八皇后问题N种解法
主要包括全排列和回溯两类，其中全排列可以递归与非递归，回溯也可以递归与非递归。于是加一起有4种解法。
#include <iostream>
#include <algorithm>
using namespace std;
template <size_t N> struct ArraySizeHelper {char _[N];};
template <typename T, size_t N> ArraySizeHelper<N> makeArraySizeHelper(T(&)[N]);
#define ARRAY_SIZE(a) sizeof(makeArraySizeHelper(a))
bool valid_permutation(const int *queen, int len)
{
bool valid = true;
for (int i = 0; i < len; ++i)
{
for (int j = i + 1; j < len; ++j)
{
if (queen[j] - queen[i] == j - i || queen[j] - queen[i] == i - j)
{
valid = false;
}
}
}
return valid;
}
// Solved by permutation non recursion.
int eightqueen_permutation_non_recur()
{
int queen[] = {0, 1, 2, 3, 4, 5, 6, 7};
int count = 0;
do
{
if (valid_permutation(queen, (int)ARRAY_SIZE(queen))) ++count;
}
while(next_permutation(queen, queen + ARRAY_SIZE(queen)));
return count;
}
void permutation(int *queen, int len, int idx, int &count)
{
if (idx == len)
{
if (valid_permutation(queen, len)) ++count;
}
else
{
for (int i = idx; i < len; ++i)
{
swap(queen[i], queen[idx]);
permutation(queen, len, idx + 1, count);
swap(queen[i], queen[idx]);
}
}
}
// Solved by permutation recursion.
int eightqueen_permutation_recur()
{
int queen[] = {0, 1, 2, 3, 4, 5, 6, 7};
int count = 0;
permutation(queen, (int)ARRAY_SIZE(queen), 0, count);
return count;
}
bool valid_backtracking(const int *queen, int len)
{
for (int i = 0; i < len; ++i)
{
const int diff = abs(queen[i] - queen[len]);
if (diff == 0 || diff == len - i) return false;
}
return true;
}
void placequeen(int *queen, int len, int idx, int &count)
{
if (idx == len)
{
++count;
}
else
{
for (int i = 0; i < len; ++i)
{
queen[idx] = i;
if (valid_backtracking(queen, idx))
{
placequeen(queen, len, idx + 1, count);
}
}
}
}
// Solved by backtracking(DFS) recursion.
int eightqueen_backtracking_recur()
{
int queen[8];
int count = 0;
placequeen(queen, (int)ARRAY_SIZE(queen), 0, count);
return count;
}
// Solved by backtracking(DFS) non recursion.
int eightqueen_backtracking_non_recur()
{
int queen[8] = {-1, -1, -1, -1, -1, -1, -1, -1};
int count = 0;
int step = 0;
while(step >= 0)
{
bool valid = false;
for (int i = queen[step] + 1; i < (int)ARRAY_SIZE(queen); ++i)
{
queen[step] = i;
if (valid_backtracking(queen, step))
{
step += 1;
valid = true;
break;
}
}
if (!valid)
{
queen[step] = -1;
step -= 1;
}
else if (step >= 8)
{
++count;
step -= 1;
}
}
return count;
}
int main()
{
cout << eightqueen_permutation_recur() << endl;
cout << eightqueen_permutation_non_recur() << endl;
cout << eightqueen_backtracking_recur() << endl;
cout << eightqueen_backtracking_non_recur() << endl;
return 0;
}