A*算法完美解决八数码问题

/*----------------------------------------------------

C++的八数码的原代码

-----------------------------------------------------*/

#include <iostream>
#include <ctime>
#include <vector>
using namespace std;

const int ROW = 3;
const int COL = 3;
const int MAXDISTANCE = 10000;
const int MAXNUM = 10000;

typedef struct _Node{
int digit[ROW][COL];
int dist; // distance between one state and the destination
int dep; // the depth of node
// So the comment function = dist + dep.
int index; // point to the location of parent
} Node;

Node src, dest;

vector<Node> node_v; // store the nodes

bool isEmptyOfOPEN() {
for (int i = 0; i < node_v.size(); i++) {
if (node_v[i].dist != MAXNUM)
return false;
}
return true;
}

bool isEqual(int index, int digit[][COL]) {
for (int i = 0; i < ROW; i++)
for (int j = 0; j < COL; j++) {
if (node_v[index].digit[i][j] != digit[i][j])
return false;
}
return true;
}

ostream& operator<<(ostream& os, Node& node) {
for (int i = 0; i < ROW; i++) {
for (int j = 0; j < COL; j++)
os << node.digit[i][j] << ' ';
os << endl;
}
return os;
}

void PrintSteps(int index, vector<Node>& rstep_v) {
rstep_v.push_back(node_v[index]);
index = node_v[index].index;
while (index != 0) {
rstep_v.push_back(node_v[index]);
index = node_v[index].index;
}

for (int i = rstep_v.size() - 1; i >= 0; i--)
cout << "Step " << rstep_v.size() - i
<< endl << rstep_v[i] << endl;
}

void Swap(int& a, int& b) {
int t;
t = a;
a = b;
b = t;
}

void Assign(Node& node, int index) {
for (int i = 0; i < ROW; i++)
for (int j = 0; j < COL; j++)
node.digit[i][j] = node_v[index].digit[i][j];
}

int GetMinNode() {
int dist = MAXNUM;
int loc; // the location of minimize node
for (int i = 0; i < node_v.size(); i++) {
if (node_v[i].dist == MAXNUM)
continue;
else if ((node_v[i].dist + node_v[i].dep) < dist) {
loc = i;
dist = node_v[i].dist + node_v[i].dep;
}
}

return loc;
}

bool isExpandable(Node& node) {
for (int i = 0; i < node_v.size(); i++) {
if (isEqual(i, node.digit))
return false;
}
return true;
}

int Distance(Node& node, int digit[][COL]) {
int distance = 0;
bool flag = false;
for(int i = 0; i < ROW; i++)
for (int j = 0; j < COL; j++)
for (int k = 0; k < ROW; k++) {
for (int l = 0; l < COL; l++) {
if (node.digit[i][j] == digit[k][l]) {
distance += abs(i - k) + abs(j - l);
flag = true;
break;
}
else
flag = false;
}
if (flag)
break;
}
return distance;
}

int MinDistance(int a, int b) {
return (a < b ? a : b);
}

void ProcessNode(int index) {
int x, y;
bool flag;
for (int i = 0; i < ROW; i++) {
for (int j = 0; j < COL; j++) {
if (node_v[index].digit[i][j] == 0) {
x =i; y = j;
flag = true;
break;
}
else flag = false;
}
if(flag)
break;
}

Node node_up;
Assign(node_up, index);
int dist_up = MAXDISTANCE;
if (x > 0) {
Swap(node_up.digit[x][y], node_up.digit[x - 1][y]);
if (isExpandable(node_up)) {
dist_up = Distance(node_up, dest.digit);
node_up.index = index;
node_up.dist = dist_up;
node_up.dep = node_v[index].dep + 1;
node_v.push_back(node_up);
}
}

Node node_down;
Assign(node_down, index);
int dist_down = MAXDISTANCE;
if (x < 2) {
Swap(node_down.digit[x][y], node_down.digit[x + 1][y]);
if (isExpandable(node_down)) {
dist_down = Distance(node_down, dest.digit);
node_down.index = index;
node_down.dist = dist_down;
node_down.dep = node_v[index].dep + 1;
node_v.push_back(node_down);
}
}

Node node_left;
Assign(node_left, index);
int dist_left = MAXDISTANCE;
if (y > 0) {
Swap(node_left.digit[x][y], node_left.digit[x][y - 1]);
if (isExpandable(node_left)) {
dist_left = Distance(node_left, dest.digit);
node_left.index = index;
node_left.dist = dist_left;
node_left.dep = node_v[index].dep + 1;
node_v.push_back(node_left);
}
}

Node node_right;
Assign(node_right, index);
int dist_right = MAXDISTANCE;
if (y < 2) {
Swap(node_right.digit[x][y], node_right.digit[x][y + 1]);
if (isExpandable(node_right)) {
dist_right = Distance(node_right, dest.digit);
node_right.index = index;
node_right.dist = dist_right;
node_right.dep = node_v[index].dep + 1;
node_v.push_back(node_right);
}
}

node_v[index].dist = MAXNUM;
}

int main() {
int number;

cout << "Input source:" << endl;
for (int i = 0; i < ROW; i++)
for (int j = 0; j < COL; j++) {
cin >> number;
src.digit[i][j] = number;
}
src.index = 0;
src.dep = 1;

cout << "Input destination:" << endl;
for (int m = 0; m < ROW; m++)
for (int n = 0; n < COL; n++) {
cin >> number;
dest.digit[m][n] = number;
}

node_v.push_back(src);

cout << "Search..." << endl;
clock_t start = clock();
while (1) {
if (isEmptyOfOPEN()) {
cout << "Cann't solve this statement!" << endl;
return -1;
}
else {
int loc; // the location of the minimize node
loc = GetMinNode();
if(isEqual(loc, dest.digit)) {
vector<Node> rstep_v;
cout << "Source:" << endl;
cout << src << endl;
PrintSteps(loc, rstep_v);
cout << "Successful!" << endl;
cout << "Using " << (clock() - start) / CLOCKS_PER_SEC
<< " seconds." << endl;
break;
}
else
ProcessNode(loc);
}
}

return 0;
}
//程序完美运行