USACO Magic Squares 解题报告

在发现8!=40320之后，我发现空间不是影响因素了。只要不重复运算，时间和空间都是足够的。

值得借鉴的地方：

1.对于转换的处理：

/* the set of transformations, in order */

static int tforms[3][8] = { {8, 7, 6, 5, 4, 3, 2, 1}, {4, 1, 2, 3, 6, 7, 8, 5}, 

{1, 7, 2, 4, 5, 3, 6, 8} };

这里是另外一种思路，处理起来相对更简单些。思路是直接将转化理解为对不同拷贝位置（初始位置转换后的位置）的映射。比如第一个转化里面第0为应该拷贝第7位(8-1)。第一个转化其实就是这一个数组，即拷贝位置的映射。

2.康拓展开

康拓展开是个好定理：作用是求一个排列如45213在这个5个数的全排列中的序列。可以直接移步这里：http://blog.csdn.net/fairyroad/article/details/7555773

代码写得很好。

/*ID: thestor1LANG: C++TASK: msquare*/#include <iostream>#include <cmath>#include <cstdio>#include <cstring>#include <vector>#include <cassert>#include <string>#include <algorithm>#include <stack>#include <set>using namespace std;const int size = 8;const int MAX = 40320;//8! = 40320struct Square{int h;int square[size];char op;int prev;Square(){h = -1;}int hash(){if(h > 0){return h;}int h = 0;for(int i = 0; i < size; ++i){h = (h << 3) + square[i];}return h;}};Square squares[MAX];bool equal(Square &s1, Square &s2){return s1.hash() == s2.hash();}bool equal(int *s1, int *s2){for(int i = 0; i < size; ++i){if(s1[i] != s2[i]){return false;}}return true;}void copy(int *s, int *d){for(int i = 0; i < size; ++i){d[i] = s[i];}}void A(int *square){for(int i = 0; i <= 3; ++i){int tmp = square[i];square[i] = square[7 - i];square[7 - i] = tmp;}}void B(int *square){int tmp = square[3];for(int i = 3; i >= 1; --i){square[i] = square[i - 1];}square[0] = tmp;tmp = square[4];for(int i = 4; i <= 6; ++i){square[i] = square[i + 1];}square[7] = tmp;}void C(int *square){int tmp = square[1];square[1] = square[6];square[6] = square[5];square[5] = square[2];square[2] = tmp;}int main(){FILE *fin  = fopen ("msquare.in", "r");FILE *fout = fopen ("msquare.out", "w");//freopen("log.txt", "w", stdout);Square targetSq;//int target[size];for(int i = 0; i < size; ++i){fscanf(fin, "%d", &targetSq.square[i]);}set<int> sqs;int top = 0;for(int i = 0; i < size; ++i){squares[top].square[i] = i + 1;}sqs.insert(squares[top].hash());top++;int final = -1;for(int i = 0; i < top; ++i){//fprintf(stdout, "i: %d, top: %d\n", i, top);Square sq = squares[i];if(equal(sq, targetSq)){final = i;break;}copy(sq.square, squares[top].square);A(squares[top].square);if(sqs.find(squares[top].hash()) == sqs.end()){squares[top].prev = i;squares[top].op = 'A';sqs.insert(squares[top].hash());top++;}copy(sq.square, squares[top].square);B(squares[top].square);if(sqs.find(squares[top].hash()) == sqs.end()){squares[top].prev = i;squares[top].op = 'B';sqs.insert(squares[top].hash());top++;}copy(sq.square, squares[top].square);C(squares[top].square);if(sqs.find(squares[top].hash()) == sqs.end()){squares[top].prev = i;squares[top].op = 'C';sqs.insert(squares[top].hash());top++;}}stack<char> seq;while(final != 0){seq.push(squares[final].op);final = squares[final].prev;}fprintf(fout, "%d\n", seq.size());while(!seq.empty()){fprintf(fout, "%c", seq.top());seq.pop();}fprintf(fout, "\n");return 0;}