CSES - Datatähti 2019 alku

Submission details
Task:	Ruudukko
Sender:	Olli
Submission time:	2018-10-02 17:22:50 +0300
Language:	C++
Status:	READY
Result:	45

Feedback
group	verdict	score
#1	ACCEPTED	31
#2	ACCEPTED	14
#3	WRONG ANSWER	0

Test results
test	verdict	time	group
#1	ACCEPTED	0.02 s	1	details
#2	ACCEPTED	0.03 s	1	details
#3	ACCEPTED	0.01 s	1	details
#4	ACCEPTED	0.01 s	1	details
#5	ACCEPTED	0.02 s	1	details
#6	ACCEPTED	0.01 s	1	details
#7	ACCEPTED	0.02 s	1	details
#8	ACCEPTED	0.02 s	1	details
#9	ACCEPTED	0.02 s	1	details
#10	ACCEPTED	0.02 s	1	details
#11	ACCEPTED	0.02 s	2	details
#12	ACCEPTED	0.03 s	2	details
#13	ACCEPTED	0.02 s	2	details
#14	ACCEPTED	0.04 s	2	details
#15	ACCEPTED	0.07 s	2	details
#16	ACCEPTED	0.10 s	2	details
#17	ACCEPTED	0.11 s	2	details
#18	ACCEPTED	0.13 s	2	details
#19	ACCEPTED	0.12 s	2	details
#20	ACCEPTED	0.12 s	2	details
#21	WRONG ANSWER	0.12 s	3	details
#22	WRONG ANSWER	0.12 s	3	details
#23	WRONG ANSWER	0.11 s	3	details
#24	ACCEPTED	0.11 s	3	details
#25	ACCEPTED	0.11 s	3	details
#26	WRONG ANSWER	0.13 s	3	details
#27	WRONG ANSWER	0.11 s	3	details
#28	WRONG ANSWER	0.12 s	3	details
#29	WRONG ANSWER	0.12 s	3	details
#30	ACCEPTED	0.12 s	3	details

Code

#include <iostream>
#include <queue>
#include <vector>

using namespace std;

bool printStuff = false;

typedef long long ll;

const int N = 555;
const int M = 1e9 + 7;

char t[N][N];

ll n;

int aA;
int amB;

void swaR(int a, int b) {
	for(int x = 1; x <= n; ++x) {
		char c = t[a][x];
		char d = t[b][x];
		t[a][x] = d;
		t[b][x] = c;
	}
}

void swaC(int a, int b) {
	for(int y = 1; y <= n; ++y) {
		char c = t[y][a];
		char d = t[y][b];
		t[y][a] = d;
		t[y][b] = c;
	}
}

void print() {

	for(int y = 1; y <= n; ++y) {
		for(int x = 1; x <= n; ++x) {
			cout << t[y][x];
		}
		cout << "\n";
	}
	cout << "\n";
}

void sor() {

	vector<int> broken;

	for(int y = n; y >= n - amB + 1; --y) {
		bool conB = false;
		for(int x = 1; x <= n; ++x) {
			if(t[y][x] == 'B') {
				conB = true;
				break;
			}
		}

		if(!conB) broken.push_back(y);
	}

	for(int y = n - amB; y >= 1; --y) {
		bool conB = false;
		for(int x = 1; x <= n; ++x) {
			if(t[y][x] == 'B') {
				conB = true;
				break;
			}
		}
		if(!conB) {
			continue;
		}
		int k = broken[broken.size() - 1];
		swaR(k, y);
		broken.pop_back();
	}


	for(int y = n; y >= n - amB + 1; --y) {
		int col = -1;
		for(int x = 1; x <= n; ++x) {
			if(t[y][x] == 'B') {
				col = x;
			}
		}
		swaC(n - y + 1, col);
	}

	aA = 0;
	for(int x = amB + 1; x <= n; ++x) {
		for(int y = n - amB; y >= 1; --y) {
			if(t[y][x] == 'A') {
				++aA;
			}
		}
	}

	for(int y = n - amB; y >= n - amB - aA + 1; --y) {
		bool conA = false;
		for(int x = amB + 1; x <= n; ++x) {
			if(t[y][x] == 'A') {
				conA = true;
				break;
			}
		}

		if(!conA) {
			broken.push_back(y);
		}
	}

	for(int y = n - amB - aA; y >= 1; --y) {
		bool conA = false;
		for(int x = amB + 1; x <= n; ++x) {
			if(t[y][x] == 'A') {
				conA = true;
				break;
			}
		}
		if(conA) {
			int k = broken[broken.size() - 1];
			swaR(k, y);
			broken.pop_back();
		}
	}


	for(int y = n - amB; y >= n - amB - aA + 1; --y) {
		int col = -1;
		for(int x = amB + 1; x <= n; ++x) {
			if(t[y][x] == 'A') {
				col = x;
				break;
			}
		}
		swaC(n - y + 1, col);
	}

	if(printStuff) {
		cout << n << "\n";
		print();
	}
}


ll dp[N][N];


void fillDP() {
	dp[0][0] = 1;
	for(int x = 1; x <= n; ++x) {
		dp[x][0] = dp[x-1][0]*x;
		dp[x][0] %= M;
	}

	for(ll y = 1; y <= n; ++y) {
		for(ll x = y; x <= n; ++x) {
			dp[x][y] = dp[x-1][y-1]*(x-y);
			dp[x][y] %= M;
			if(y == 1) continue;
			dp[x][y] += dp[x-1][y-2]*(y-1);
			dp[x][y] %= M;
		}
	}
}

ll exp(ll a, ll e) {
	if(e == 0) return 1;
	if(e%2 == 0)  {
		ll c = exp(a, e/2);
		return (c*c)%M;
	}
	ll c = exp(a, e-1);
	return (c*a)%M;
}

ll fact[N];
ll binom[N][N];

bool marked[N];

int main() {
	cin >> n;
	for(int y = 1; y <= n; ++y) {
		for(int x = 1; x <= n; ++x) {
			char c;
			cin >> c;
			t[y][x] = c;
			if(c == 'B') ++amB;
		}
	}
	sor();

	fillDP();
	fact[0] = 1;
	for(ll i = 1; i <= n; ++i) {
		fact[i] = fact[i-1]*i;
		fact[i] %= M;
	}
	for(int m = 0; m <= n; ++m) {
		for(int k = 0; k <= m; ++k) {
			ll b = fact[m];
			b *= exp(fact[k], M-2);
			b %= M;
			b *= exp(fact[m-k], M-2);
			b %= M;
			binom[m][k] = b;
		}
	}

	ll ans = 0;



	int a1 = 0;
	int a2 = 0;
	int a3 = 0;


	//calculate a2
	for(int y = 1; y <= n - amB - aA; ++y) {
		for(int x = 1; x <= amB; ++x) {
			if(t[y][x] == 'A') {
				++a2;
			}
		}
	}

	//calculate a3;

	for(int y = n - amB; y <= n; ++y) {
		for(int x = amB + aA + 1; x <= n; ++x) {
			if(t[y][x] == 'A') {
				++a3;
			}
		}
	}
	//calculate a1;
	for(int x = 1; x <= amB; ++x) {
		for(int y = n - amB + 1; y <= n; ++y) {
			if(t[y][x] == 'A') {
				++a1;

			}
		}
	}
/*
	for(int i = 0; i <= n; ++i) {
		for(int a = 0; a <= i; ++a) {
			cout << dp[i][a] << " ";
		}
		cout << "\n";
	}
	cout << "\n";
*/
	int initialB = 0;
	//How many B:s have been hit initially

	for(int x = 1; x <= amB; ++x) {
		for(int y = 1; y <= n; ++y) {
			if(t[y][x] == 'A') {
				if(!marked[x]) {
					++initialB;
					marked[x] = true;
				}
				if(y >= n - amB + 1) {
					if(!marked[n-y+1]) {
						++initialB;
						marked[n-y+1] = true;
					}
				}
			}

		}
	}
	for(int y = n - amB + 1; y <= n; ++y) {
		for(int x = amB + 1; x <= n; ++x) {
			if(t[y][x] == 'A') {
				if(!marked[n - y + 1]) {
					++initialB;
					marked[n-y+1] = true;
				}
			}
		}
	}

	int hitAbove = 0;
	int noHitAbove = 0;
	int hitRight = 0;
	int noHitRight = 0;

	for(int x = 1; x <= amB; ++x) {
		bool contains = false;
		for(int y = 1; y <= n; ++y) {
			if(t[y][x] == 'A') {
				contains = true;
				break;
			}
		}
		if(contains) continue;
		for(int y = 1; y <= n; ++y) {
			if(t[y][x] == 'B') {
				if(marked[x]) {
					++noHitAbove;
				} else {
					++hitAbove;
				}
				break;
			}
		}
	}

	for(int y = n - amB + 1; y <= n; ++y) {
		bool contains = false;
		for(int x = 1; x <= n; ++x) {
			if(t[y][x] == 'A') {
				contains = true;
				break;
			}
		}
		if(contains) continue;
		for(int x = 1; x <= n; ++x) {
			if(t[y][x] == 'B') {
				if(marked[x]) {
					++noHitRight;
				} else {
					++hitRight;
				}
				break;
			}
		}
	}


	for(ll f2 = max(a2, a3); f2 <= min((ll) amB - a1, n - amB - aA); ++f2) {
		for(ll amountOfB = initialB; amountOfB <= amB; ++amountOfB) {
			//We will have amountOfB of B:s that have been hit
			//We have to hit amountOfB - initialB more
			ll A23 = 0;
			int t = amountOfB - initialB;
			if(t > f2 - a2 + f2 - a3) continue;
			int s = n - amB - aA;
			if(s < a2 || s < a3) continue;
			
			if(printStuff) {
				cout << "\n\n";
				cout << "The configuration we have: \n";
				cout << "We have to hit " << t << " more B:s\n";
				cout << "We should add " << f2 - a2 << " and " << f2 - a3 << " new ones \n";
				cout << "There are " << noHitAbove << " and " << noHitRight << " choices that do not hit\n";
				cout << "and " << hitAbove << " and " << hitRight << " choices that hit a new one \n";
			}
			for(int o2 = 0; o2 <= t; ++o2) {
				int d2 = f2 - a2;
				ll A2 = binom[noHitAbove][d2 - o2]*binom[hitAbove][o2];
				A2 %= M;
				A2 *= fact[s - a2];
				A2 %= M;
				A2 *= exp(fact[s - a2 - d2], M-2);
				A2 %= M;


				int o3 = t - o2;
				int d3 = f2 - a3;
				if(o3 > d3) continue;
				if(hitRight < o2) continue;
				ll A3 = binom[hitRight - o2][o3] * binom[noHitRight + o2][d3];
				A3 %= M;
				A3 *= fact[s - a3];
				A3 %= M;
				A3 *= exp(fact[s - a3 - d3], M-2);
				A3 %= M;
				A23 += A2*A3;
				if(printStuff) {
					cout << "So if " << o2 << " " << o3 << " we have " << A2 << " " << A3 << "\n";
					cout << "Because we have " << s - a2 << " and " << s - a3 << " possible depths\n";
					cout << "And difference d3 is " << d3 << "\n";
					cout << binom[hitRight - o2][o3] << " " << binom[noHitRight + o2][d3] << " " << binom[s-a3][d3] << "\n";

				}
				A23 %= M;

			}
			if(printStuff) {
				cout << "The result is, we have " << A23 << " choices for the A:s\n";
			}
			if(A23 == 0) continue;


			ll f1 = amB - f2;
			ll d1 = f1 - a1;
			ll A1 = dp[d1][amB - amountOfB];
			if(printStuff) {
				cout << "In this case we have " << A1 << " choices for A1\n";
				cout << "That's because we added " << d1 << " new A:s to the grid\n";
				cout << "and there are " << amB - amountOfB << " B:s in the small area\n";
				cout << "The amount of B:s hitted is " << amountOfB << "\n";
			}
			ll f4 = n - 2*f2 - f1 - aA;

			ll A4 = 1;
			for(ll i = 1; i <= f4; ++i) {
				A4 *= i;
				A4 %= M;
			}


			ll B = dp[n - amB][aA + f4];

			ll cur = A23;
			cur %= M;
			cur *= A1;
			cur %= M;
			cur *= A4;
			cur %= M;
			cur *= B;
			cur %= M;
			if(printStuff) {
				cout << "Statistics for " << f2 << " " << amountOfB << "\n";
				cout << "Number of ways for A:s " << A1*A23*A4 << "\n";
				cout << "Number of ways for A1 is " << A1 << " and for A23 it's " << A23 << " and for A4 " << A4 << "\n";
				cout << "Number of ways for B:s " << B << "\n";
				cout << "Total number of ways: " << A1*A23*A4*B << "\n";
				cout << "\n\n";
			}
			ans += cur;
			ans %= M;
		}
	}

	cout << ans << "\n";


}

Test details

Test 1

Group: 1

Verdict: ACCEPTED

input
`2 .. ..` view save

correct output
`2` view save

user output
`2` view save

Test 2

Group: 1

Verdict: ACCEPTED

input
`2 .. A.` view save

correct output
`1` view save

user output
`1` view save

Test 3

Group: 1

Verdict: ACCEPTED

input
`2 B. .A` view save

correct output
`0` view save

user output
`0` view save

Test 4

Group: 1

Verdict: ACCEPTED

input
`3 ... ... ...` view save

correct output
`12` view save

user output
`12` view save

Test 5

Group: 1

Verdict: ACCEPTED

input
`4 .... .... .... ....` view save

correct output
`216` view save

user output
`216` view save

Test 6

Group: 1

Verdict: ACCEPTED

input
`5 ..... ..... ..... ..... ...` view save

correct output
`5280` view save

user output
`5280` view save

Test 7

Group: 1

Verdict: ACCEPTED

input
`5 ....A ..... ..... ..... ...` view save

correct output
`264` view save

user output
`264` view save

Test 8

Group: 1

Verdict: ACCEPTED

input
`5 B.... ..... ..... .A.B. ...` view save

correct output
`22` view save

user output
`22` view save

Test 9

Group: 1

Verdict: ACCEPTED

input
`5 B.A.. ....A ..... A.B.. ...` view save

correct output
`2` view save

user output
`2` view save

Test 10

Group: 1

Verdict: ACCEPTED

input
`5 A.B.. BA... .B.A. ...BA ...` view save

correct output
`1` view save

user output
`1` view save

Test 11

Group: 2

Verdict: ACCEPTED

input
`10 .......... .......... .......... .......... ...` view save

correct output
`306442892` view save

user output
`306442892` view save

Test 12

Group: 2

Verdict: ACCEPTED

input
`50 .................................` view save

correct output
`694861480` view save

user output
`694861480` view save

Test 13

Group: 2

Verdict: ACCEPTED

input
`111 .................................` view save

correct output
`555319110` view save

user output
`555319110` view save

Test 14

Group: 2

Verdict: ACCEPTED

input
`222 .................................` view save

correct output
`108372237` view save

user output
`108372237` view save

Test 15

Group: 2

Verdict: ACCEPTED

input
`333 .................................` view save

correct output
`259107857` view save

user output
`259107857` view save

Test 16

Group: 2

Verdict: ACCEPTED

input
`444 .................................` view save

correct output
`19906314` view save

user output
`19906314` view save

Test 17

Group: 2

Verdict: ACCEPTED

input
`497 .................................` view save

correct output
`224313667` view save

user output
`224313667` view save

Test 18

Group: 2

Verdict: ACCEPTED

input
`498 .................................` view save

correct output
`929574601` view save

user output
`929574601` view save

Test 19

Group: 2

Verdict: ACCEPTED

input
`499 .................................` view save

correct output
`600226043` view save

user output
`600226043` view save

Test 20

Group: 2

Verdict: ACCEPTED

input
`500 .................................` view save

correct output
`198353194` view save

user output
`198353194` view save

Test 21

Group: 3

Verdict: WRONG ANSWER

input
`499 .................................` view save

correct output
`840243733` view save

user output
`472998430` view save

Test 22

Group: 3

Verdict: WRONG ANSWER

input
`499 ........................A........` view save

correct output
`4146290` view save

user output
`339256637` view save

Test 23

Group: 3

Verdict: WRONG ANSWER

input
`499 B.........A......................` view save

correct output
`173518884` view save

user output
`805863113` view save

Test 24

Group: 3

Verdict: ACCEPTED

input
`499 ...A....B........................` view save

correct output
`20044800` view save

user output
`20044800` view save

Test 25

Group: 3

Verdict: ACCEPTED

input
`499 AB...............................` view save

correct output
`2` view save

user output
`2` view save

Test 26

Group: 3

Verdict: WRONG ANSWER

input
`500 .................................` view save

correct output
`121064146` view save

user output
`453728449` view save

Test 27

Group: 3

Verdict: WRONG ANSWER

input
`500 .................................` view save

correct output
`848435259` view save

user output
`631716298` view save

Test 28

Group: 3

Verdict: WRONG ANSWER

input
`500 .....B........A..................` view save

correct output
`296240911` view save

user output
`925231462` view save

Test 29

Group: 3

Verdict: WRONG ANSWER

input
`500 .A......B........................` view save

correct output
`2196` view save

user output
`3060` view save

Test 30

Group: 3

Verdict: ACCEPTED

input
`500 ...AB............................` view save

correct output
`1` view save

user output
`1` view save

Datatähti 2019 alku

Ruudukko

Code

Test details

Test 1

Test 2

Test 3

Test 4

Test 5

Test 6

Test 7

Test 8

Test 9

Test 10

Test 11

Test 12

Test 13

Test 14

Test 15

Test 16

Test 17

Test 18

Test 19

Test 20

Test 21

Test 22

Test 23

Test 24

Test 25

Test 26

Test 27

Test 28

Test 29

Test 30

Tasks

Submissions (Olli)