跳舞链解数独 静态数组优化

前几天有人问我之前写的那个跳舞链解数独的程序的内存泄漏问题如何解决，因此回顾了一下我的那个程序。现在看来那个程序简直不忍直视，于是大刀阔斧的改了。主要是把动态内存分配都改为了静态预分配，这样就可以避免频繁的调用malloc和free。同时静态分配的好处就是内存访问局部性比较好，cache不容易miss。而且在一行四个节点连续分配的情况下，就没有必要存储左右指针了。而且在连续分配的时候，指针都可以蜕变为数组索引，访问就比较简单了。还有一个好处就是整个程序可读性大大增强。现在这个版本的代码如下，利用http://staffhome.ecm.uwa.edu.au/~00013890/sudokumin.php中的测试文件，总耗时 16967ms.这个耗时是在不输出结果数独的情况下测试的，带输出的测试没有去做，屏幕太闪。整个代码如下，虽说刮着c++的招牌，其实全是c。。。

#include <iostream>
#include <vector>
#include <stack>
#include <map>
#include <ctime>
#include <fstream>
using namespace std;
#define shift_base 0x80000000
struct basic_node
{
    //这里之所以没有left和right是因为我们每次分配一行的时候，是四个点一起分的，所以可以直接通过加减1来搞定左右关系
    int down;
    int up;
    int column;
};
struct basic_node total_nodes[324 + 81 * 9 * 4];//324个头节点，81个格子，每个格子有9种情况，每种情况有四个点。
int avail_node_index = 324;//分配节点时的编号
int node_stack[81];
int stack_index = 0;
struct node_heap
{
    int cul_value;//代表这个列中的1的个数
    int position_index;//代表着个点所指示的列的索引
};
struct node_heap mutual_index[324];//这个是堆
int current_heap_number = 323;//这个是当前可用的堆中的节点数
int available_column = 323;//这个是当前可用列数
int position_index[324];//这个是列在堆中的位置
int out[9][9] = { { 8, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 3, 6, 0, 0, 0, 0, 0 }, { 0, 7, 0, 0, 9, 0, 2, 0, 0 }, 
{0, 5, 0, 0, 0, 7, 0, 0, 0}, { 0, 0, 0, 0, 4, 5, 7, 0, 0 }, { 0, 0, 0, 1, 0, 0, 0, 3, 0 }, { 0, 0, 1, 0, 0, 0, 0, 6, 8 }, 
{0, 0, 8, 5, 0, 0, 0, 1, 0}, { 0, 9, 0, 0, 0, 0, 4, 0, 0 } };

void initial(void)
{
    for (int i = 0; i < 324; i++)
    {
        total_nodes[i].column = i;
        total_nodes[i].down = i;
        total_nodes[i].up = i;
        mutual_index[i].cul_value= 0;
        mutual_index[i].position_index = i;
        position_index[i] = i;
    }
    stack_index = 0;
    available_column = 323;
    current_heap_number = 323;
    avail_node_index = 324;
}
void swap_heap(int index_one, int index_two)//交换在堆中的两个元素的值，及相关数据索引
{
    int intermidate_one, intermidate_two;
    intermidate_one = mutual_index[index_one].cul_value;
    intermidate_two = mutual_index[index_one].position_index;
    mutual_index[index_one].cul_value = mutual_index[index_two].cul_value;
    mutual_index[index_one].position_index = mutual_index[index_two].position_index;
    mutual_index[index_two].cul_value = intermidate_one;
    mutual_index[index_two].position_index = intermidate_two;
    position_index[mutual_index[index_two].position_index] = index_two;
    position_index[mutual_index[index_one].position_index] = index_one;
}
void heap_initial()//初始化堆，这个动作是在所有的行插入完成之后做的
{
    int k, i = 0;
    int current_min;
    for (i = (current_heap_number - 1) / 2; i >= 0; i--)
    {
        k = i;
        while (2 * k + 1 <= current_heap_number)
        {
            current_min = mutual_index[k].cul_value;
            current_min = current_min < mutual_index[2 * k + 1].cul_value ? current_min : mutual_index[2 * k + 1].cul_value;
            if (2 * k + 2 <= current_heap_number)
            {
                current_min = current_min < mutual_index[2 * k + 2].cul_value ? current_min : mutual_index[2 * k + 2].cul_value;
            }
            if (current_min == mutual_index[k].cul_value)
            {
                break;
            }
            else
            {
                if (current_min == mutual_index[2 * k + 1].cul_value)
                {
                    swap_heap(k, 2 * k + 1);
                    k = 2 * k + 1;
                }
                else
                {
                    swap_heap(k, 2 * k + 2);
                    k = 2 * k + 2;
                }
            }
        }
    }
}
void delete_minimal()//删除堆中最小的元素
{
    int k;
    int current_min;
    if (current_heap_number != 0)
    {
        swap_heap(0, current_heap_number);//交换最高元素与最低元素
        current_heap_number--;//然后将堆的大小进行缩减
        k = 0;
        while (2 * k + 1 <= current_heap_number)//然后，下面便是一些维护性的工作，用来维护最小堆
        {
            current_min = mutual_index[k].cul_value;
            current_min = current_min < mutual_index[2 * k + 1].cul_value ? current_min : mutual_index[2 * k + 1].cul_value;
            if (2 * k + 2 <= current_heap_number)
            {
                current_min = current_min < mutual_index[2 * k + 2].cul_value ? current_min : mutual_index[2 * k + 2].cul_value;
            }
            if (current_min == mutual_index[k].cul_value)
            {
                return;
            }
            else
            {
                if (current_min == mutual_index[2 * k + 1].cul_value)
                {
                    swap_heap(k, 2 * k + 1);
                    k = 2 * k + 1;
                }
                else
                {
                    swap_heap(k, 2 * k + 2);
                    k = 2 * k + 2;
                }
            }
        }
    }
    else//如果只剩下一个元素，那就不需要进行交换，直接将堆元素的个数降低一
    {
        current_heap_number = -1;
    }
}
void heap_renew(int target_position, int new_value)//对于第target_position列，进行度数更新
{
    int heap_target_position, k, current_min;
    heap_target_position = position_index[target_position];//这个是这一列在堆中所在的位置
    k = heap_target_position;
    if (new_value < mutual_index[k].cul_value)//如果值是减少的，就直接进行赋值，然后维护堆的性质
    {
        mutual_index[k].cul_value = new_value;
        while (k > 0 && (mutual_index[(k - 1) / 2].cul_value > mutual_index[k].cul_value))//维护堆
        {
            swap_heap((k - 1) / 2, k);
            k = (k - 1) / 2;
        }
        if (new_value == 0)//如果是赋值为0，则从堆中进行删除，因为我们每次操纵一个元素，所以最多会有一个元素为0，所以肯定是最小值。
        {
            delete_minimal();
        }
    }
    else//对于值增大的情况
    {
        mutual_index[k].cul_value = new_value;
        if (new_value == 1)//如果新的值是1，则把这个元素重新加入堆中
        {
            current_heap_number++;//扩大堆的范围，我们可以证明重新加入堆中的元素一定是排在堆的末尾，当然条件是删除与插入的顺序是对应相反的
            while (k > 0 && (mutual_index[(k - 1) / 2].cul_value > mutual_index[k].cul_value))//由于新的值是1，所以不可能比上一个数大
            {
                swap_heap((k - 1) / 2, k);
                k = (k - 1) / 2;
            }
        }
        else//如果不是1，说明已经在堆中，所以不需要扩大堆的范围，直接赋值之后进行维护堆结构就行
        {
            while (2 * k + 1 <= current_heap_number)
            {
                current_min = mutual_index[k].cul_value;
                current_min = current_min < mutual_index[2 * k + 1].cul_value ? current_min : mutual_index[2 * k + 1].cul_value;
                if (2 * k + 2 <= current_heap_number)
                {
                    current_min = current_min < mutual_index[2 * k + 2].cul_value ? current_min : mutual_index[2 * k + 2].cul_value;
                }
                if (current_min == mutual_index[k].cul_value)
                {
                    break;
                }
                else
                {
                    if (current_min == mutual_index[2 * k + 1].cul_value)
                    {
                        swap_heap(k, 2 * k + 1);
                        k = 2 * k + 1;
                    }
                    else
                    {
                        swap_heap(k, 2 * k + 2);
                        k = 2 * k + 2;
                    }
                }
            }
        }
    }
}
void node_heap_decrease(int node_index)//对于一个点进行她所在的行的删除，因为一行中一定有四个元素，所以有四列，我们对这四列的度数都进行减少1
{
    int leftmost_node;//当前节点所在行的最左节点的索引
    leftmost_node = node_index - (node_index % 4);
    heap_renew(total_nodes[leftmost_node].column, mutual_index[position_index[total_nodes[leftmost_node].column]].cul_value -1);
    leftmost_node++;
    heap_renew(total_nodes[leftmost_node].column, mutual_index[position_index[total_nodes[leftmost_node].column]].cul_value -1);
    leftmost_node++;
    heap_renew(total_nodes[leftmost_node].column, mutual_index[position_index[total_nodes[leftmost_node].column]].cul_value -1);
    leftmost_node++;
    heap_renew(total_nodes[leftmost_node].column, mutual_index[position_index[total_nodes[leftmost_node].column]].cul_value -1);
}
void node_heap_increase(int node_index)//增加与减少的顺序是刚好相反的
{
    int leftmost_node;//当前节点所在行的最右节点的索引
    leftmost_node = node_index - (node_index % 4)+3;
    heap_renew(total_nodes[leftmost_node].column, mutual_index[position_index[total_nodes[leftmost_node].column]].cul_value + 1);
    leftmost_node--;
    heap_renew(total_nodes[leftmost_node].column, mutual_index[position_index[total_nodes[leftmost_node].column]].cul_value + 1);
    leftmost_node--;
    heap_renew(total_nodes[leftmost_node].column, mutual_index[position_index[total_nodes[leftmost_node].column]].cul_value + 1);
    leftmost_node--;
    heap_renew(total_nodes[leftmost_node].column, mutual_index[position_index[total_nodes[leftmost_node].column]].cul_value + 1);
}
void insert_row(int current_row_index, int current_column_index, int value)
{
    int current_leftmost = avail_node_index;
    avail_node_index += 4;
    int column_index;
    column_index = current_row_index * 9 + value - 1;
    total_nodes[current_leftmost].column = column_index;
    total_nodes[current_leftmost].down = column_index;
    total_nodes[current_leftmost].up = total_nodes[column_index].up;
    total_nodes[total_nodes[column_index].up].down = current_leftmost;
    total_nodes[column_index].up = current_leftmost;
    mutual_index[column_index].cul_value++;
    current_leftmost++;
    column_index = 81 + current_column_index * 9 + value - 1;
    total_nodes[current_leftmost].column = column_index;
    total_nodes[current_leftmost].down = column_index;
    total_nodes[current_leftmost].up = total_nodes[column_index].up;
    total_nodes[total_nodes[column_index].up].down = current_leftmost;
    total_nodes[column_index].up = current_leftmost;
    mutual_index[column_index].cul_value++;
    current_leftmost++;
    column_index= 162 + ((current_row_index / 3) * 3 + current_column_index / 3) * 9 + value - 1;
    total_nodes[current_leftmost].column = column_index;
    total_nodes[current_leftmost].down = column_index;
    total_nodes[current_leftmost].up = total_nodes[column_index].up;
    total_nodes[total_nodes[column_index].up].down = current_leftmost;
    total_nodes[column_index].up = current_leftmost;
    mutual_index[column_index].cul_value++;
    current_leftmost++;
    column_index = 243 + current_row_index * 9 + current_column_index;
    total_nodes[current_leftmost].column = column_index;
    total_nodes[current_leftmost].down = column_index;
    total_nodes[current_leftmost].up = total_nodes[column_index].up;
    total_nodes[total_nodes[column_index].up].down = current_leftmost;
    total_nodes[column_index].up = current_leftmost;
    mutual_index[column_index].cul_value++;
}
void print_result()//打印出结果
{
    int i, j, k, current_index;
    int m, n;
    int output[9][9];
    for (i = 0; i < 9; i++)
    {
        for (j = 0; j < 9; j++)
        {
            output[i][j] = 0;
        }
    }
    for (m = 0; m < stack_index; m++)
    {
        current_index = node_stack[m]-node_stack[m]%4;
        k = total_nodes[current_index].column % 9;
        i = (total_nodes[current_index].column-total_nodes[current_index].column % 9)/9;
        current_index ++;
        j = (total_nodes[current_index].column - total_nodes[current_index].column % 9-81) / 9;
        output[i][j] = k + 1;
    }
    printf("***********************
");
    for (m = 0; m < 9; m++)
    {
        for (n = 0; n < 9; n++)
        {
            printf("%d ", output[m][n]);
        }
        printf("
");
    }
}

void creat_dlx_sudoku()//利用矩阵来建立十字网格
{
    int i, j, k;
    int row_position[9][9];//这个是行
    int column_position[9][9];//这个是列
    int small_position[9][9];//这个是每一个小方格
    initial();
    for (i = 0; i < 9; i++)
    {
        for (j = 0; j < 9; j++)
        {
            row_position[i][j] = 1;
            column_position[i][j] = 1;
            small_position[i][j] = 1;
        }
        
    }
    for (i = 0; i < 9; i++)
    {
        for (j = 0; j < 9; j++)
        {
            if (out[i][j] != 0)
            {
                row_position[i][out[i][j]-1] = 0;
                column_position[j][out[i][j]-1] = 0;
                small_position[(i / 3) * 3 + j / 3][out[i][j]-1] = 0;
            }
        }
    }
    for (i = 0; i < 9; i++)
    {
        for (j = 0; j < 9; j++)
        {
            if (out[i][j] != 0)
            {
                insert_row(i, j, out[i][j]);
            }
            else
            {
                for (k = 0; k < 9; k++)
                {
                    if ((row_position[i][k] * column_position[j][k] * small_position[(i / 3) * 3 + j / 3][k])==1)
                    {
                        insert_row(i, j, k + 1);
                    }
                    else
                    {
                        //do nothing
                    }
                }
            }
        }
    }
    heap_initial();
}
void in_stack(int target_to_stack)
{
    int leftmost = target_to_stack - target_to_stack % 4;
    for (int i = 0; i < 4; i++)//对于当前行的每一列
    {
        int current_column_traversal = leftmost + i;
        current_column_traversal = total_nodes[current_column_traversal].down;
        while (current_column_traversal != leftmost + i)//删除当前列相交的行
        {
            if (current_column_traversal != total_nodes[current_column_traversal].column)//即不是头行
            {
                int temp_node = current_column_traversal - current_column_traversal % 4-1;
                for (int j = 0; j < 4; j++)
                {
                    temp_node++;
                    if (temp_node != current_column_traversal)
                    {
                        total_nodes[total_nodes[temp_node].down].up = total_nodes[temp_node].up;
                        total_nodes[total_nodes[temp_node].up].down = total_nodes[temp_node].down;
                    }
                }
                node_heap_decrease(temp_node);
            }
            current_column_traversal = total_nodes[current_column_traversal].down;
        }
    }
    node_heap_decrease(target_to_stack);//最后对当前行进行删除
    node_stack[stack_index++] = target_to_stack;//然后才是入栈
    available_column -= 4;
    //print_result();
}
void out_stack()//注意出栈的时候是相反的操作，所有删除都相反
{
    int target_to_stack = node_stack[--stack_index];
    int rightmost = target_to_stack - target_to_stack % 4+3;
    for (int i = 0; i < 4; i++)//对于当前行的每一列
    {
        int current_column_traversal = rightmost - i;
        current_column_traversal = total_nodes[current_column_traversal].up;
        while (current_column_traversal != rightmost - i)//删除当前列相交的行
        {
            if (current_column_traversal != total_nodes[current_column_traversal].column)//即不是头行
            {
                int temp_node = current_column_traversal - current_column_traversal % 4+4;
                for (int j = 0; j < 4; j++)
                {
                    temp_node --;
                    if (temp_node != current_column_traversal)
                    {
                        total_nodes[total_nodes[temp_node].down].up = temp_node;
                        total_nodes[total_nodes[temp_node].up].down = temp_node;
                    }
                }
                node_heap_increase(temp_node);
            }
            current_column_traversal = total_nodes[current_column_traversal].up;
        }
    }
    node_heap_increase(target_to_stack);//最后对当前行进行回复
    available_column += 4;
    //print_result();
}
int find_next()//用来找下一个可以入栈的元素，如果无法入栈或者已经找到了解，则返回并进行回溯操作
{
    int target_position;
    int temp_node_one;
    if (available_column == current_heap_number)
    {
        if (available_column == -1)
        {
            //print_result();
            return 2;
        }
        else
        {
            target_position = mutual_index[0].position_index;
            temp_node_one = total_nodes[target_position].down;
            in_stack(temp_node_one);
            return 1;
        }
    }
    else
    {
        return 0;
    }
}
void seek_sudoku()
{
    int find_result = 0;
    int temp_node_one;
    while (1)
    {
        find_result = find_next();
        if (!find_result)//如果无法入栈且目前没有找到解，则出栈
        {
            temp_node_one = node_stack[stack_index - 1];
            out_stack();
            temp_node_one = total_nodes[temp_node_one].down;
            while ((temp_node_one==total_nodes[temp_node_one].column))//如果当前元素是当前列头节点，则递归出栈
            {
                if (stack_index == 0)//如果栈空，则所有的搜索空间已经搜索完全 返回
                {
                    return;
                }
                else
                {
                    temp_node_one = node_stack[stack_index - 1];
                    out_stack();
                    temp_node_one = total_nodes[temp_node_one].down;
                }
            }
            in_stack(temp_node_one);//将所选元素入栈
        }
        else
        {
            if (find_result / 2)//如果已经找到结果，则返回，事实上我们可以更改这个逻辑来应对有多个解的情况，并把它全部打印
            {
                return;
            }
        }
    }
}
int main()
{
    clock_t clock_one, clock_two, clock_three;
    ifstream suduko_file("sudoku.txt");
    char temp[82];
    clock_one = clock();
    int line = 1;
    while (line!=49152)
    {
        suduko_file.getline(temp, 82);
        for (int i = 0; i < 9; i++)
        {
            for (int j = 0; j < 9; j++)
            {
                out[i][j] = temp[i * 9 + j] - '0';
            }
        }
        creat_dlx_sudoku();
        seek_sudoku();
        line++;
    }
    clock_three = clock();
    printf("%d mscond passed in seek_sudoku
", clock_three - clock_one);
}