[Topcoder]AvoidRoads（dp，hash）

题目连接：https://community.topcoder.com/stat?c=problem_statement&pm=1889&rd=4709

题意：给一张n*m的地图，上面有些路不能走，每次只能向左走或者向下走。问从(0,0)走到(n,m)一共有多少种走法。

动态规划，先哈希标记出所有无法走的道路，然后做DP。

转移方程：

如果(i-1,j)可以走到(i,j)：dp(i,j)+=dp(i-1,j)

如果(i,j-1)可以走到(i,j)：dp(i,j)+=dp(i,j-1)

 // BEGIN CUT HERE

 // END CUT HERE
 #line 5 "AvoidRoads.cpp"
 #include <cstdlib>
 #include <cctype>
 #include <cstring>
 #include <cstdio>
 #include <cmath>
 #include <algorithm>
 #include <vector>
 #include <string>
 #include <iostream>
 #include <sstream>
 #include <map>
 #include <set>
 #include <queue>
 #include <stack>
 #include <fstream>
 #include <numeric>
 #include <iomanip>
 #include <bitset>
 #include <list>
 #include <stdexcept>
 #include <functional>
 #include <utility>
 #include <ctime>
 using namespace std;

 typedef long long ll;
 const int mod = ;
 bool cut[mod];
 unsigned long long dp[][];

 int cv(int x1, int y1, int x2, int y2) {
     return ((((x1 *  % mod) + y1 *  % mod) + x2 * ) % mod + y2 * ) % mod;
 }

 class AvoidRoads
 {
         public:
         long long numWays(int width, int height, vector<string> bad) {
             int x1,y1,x2,y2;
             int& n = width;
             int& m = height;
             memset(cut, , sizeof(cut));
             memset(dp, , sizeof(dp));
             for(int i = ; i < bad.size(); i++) {
                 stringstream ss;
                 ss << bad[i];
                 ss >> x1 >> y1 >> x2 >> y2;
                 cut[cv(x1,y1,x2,y2)] = ;
                 cut[cv(x2,y2,x1,y1)] = ;

             }
             dp[][] = ;
             for(int i = ; i < n; i++) {
                 if(!cut[cv(i,,i+,)]) dp[i+][] = dp[i][];
                 else break;
             }
             for(int i = ; i < m; i++) {
                 if(!cut[cv(,i,,i+)]) dp[][i+] = dp[][i];
                 else break;
             }
             for(int i = ; i <= n; i++) {
                 for(int j = ; j <= m; j++) {
                     if(!cut[cv(i-,j,i,j)]) dp[i][j] += dp[i-][j];
                     if(!cut[cv(i,j-,i,j)]) dp[i][j] += dp[i][j-];
                 }
             }
             return dp[n][m];
         }

 // BEGIN CUT HERE
     public:
     void run_test(int Case) { if ((Case == -) || (Case == )) test_case_0(); if ((Case == -) || (Case == )) test_case_1(); if ((Case == -) || (Case == )) test_case_2(); if ((Case == -) || (Case == )) test_case_3(); }
     private:
     template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
     void verify_case(int Case, const long long &Expected, const long long &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } }
     void test_case_0() { int Arg0 = ; int Arg1 = ; string Arr2[] = {"0 0 0 1","6 6 5 6"}; vector <string> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[]))); long long Arg3 = 252LL; verify_case(, Arg3, numWays(Arg0, Arg1, Arg2)); }
     void test_case_1() { int Arg0 = ; int Arg1 = ; string Arr2[] = {}; vector <string> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[]))); long long Arg3 = 2LL; verify_case(, Arg3, numWays(Arg0, Arg1, Arg2)); }
     void test_case_2() { int Arg0 = ; int Arg1 = ; string Arr2[] = {}; vector <string> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[]))); long long Arg3 = 6406484391866534976LL; verify_case(, Arg3, numWays(Arg0, Arg1, Arg2)); }
     void test_case_3() { int Arg0 = ; int Arg1 = ; string Arr2[] = {"0 0 1 0", "1 2 2 2", "1 1 2 1"}; vector <string> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[]))); long long Arg3 = 0LL; verify_case(, Arg3, numWays(Arg0, Arg1, Arg2)); }

 // END CUT HERE

 };

 // BEGIN CUT HERE
 int main()
 {
         AvoidRoads ___test;
         ___test.run_test(-);
         return ;
 }
 // END CUT HERE