents)
{
return false;
}
if (first->num_5_cents < second->num_5_cents)
{
return true;
}
else if (first->num_5_cents > second->num_5_cents)
{
return false;
}
if (first->num_10_cents < second->num_10_cents)
{
return true;
}
else if (first->num_10_cents > second->num_10_cents)
{
return false;
}
if (first->num_20_cents < second->num_20_cents)
{
return true;
}
else if (first->num_20_cents > second->num_20_cents)
{
return false;
}
if (first->num_50_cents < second->num_50_cents)
{
return true;
}
else if (first->num_50_cents > second->num_50_cents)
{
return false;
}
if (first->num_1_dollar < second->num_1_dollar)
{
return true;
}
else if (first->num_1_dollar > second->num_1_dollar)
{
return false;
}
if (first->num_2_dollars < second->num_2_dollars)
{
return true;
}
else if (first->num_2_dollars > second->num_2_dollars)
{
return false;
}
if (first->used_coin < second->used_coin)
{
return true;
}
else if (first->used_coin > second->used_coin)
{
return false;
}

return false;
}
};

int UVa166()
{
set<UVa166_State*, UVa166_State_less> visited;
while (true)
{
UVa166_State* initial_state = new UVa166_State();
cin >> initial_state->num_5_cents;
cin >> initial_state->num_10_cents;
cin >> initial_state->num_20_cents;
cin >> initial_state->num_50_cents;
cin >> initial_state->num_1_dollar;
cin >> initial_state->num_2_dollars;
if (initial_state->num_5_cents < 0) { throw 0; }
if (initial_state->num_10_cents < 0) { throw 0; }
if (initial_state->num_20_cents < 0) { throw 0; }
if (initial_state->num_50_cents < 0) { throw 0; }
if (initial_state->num_1_dollar < 0) { throw 0; }
if (initial_state->num_2_dollars < 0) { throw 0; }
initial_state->value_in_cents = 0;
initial_state->used_coin = 0;
if ((initial_state->num_5_cents + initial_state->num_10_cents + initial_state->num_20_cents + initial_state->num_50_cents + initial_state->num_1_dollar + initial_state->num_2_dollars) == 0)
{
break;
}
double value;
cin >> value;
if (value < 0) { throw 0; }
initial_state->value_in_cents = (int)(value * 100 + 0.1);
if (initial_state->value_in_cents % 5 != 0)
{
throw 0;
}
queue<UVa166_State*> bfs_queue;
bfs_queue.push(initial_state);
bool found = false;
while (bfs_queue.size() > 0)
{
UVa166_State* current = bfs_queue.front();
bfs_queue.pop();
if (current->value_in_cents == 0)
{
found = true;
cout << setw(3) << current->used_coin << endl;
break;
}
else if (current->value_in_cents > 0)
{
if (current->num_5_cents > 0)
{
UVa166_State* new_state = new UVa166_State();
new_state->num_5_cents = current->num_5_cents - 1;
new_state->num_10_cents = current->num_10_cents;
new_state->num_20_cents = current->num_20_cents;
new_state->num_50_cents = current->num_50_cents;
new_state->num_1_dollar = current->num_1_dollar;
new_state->num_2_dollars = current->num_2_dollars;
new_state->value_in_cents = current->value_in_cents - 5;
new_state->used_coin = current->used_coin + 1;
if (visited.find(new_state) == visited.end())
{
visited.insert(new_state);
bfs_queue.push(new_state);
}
}
if (current->num_10_cents > 0)
{
UVa166_State* new_state = new UVa166_State();
new_state->num_5_cents = current->num_5_cents;
new_state->num_10_cents = current->num_10_cents - 1;
new_state->num_20_cents = current->num_20_cents;
new_state->num_50_cents = current->num_50_cents;
new_state->num_1_dollar = current->num_1_dollar;
new_state->num_2_dollars = current->num_2_dollars;
new_state->value_in_cents = current->value_in_cents - 10;
new_state->used_coin = current->used_coin + 1;
if (visited.find(new_state) == visited.end())
{
visited.insert(new_state);
bfs_queue.push(new_state);
}
}
if (current->num_20_cents > 0)
{
UVa166_State* new_state = new UVa166_State();
new_state->num_5_cents = current->num_5_cents;
new_state->num_10_cents = current->num_10_cents;
new_state->num_20_cents = current->num_20_cents - 1;
new_state->num_50_cents = current->num_50_cents;
new_state->num_1_dollar = current->num_1_dollar;
new_state->num_2_dollars = current->num_2_dollars;
new_state->value_in_cents = current->value_in_cents - 20;
new_state->used_coin = current->used_coin + 1;
if (visited.find(new_state) == visited.end())
{
visited.insert(new_state);
bfs_queue.push(new_state);
}
}
if (current->num_50_cents > 0)
{
UVa166_State* new_state = new UVa166_State();
new_state->num_5_cents = current->num_5_cents;
new_state->num_10_cents = current->num_10_cents;
new_state->num_20_cents = current->num_20_cents;
new_state->num_50_cents = current->num_50_cents - 1;
new_state->num_1_dollar = current->num_1_dollar;
new_state->num_2_dollars = current->num_2_dollars;
new_state->value_in_cents = current->value_in_cents - 50;
new_state->used_coin = current->used_coin + 1;
if (visited.find(new_state) == visited.end())
{
visited.insert(new_state);
bfs_queue.push(new_state);
}
}
if (current->num_1_dollar > 0)
{
UVa166_State* new_state = new UVa166_State();
new_state->num_5_cents = current->num_5_cents;
new_state->num_10_cents = current->num_10_cents;
new_state->num_20_cents = current->num_20_cents;
new_state->num_50_cents = current->num_50_cents;
new_state->num_1_dollar = current->num_1_dollar - 1;
new_state->num_2_dollars = current->num_2_dollars;
new_state->value_in_cents = current->value_in_cents - 100;
new_state->used_coin = current->used_coin + 1;
if (visited.find(new_state) == visited.end())
{
visited.insert(new_state);
bfs_queue.push(new_state);
}
}
if (current->num_2_dollars > 0)
{
UVa166_State* new_state = new UVa166_State();
new_state->num_5_cents = current->num_5_cents;
new_state->num_10_cents = current->num_10_cents;
new_state->num_20_cents = current->num_20_cents;
new_state->num_50_cents = current->num_50_cents;
new_state->num_1_dollar = current->num_1_dollar;
new_state->num_2_dollars = current->num_2_dollars - 1;
new_state->value_in_cents = current->value_in_cents - 200;
new_state->used_coin = current->used_coin + 1;
if (visited.find(new_state) == visited.end())
{
visited.insert(new_state);
bfs_queue.push(new_state);
}
}
}
else
{
{
UVa166_State* new_state = new UVa166_State();
new_state->num_5_cents = current->num_5_cents;
new_state->num_10_cents = current->num_10_cents;
new_state->num_20_cents = current->num_20_cents;
new_state->num_50_cents = current->num_50_cents;
new_state->num_1_dollar = current->num_1_dollar;
new_state->num_2_dollars = current->num_2_dollars;
new_state->value_in_cents = current->value_in_cents + 5;
new_state->used_coin = current->used_coin + 1;
if (visited.find(new_state) == visited.end())
{
visited.insert(new_state);
bfs_queue.push(new_state);
}
}
{
UVa166_State* new_state = new UVa166_State();
new_state->num_5_cents = current->num_5_cents;
new_state->num_10_cents = current->num_10_cents;
new_state->num_20_cents = current->num_20_cents;
new_state->num_50_cents = current->num_50_cents;
new_state->num_1_dollar = current->num_1_dollar;
new_state->num_2_dollars = current->num_2_dollars;
new_state->value_in_cents = current->value_in_cents + 10;
new_state->used_coin = current->used_coin + 1;
if (visited.find(new_state) == visited.end())
{
visited.insert(new_state);
bfs_queue.push(new_state);
}
}
{
UVa166_State* new_state = new UVa166_State();
new_state->num_5_cents = current->num_5_cents;
new_state->num_10_cents = current->num_10_cents;
new_state->num_20_cents = current->num_20_cents;
new_state->num_50_cents = current->num_50_cents;
new_state->num_1_dollar = current->num_1_dollar;
new_state->num_2_dollars = current->num_2_dollars;
new_state->value_in_cents = current->value_in_cents + 20;
new_state->used_coin = current->used_coin + 1;
if (visited.find(new_state) == visited.end())
{
visited.insert(new_state);
bfs_queue.push(new_state);
}
}
{
UVa166_State* new_state = new UVa166_State();
new_state->num_5_cents = current->num_5_cents;
new_state->num_10_cents = current->num_10_cents;
new_state->num_20_cents = current->num_20_cents;
new_state->num_50_cents = current->num_50_cents;
new_state->num_1_dollar = current->num_1_dollar;
new_state->num_2_dollars = current->num_2_dollars;
new_state->value_in_cents = current->value_in_cents + 50;
new_state->used_coin = current->used_coin + 1;
if (visited.find(new_state) == visited.end())
{
visited.insert(new_state);
bfs_queue.push(new_state);
}
}
{
UVa166_State* new_state = new UVa166_State();
new_state->num_5_cents = current->num_5_cents;
new_state->num_10_cents = current->num_10_cents;
new_state->num_20_cents = current->num_20_cents;
new_state->num_50_cents = current->num_50_cents;
new_state->num_1_dollar = current->num_1_dollar;
new_state->num_2_dollars = current->num_2_dollars;
new_state->value_in_cents = current->value_in_cents + 100;
new_state->used_coin = current->used_coin + 1;
if (visited.find(new_state) == visited.end())
{
visited.insert(new_state);
bfs_queue.push(new_state);
}
}
{
UVa166_State* new_state = new UVa166_State();
new_state->num_5_cents = current->num_5_cents;
new_state->num_10_cents = current->num_10_cents;
new_state->num_20_cents = current->num_20_cents;
new_state->num_50_cents = current->num_50_cents;
new_state->num_1_dollar = current->num_1_dollar;
new_state->num_2_dollars = current->num_2_dollars;
new_state->value_in_cents = current->value_in_cents + 200;
new_state->used_coin = current->used_coin + 1;
if (visited.find(new_state) == visited.end())
{
visited.insert(new_state);
bfs_queue.push(new_state);
}
}
}
}
if (!found)
{
throw 0;
}
}

return 0;
}

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