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IDSubmission IDProblemHackerOwnerResultSubmit timeJudge time
#581#296771#7858. Basic Equation SolvingliswtDualqwqSuccess!2024-03-20 11:11:592024-03-20 11:12:01

Details

Extra Test:

Time Limit Exceeded

input:

10
A<BCD
E<FGH
I<JKL
M<NOP
Q<RST
U<VWX
Y<ZAB
C<DEF
G<HIJ
K<LMN

output:


result:


IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#296771#7858. Basic Equation SolvingDualqwqTL 7083ms4652kbC++204.0kb2024-01-03 16:08:032024-03-20 11:12:35

answer

#include <bits/stdc++.h>
using namespace std;
const int N = 15,M = 40,Sz = 1 << 11,P = 998244353;
inline void Plus(int &x,const int &y) { x += y;if(x >= P) x -= P;}
int n;
string s1[N],s2[N];
char opp[N];
int nq[N];
inline int Id(char x) { return isdigit(x) ? x - '0' : x - 'A' + 10;}
int ufs[M];
int find(int x) { return ufs[x] == x ? x : ufs[x] = find(ufs[x]);}
inline void Merge(int x,int y) { ufs[find(x)] = find(y);}
int tot,X[N],Y[N]; // X[i] < Y[i]
vector<int> can[Sz]; // 预处理把 T 放在 S 中的最后是否可行,3^V * n
vector<int> con[M];
bool dig[Sz][10];
inline bool buildlim() {
	for(int i = 0;i < M;i++) ufs[i] = i;
	tot = 0;
	for(int i = 1;i <= n;i++) if(opp[i] != '=') {
		for(int j = 0;j < nq[i];j++)
			Merge(Id(s1[i][j]),Id(s2[i][j]));
		++tot,X[tot] = Id(s1[i][nq[i]]),Y[tot] = Id(s2[i][nq[i]]);
		if(opp[i] == '>') swap(X[tot],Y[tot]);
	} else for(int j = 0;j < s1[i].size();j++) Merge(Id(s1[i][j]),Id(s2[i][j]));
	for(int i = 0;i < M;i++) con[i].clear();
	for(int i = 1;i <= tot;i++) if(find(X[i]) == find(Y[i])) return false;
	for(int i = 0;i < 10;i++)
		for(int j = i + 1;j < 10;j++) if(find(i) == find(j)) return false;
	for(int i = 1;i <= tot;i++) {
		X[i] = find(X[i]);Y[i] = find(Y[i]);
		con[X[i]].push_back(Y[i]),con[Y[i]].push_back(X[i]);
	}
	return true;
}
int bel[M],idcnt;
int dp[10][Sz];
inline int Calc0(vector<int> V) {
	int siz = V.size();idcnt = 0;
	// printf("siz:%d\n",siz);
	for(int i = 0;i < M;i++) bel[i] = -1;
	for(auto i : V) bel[i] = idcnt++;
	for(int i = 0;i < (1 << siz);i++) {
		int cnt = __builtin_popcount(i);
		can[i].clear();can[i].resize(1 << cnt);
		for(int j = i,d = 0;j;j = (j - 1) & i,++d) {
			can[i][d] = true;
			for(int k = 1;k <= tot;k++)
				if(bel[X[k]] != -1 && bel[Y[k]] != -1 && (j >> bel[X[k]] & 1) && ((i - j >> bel[Y[k]]) & 1))
					can[i][d] = false;
		}
	}
	for(int i = 0;i < (1 << siz);++i) {
		for(int j = 0;j < 10;j++) dig[i][j] = true;
		int c1 = -1,c2 = -1;
		for(int j = 0;j < 10;j++) if(bel[find(j)] != -1 && (i >> bel[find(j)] & 1)) {
			if(c1 == -1) c1 = j;
			else c2 = j;
		}
		for(int k = 1;k <= tot;k++)
			if(bel[X[k]] != -1 && bel[Y[k]] != -1 && (i >> bel[X[k]] & 1) && (i >> bel[Y[k]] & 1)) {
				for(int j = 0;j < 10;j++) dig[i][j] = false;
				break;
			}
		if(c2 != -1) for(int j = 0;j < 10;j++) dig[i][j] = false;
		else if(c1 != -1) for(int j = 0;j < 10;j++) if(j != c1) dig[i][j] = false;
	}	
	for(int i = 0;i <= 9;i++) for(int j = 0;j < (1 << siz);++j) dp[i][j] = 0;
	for(int i = 0;i < (1 << siz);i++) if(dig[i][0])  dp[0][i] = 1;
	for(int i = 1;i <= 9;i++)
		for(int j = 0;j < (1 << siz);++j) {
			Plus(dp[i][j],dp[i - 1][j]);
			for(int k = j,d = 0;k;k = (k - 1) & j,++d)
				if(can[j][d] && dig[k][i]) Plus(dp[i][j],dp[i - 1][j - k]);
		}
	return dp[9][(1 << siz) - 1];
}
vector<int> cv;
bool usd[M];
void dfs0(int x) {
	usd[x] = true;cv.push_back(x);
	for(auto y : con[x])
		if(!usd[y]) dfs0(y);
}
inline int Calcnq() {
	int mul = 1;
	if(!buildlim()) return 0;
	// printf("nq1:%d,%d,%d,%d\n",nq[1]);
	for(int i = 0;i < M;i++) usd[i] = 0;
	for(int i = 0;i < 36;i++) if(find(i) == i && !usd[i]) {
		cv.clear();dfs0(i);//printf("i:%d\n",i);
		// printf("Calc0:%d\n",Calc0(cv));
		mul = 1ll * mul * Calc0(cv) % P;
	}
	return mul;
}
int ans = 0;
void dfsnq(int x) {
	if(x == n + 1) { Plus(ans,Calcnq());return;}
	if(opp[x] != '=') for(int i = 0;i < s1[x].size();i++) { nq[x] = i;dfsnq(x + 1);nq[x] = -1;}
	else dfsnq(x + 1);
}
int main() {
	cin >> n;
	for(int i = 1;i <= n;i++) {
		string limit;
		cin >> limit;
		int len = limit.size(),pos = 0;
		for(int j = 0;j < len;j++) if(!isdigit(limit[j]) && !isalpha(limit[j])) { opp[i] = limit[j];pos = j;break;}
		s1[i] = limit.substr(0,pos);
		s2[i] = limit.substr(pos + 1,(int)limit.size() - pos - 1);
		while(s1[i].size() < s2[i].size()) s1[i] = '0' + s1[i];
		while(s1[i].size() > s2[i].size()) s2[i] = '0' + s2[i];
		// printf("s1:%s,s2:%s\n",s1[i].c_str(),s2[i].c_str());
	}
	dfsnq(1);
	cout << ans << endl;
	return 0;
}








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