[组合数] SRM 555 Div1 Medium XorBoard

最新推荐文章于 2018-09-18 15:46:00 发布

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本文介绍了一个名为XorBoard的问题解决方案，该方案通过计算特定条件下行列操作的次数来解决问题。利用组合数学的方法，文章详细阐述了如何通过编程实现这一过程，并提供了具体的代码示例。

$Solution$

枚举行列进行奇数次操作的个数，组合数算一下就好了。

// BEGIN CUT HERE

// END CUT HERE
#line 5 "XorBoard.cpp"
#include <bits/stdc++.h>
using namespace std;

const int N = 3333;
const int MOD = 555555555;
typedef long long ll;

int n, m, nc, mc, s, ans;
int C[N][N];

inline void Add(int &x, int a) {
    x = (x + a) % MOD;
}
inline void Pre(int n) {
    for(int i = 0; i <= n; i++) {
        C[i][0] = 1;
        for(int j = 1; j <= i; j++)
            C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % MOD;
    }
}

class XorBoard {

public:
    int count(int H, int W, int Rcount, int Ccount, int S) {
        n = H; m = W; nc = Rcount; mc = Ccount; s = S;
        ans = 0; Pre(max((nc >> 1) + n, (mc >> 1) + m));

        for(int i = nc & 1; i <= n && i <= nc; i += 2)
            for(int j = mc & 1; j <= m && j <= mc; j += 2)
                if(i * (m - j) + j * (n - i) == S)
                    Add(ans, (ll)C[n][i] * C[(nc - i >> 1) + n - 1][n - 1] % MOD * C[m][j] % MOD * C[(mc - j >> 1) + m - 1][m - 1] % MOD);
        return ans;
    }

    // BEGIN CUT HERE
public:
    void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) test_case_3(); if ((Case == -1) || (Case == 4)) test_case_4(); }
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 int &Expected, const int &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 = 2; int Arg1 = 2; int Arg2 = 2; int Arg3 = 2; int Arg4 = 4; int Arg5 = 4; verify_case(0, Arg5, count(Arg0, Arg1, Arg2, Arg3, Arg4)); }
    void test_case_1() { int Arg0 = 2; int Arg1 = 2; int Arg2 = 0; int Arg3 = 0; int Arg4 = 1; int Arg5 = 0; verify_case(1, Arg5, count(Arg0, Arg1, Arg2, Arg3, Arg4)); }
    void test_case_2() { int Arg0 = 10; int Arg1 = 20; int Arg2 = 50; int Arg3 = 40; int Arg4 = 200; int Arg5 = 333759825; verify_case(2, Arg5, count(Arg0, Arg1, Arg2, Arg3, Arg4)); }
    void test_case_3() { int Arg0 = 1200; int Arg1 = 1000; int Arg2 = 800; int Arg3 = 600; int Arg4 = 4000; int Arg5 = 96859710; verify_case(3, Arg5, count(Arg0, Arg1, Arg2, Arg3, Arg4)); }
    void test_case_4() { int Arg0 = 555; int Arg1 = 555; int Arg2 = 555; int Arg3 = 555; int Arg4 = 5550; int Arg5 = 549361755; verify_case(4, Arg5, count(Arg0, Arg1, Arg2, Arg3, Arg4)); }

    // END CUT HERE


};

// BEGIN CUT HERE
int main(void) {
    XorBoard ___test;
    ___test.run_test(-1);
    system("pause");
}
// END CUT HERE