有4个瓶子,它们的容量分别是:
10升,6升, 5升, 4升
开始的状态是 [10,0,0,0],也就是说:第一个瓶子满着,其它的都空着。
允许把酒从一个瓶子倒入另一个瓶子,但只能把一个瓶子倒满或把一个瓶子倒空,不能有中间状态。这样的一次倒酒动作称为1次操作。
假设瓶子的容量和初始状态不变,对于给定的目标状态,至少需要多少次操作才能实现?
输入:最终状态 输出:最小操作次数(如无法实现,则输出-1)
例如:
输入:10 0 0 0
输出:0
输入:7 3 0 0
输出:8
利用map完成穷搜
//10升, 6升, 5升,4升
#include <iostream>
#include <map>
#include <limits>
int capacity[] = { 10, 6, 5, 4 };
class state
{
public:
state(int _b10, int _b6, int _b5, int _b4)
:count(0), value(_b10 * 1000 + _b6 * 100 + _b5 * 10 + _b4)
{
}
bool operator<(state rhs)const
{
return value < rhs.value;
}
int getvalue()const
{
return value;
}
short count;
protected:
short value;
};
std::map<int,state> open, close;
void int2array(int content[], state s)
{
int svalue = s.getvalue();
content[0] = svalue / 1000;
content[1] = svalue % 1000 / 100;
content[2] = svalue % 100 / 10;
content[3] = svalue % 10;
}
int array2int(int content[])
{
return content[0] * 1000 + content[1] * 100
+ content[2] * 10 + content[3];
}
//一步转移状态
void derive(std::pair<int, state> sp)
{
int c[4], t[4];
int2array(c, sp.second);
for (int i = 0; i < 4; ++i) // the bottle to pour from
{
if (c[i] == 0)
continue; // no action on empty bottle
for (int j = 0; j < 4; ++j) // the bottle to pour to
{
if (j == i || c[j] == capacity[j]) // don't pour to self or full bottle
continue;
//now we can derive a new state
//state s=*this;
//++s.count;
int balance = capacity[j] - c[j];
t[0] = c[0];
t[1] = c[1];
t[2] = c[2];
t[3] = c[3];
if (c[i] > balance) // source has more than target can hold
t[i] -= balance, t[j] = capacity[j];
else // target can hold everything currently in source
t[j] += t[i], t[i] = 0;
state si(t[0], t[1], t[2], t[3]);
si.count = sp.second.count + 1;
auto p = open.find(array2int(t));
auto q = close.find(array2int(t));
if (p != open.end()) // might encounter a better state
{
if (p->second.count > si.count)
p->second.count = si.count;
}
else if (q == close.end())
{
open.insert(std::pair<int, state>(array2int(t),si));
}
}
}
}
int main() {
int n = 4;
int input;
int min = INT_MAX;
int initvalue = 1;
//输入初始状态
open.insert(std::pair<int, state>(10000, state(10, 0, 0, 0)));
//输入的四个数变为一个数
for (int i = 0; i < n; i++)
{
std::cin >> input;
if (i == 0)
initvalue = input;
else
initvalue = initvalue * 10 + input;
}
//穷搜整个空间,取出open状态加入close,新状态加入open
while (!open.empty())
{
auto p = open.begin();
auto s = *p;
close.insert(s);
open.erase(p);
derive(s);
}
//printf
for (auto i = close.begin(); i != close.end(); ++i)
{
std::cout << i->first << " " << i->second.count << std::endl;
}
auto i = close.find(initvalue);
if(i != close.end())
if (min > i->second.count)
min = i->second.count;
if (min == INT_MAX)
std::cout << -1 << std::endl;
std::cout << min << std::endl;
return 0;
}
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