八皇后问题

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;
}

来源：http://www.cnblogs.com/codingmylife/archive/2012/10/04/2711839.html