一、简单搜索
FallenGemini
  2023-02-26 12:00:00 2023-02-26 12:00   2023-03-03 20:50:27      3.4k 字

AcWing 1114 棋盘问题

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/*
搜索、状压、记忆化
*/
int solve() {
	int n,k;
	std::cin >> n >> k;
	if(n == -1 && k == -1) {
		return 0;
	}
	std::vector<std::string> map(n);
	for(int i = 0; i < n; i++) {
		std::cin >> map[i];
	}
	
	std::vector f(n, std::vector<int> (1 << n, -1));

	auto dfs = [&](auto dfs, int step, int status, int num) {
		if(step == n) {
			return num == k ? 1 : 0;
		}
		if(num == k) {
			return f[step][status] = 1;
		}
		if(f[step][status] != -1) {
			return f[step][status];
		}
		int res = 0;
		res += dfs(dfs, step + 1, status, num);
		for(int i = 0; i < n; i++) {
			if(map[step][i] != '#') continue;
			if((status >> i) & 1) continue;
			res += dfs(dfs, step + 1, status | (1 << i), num + 1);
		}
		return f[step][status] = res;
	};

	std::cout << dfs(dfs,0,0,0) << '\n';
	return 1;
}

AcWing 1096 地牢大师

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/*
bfs
*/
int solve() {
	int L,R,C;
	std::cin >> L >> R >> C;
	if(L == 0 && R == 0 && C == 0) {
		return 0;
	}
	std::vector map(L,std::vector<std::string> (R));
	std::vector f(L, std::vector (R, std::vector<int> (C, 1e9)));
	int sx,sy,sz,ex,ey,ez;
	for(int i = 0; i < L; i++) {
		for(int j = 0; j < R; j++) {
			std::cin >> map[i][j];
			for(int k = 0; k < C; k++) {
				if(map[i][j][k] == 'S') {
					sx = i; sy = j; sz = k;
				}
				if(map[i][j][k] == 'E') {
					ex = i; ey = j; ez = k;
				}
			}
		}
	}

	auto bfs = [&]() -> void {
		f[sx][sy][sz] = 0;
		std::array<std::array<int,3>,6> next = 
			{{{0,0,1},{0,0,-1},{0,1,0},{0,-1,0},{1,0,0},{-1,0,0}}};
		std::queue<int> X,Y,Z;
		X.push(sx);Y.push(sy);Z.push(sz);
		
		while(!X.empty()) {
			int x = X.front(), y = Y.front(), z = Z.front();
			X.pop();Y.pop();Z.pop();
			for(int i = 0; i < 6; i++) {
				int tx = x + next[i][0], ty = y + next[i][1], tz = z + next[i][2];
				if(tx < 0 || tx >= L || ty < 0 || ty >= R || tz < 0 || tz >= C) continue;
				if(map[tx][ty][tz] == '#') continue;
				if(f[tx][ty][tz] != 1e9) continue;
				f[tx][ty][tz] = f[x][y][z] + 1;
				X.push(tx);Y.push(ty);Z.push(tz);
			}
		}
	};
	
	bfs();
	if(f[ex][ey][ez] == 1e9) {
		std::cout << "Trapped!\n";
	}
	else {
		std::cout << "Escaped in " << f[ex][ey][ez] << " minute(s).\n";
	}
	
	return 1;
}

AcWing 1100 抓住那头牛

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/*
bfs
*/
void solve() {
	int n,k;
	std::cin >> n >> k;
	std::vector<int> f(2e5,1e9);
	std::queue<int> q;

	f[n] = 0;
	q.push(n);
	while(f[k] == 1e9) {
		int x = q.front();
		q.pop();
		if(x && f[x - 1] == 1e9) {
			f[x - 1] = f[x] + 1;
			q.push(x - 1);
		}
		if(f[x + 1] == 1e9) {
			f[x + 1] = f[x] + 1;
			q.push(x + 1);
		}
		if(x < k && f[2 * x] == 1e9) {
			f[2 * x] = f[x] + 1;
			q.push(2 * x);
		}
	}

	std::cout << f[k] << '\n';
}

AcWing 4218 翻转

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/*
枚举
*/
void solve() {
	int M,N;
	std::cin >> M >> N;

	std::vector<int> map(M);
	for(int i = 0; i < M; i++) {
		for(int j = 0; j < N; j++) {
			int x;
			std::cin >> x;
			map[i] = (map[i] << 1) + x;
		}
	}
	
	// 当前行的状态 status，当前行改变的位置 change
	// 返回之后当前行的状态，即下一行需要改变的位置
	auto check = [&](int status, int change) {
		for(int i = 0; i < N; i++) {
			if((change >> i) & 1) {
				if(i) status ^= (1 << (i - 1));
				status ^= (1 << i);
				if(i + 1 < N) status ^= (1 << (i + 1));
			}
		}
		return status;
	};

	std::vector<int> res(M);
	int Num = 1e9;
	for(int i = 0; i < (1 << N); i++) {
		std::vector<int> temp(M);
		int status = map[0], change = i;
		for(int j = 0; j < M; j++) {
			temp[j] = change;
			change = check(status, change);
			if(j + 1 < M) status = map[j + 1] ^ temp[j];
		}
		
		if(change != 0) continue;
		int num = 0;
		for(int val : temp) {
			while(val) {
				if(val & 1) num++;
				val >>= 1;
			}
		}
		if(num < Num) {
			Num = num;
			res = temp;
		}
	}

	if(Num == 1e9) {
		std::cout << "IMPOSSIBLE\n";
	}
	else {
		for(int i = 0; i < M; i++) {
			for(int j = N - 1; j >= 0; j--) {
				std::cout << ((res[i] >> j) & 1) << " \n"[j == 0];
			}
		}
	}
}

AcWing 4219 找倍数

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int solve() {
	int n;
	std::cin >> n;

	if(!n) return 0;

	auto bfs = [&]() -> std::string {
		std::queue<std::pair<std::string,int>> q;
		q.push(std::make_pair("1",1));
		while(true) {
			std::string s = q.front().first;
			int val = q.front().second;
			if(!val) break;
			q.pop();

			q.push(std::make_pair(s + "0", (val * 10) % n));
			q.push(std::make_pair(s + "1", (val * 10 + 1) % n));
		}
		return q.front().first;
	};

	std::cout << bfs() << '\n';
	return 1;
}

AcWing 4220 质数路径

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std::vector<bool> book(10000);
void init() {
	for(int i = 1000; i <= 9999; i++) {
		book[i] = true;
		for(int j = 2; j * j <= i; j++) {
			if(i % j == 0) book[i] = false;
		}
	}
}
void solve() {
	int A,B;
	std::cin >> A >> B;
	
	std::vector<int> f(10000,1e9);
	f[A] = 0;

	std::queue<int> q;
	q.push(A);
	while(!q.empty()) {
		int val = q.front();
		q.pop();

		int temp;
		for(int i = 1; i <= 9; i++) {
			temp = val % 1000 + i * 1000;
			if(book[temp] && f[temp] == 1e9) {
				f[temp] = f[val] + 1;
				q.push(temp);
			}
		}
		for(int i = 0; i <= 9; i++) {
			temp = (val / 1000) * 1000 + val % 100 + i * 100;
			if(book[temp] && f[temp] == 1e9) {
				f[temp] = f[val] + 1;
				q.push(temp);
			}

			temp = (val / 100) * 100 + val % 10 + i * 10;
			if(book[temp] && f[temp] == 1e9) {
				f[temp] = f[val] + 1;
				q.push(temp);
			}

			temp = (val / 10) * 10 + i;
			if(book[temp] && f[temp] == 1e9) {
				f[temp] = f[val] + 1;
				q.push(temp);
			}
		}
	}
	
	if(f[B] == 1e9) std::cout << "Impossible\n";
	else std::cout << f[B] << '\n';
}

AcWing 4221 洗牌

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int solve() {
	int C;
	std::cin >> C;
	std::string A,B,S,temp;
	std::cin >> A >> B >> S;

	std::map<std::string,bool> map;
	int res = 0;
	while(true) {
		res++;
		temp = "";
		for(int i = 0; i < C; i++) {
			temp = temp + B[i] + A[i];
		}
		
		if(temp == S) return res;
		if(map[temp]) return -1;
		map[temp] = true;
		A = temp.substr(0,C);
		B = temp.substr(C,C);
	}

}

AcWing 4222 罐子

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void solve() {
	int A,B,C;
	std::cin >> A >> B >> C;

	std::vector f(A + 1,std::vector<int> (B + 1,1e9));
	std::vector op(A + 1,std::vector<std::string> (B + 1));
	f[0][0] = 0;

	std::queue<std::pair<int,int>> q;
	q.push(std::make_pair(0,0));

	while(!q.empty()) {
		int x = q.front().first;
		int y = q.front().second;
		if(x == C || y == C) break;
		q.pop();

		if(f[0][y] == 1e9) {
			f[0][y] = f[x][y] + 1;
			op[0][y] = op[x][y] + "1";
			q.push(std::make_pair(0,y));
		}
		if(f[x][0] == 1e9) {
			f[x][0] = f[x][y] + 1;
			op[x][0] = op[x][y] + "2";
			q.push(std::make_pair(x,0));
		}
		if(f[A][y] == 1e9) {
			f[A][y] = f[x][y] + 1;
			op[A][y] = op[x][y] + "3";
			q.push(std::make_pair(A,y));
		}
		if(f[x][B] == 1e9) {
			f[x][B] = f[x][y] + 1;
			op[x][B] = op[x][y] + "4";
			q.push(std::make_pair(x,B));
		}
		
		int tempA = std::min(A,x + y), tempB = std::max(0, x + y - A);
		if(f[tempA][tempB] == 1e9) {
			f[tempA][tempB] = f[x][y] + 1;
			op[tempA][tempB] = op[x][y] + "5";
			q.push(std::make_pair(tempA,tempB));
		}

		tempA = std::max(0, x + y - B), tempB = std::min(B, x + y);
		if(f[tempA][tempB] == 1e9) {
			f[tempA][tempB] = f[x][y] + 1;
			op[tempA][tempB] = op[x][y] + "6";
			q.push(std::make_pair(tempA,tempB));
		}
	}

	int resA = q.front().first,resB = q.front().second;
	if(resA != C && resB != C) {
		std::cout << "impossible\n";
		return;
	}
	
	std::cout << f[resA][resB] << '\n';
	for(int i = 0; i < f[resA][resB]; i++) {
		int val = op[resA][resB][i] - '0';
		switch(val) {
			case 1: std::cout << "DROP(1)" << '\n';break;
			case 2: std::cout << "DROP(2)" << '\n';break;
			case 3: std::cout << "FILL(1)" << '\n';break;
			case 4: std::cout << "FILL(2)" << '\n';break;
			case 5: std::cout << "POUR(2,1)" << '\n';break;
			case 6: std::cout << "POUR(1,2)" << '\n';break;	
		}
	}
}

AcWing 4223 点火游戏

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int solve() {
	int N,M;
	std::cin >> N >> M;

	std::vector<std::string> map(N);
	for(int i = 0; i < N; i++) {
		std::cin >> map[i];
	}

	std::vector<std::pair<int,int>> grass;
	for(int i = 0; i < N; i++) {
		for(int j = 0; j < M; j++) {
			if(map[i][j] == '#') {
				grass.push_back(std::make_pair(i,j));
			}
		}
	}

	auto bfs = [&](std::pair<int,int> a){
		std::array<std::array<int,2>,4> nxt = {{{0,1},{0,-1},{1,0},{-1,0}}};
		std::vector f(N,std::vector<int> (M,1e9));
		f[a.first][a.second] = 0;

		std::queue<std::pair<int,int>> q;
		q.push(a);
		while(!q.empty()) {
			int x = q.front().first, y = q.front().second;
			q.pop();
			for(int i = 0; i < 4; i++) {
				int tx = x + nxt[i][0], ty = y + nxt[i][1];
				if(tx < 0 || tx >= N || ty < 0 || ty >= M) continue;
				if(map[tx][ty] == '.') continue;
				if(f[tx][ty] != 1e9) continue;
				f[tx][ty] = f[x][y] + 1;
				q.push(std::make_pair(tx,ty));
			}
		}

		return f;
	};

	std::vector dis(grass.size(),std::vector (N,std::vector<int> (M)));
	for(int i = 0; i < grass.size(); i++) {
		dis[i] = bfs(grass[i]);
	}

	int ans = 1e9;
	for(int i = 0; i < grass.size(); i++) {
		for(int j = i; j < grass.size(); j++) {
			int val = 0;
			for(int k = 0; k < grass.size(); k++) {
				int x = grass[k].first,y = grass[k].second;
				val = std::max(val,
					std::min(dis[i][x][y],dis[j][x][y]));
			}
			ans = std::min(ans, val);
		}
	}
	return ans == 1e9 ? -1 : ans;
}

AcWing 4224 起火迷宫

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void solve() {
	int R,C;
	std::cin >> R >> C;

	std::vector<std::string> map(R);
	for(int i = 0; i < R; i++) {
		std::cin >> map[i];
	}

	std::queue<std::pair<int,int>> J,F;
	for(int i = 0; i < R; i++) {
		for(int j = 0; j < C; j++) {
			if(map[i][j] == 'J') J.push(std::make_pair(i,j));
			if(map[i][j] == 'F') F.push(std::make_pair(i,j));
		}
	}

	int time = 0;
	bool flag = false;
	std::array<std::array<int,2>,4> nxt = {{{1,0},{-1,0},{0,1},{0,-1}}};
	while(!J.empty()) {
		time++;
		std::queue<std::pair<int,int>> temp;
		while(!F.empty()) {
			int x = F.front().first, y = F.front().second;
			F.pop();
			for(int i = 0; i < 4; i++) {
				int tx = x + nxt[i][0], ty = y + nxt[i][1];
				if(tx < 0 || tx >= R || ty < 0 || ty >= C) continue;
				if(map[tx][ty] == '#' || map[tx][ty] == 'F') continue;
				map[tx][ty] = 'F';
				temp.push(std::make_pair(tx,ty));
			}
		}
		std::swap(temp,F);
		while(!J.empty()) {
			int x = J.front().first, y = J.front().second;
			J.pop();
			for(int i = 0; i < 4; i++) {
				int tx = x + nxt[i][0], ty = y + nxt[i][1];
				if(tx < 0 || tx >= R || ty < 0 || ty >= C) {
					flag = true;
					break;
				}
				if(map[tx][ty] != '.') continue;
				map[tx][ty] = 'J';
				temp.push(std::make_pair(tx,ty));
			}
		}
		std::swap(temp,J);
		if(flag) break;
	}

	if(flag) std::cout << time << '\n';
	else std::cout << "IMPOSSIBLE\n";
}

AcWing 1076 迷宫问题

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void solve() {
	int n;
	std::cin >> n;

	std::vector map(n,std::vector<int> (n));
	for(int i = 0; i < n; i++) {
		for(int j = 0; j < n; j++) {
			std::cin >> map[i][j];
		}
	}

	std::vector pre(n,std::vector<std::pair<int,int>> (n,std::pair(-1,-1)));
	std::queue<std::pair<int,int>> q;
	std::array<std::array<int,2>,4> nxt = {{{1,0},{-1,0},{0,1},{0,-1}}};
	q.push(std::pair(0,0));
	pre[0][0] = std::pair(-2,-2);
	while(pre[n - 1][n - 1] == std::pair(-1,-1)) {
		int x = q.front().first, y = q.front().second;
		q.pop();
		for(int i = 0; i < 4; i++) {
			int tx = x + nxt[i][0], ty = y + nxt[i][1];
			if(tx < 0 || tx >= n || ty < 0 || ty >= n) continue;
			if(map[tx][ty] == 1) continue;
			if(pre[tx][ty] == std::pair(-1,-1)) {
				pre[tx][ty] = std::pair(x,y);
				q.push(std::pair(tx,ty));
			}
		}
	}

	std::stack<std::pair<int,int>> stack;
	std::pair<int,int> res = std::pair(n - 1, n - 1);
	while(res != std::pair(-2,-2)) {
		stack.push(res);
		res = pre[res.first][res.second];
	}

	while(!stack.empty()) {
		std::cout << stack.top().first << ' ' << stack.top().second << '\n';
		stack.pop();
	}
}

AcWing 4225 石油储备

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int solve() {
	int n,m;
	std::cin >> n >> m;
	if(n == 0 && m == 0) 
		return 0;

	std::vector<std::string> map(n);
	for(int i = 0;i < n; i++) {
		std::cin >> map[i];
	}

	auto bfs = [&](int sx,int sy) -> void {
		std::queue<std::pair<int,int>> q;
		std::array<std::array<int,2>,8> nxt = {{{1,0},{-1,0},{0,1},{0,-1},{1,1},{1,-1},{-1,1},{-1,-1}}};

		q.push(std::pair<int,int> (sx,sy));
		map[sx][sy] = '*';

		while(!q.empty()) {
			int x = q.front().first, y = q.front().second;
			q.pop();
			for(int i = 0; i < 8; i++) {
				int tx = x + nxt[i][0], ty = y + nxt[i][1];
				if(tx < 0 || tx >= n || ty < 0 || ty >= m) continue;
				if(map[tx][ty] == '*') continue;
				map[tx][ty] = '*';
				q.push(std::pair<int,int> (tx,ty));
			}
		}
	};

	int res = 0;
	for(int i = 0; i < n; i++) {
		for(int j = 0; j < m; j++) {
			if(map[i][j] == '@') {
				bfs(i,j);
				res++;
			}
		}
	}

	std::cout << res << '\n';
	return 1;
}

AcWing 4226 非常可乐

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int solve() {
	int S,N,M;
	std::cin >> S >> N >> M;
	if(S == 0 && N == 0 && M == 0)
		return 0;

	std::array<int,3> begin = {S,0,0};
	std::map<std::array<int,3>,int> map;
	std::queue<std::array<int,3>> q;
	map[begin] = 1;
	q.push(begin);

	auto check = [&](std::array<int,3> x) -> bool {
		std::sort(x.begin(),x.end());
		if(x[0] == 0 && x[1] == S / 2 && x[2] == S / 2) return true;
		return false;
	};

	while(!q.empty()) {
		std::array<int,3> A = q.front(),temp;
		q.pop();
		temp = A;
		temp[1] = std::min(N,A[0] + A[1]);
		temp[0] = std::max(0,A[0] + A[1] - N);
		if(map[temp] == 0) {
			map[temp] = map[A] + 1;
			if(check(temp)) {
				std::cout << map[temp] - 1 << '\n';
				return 1;
			}
			q.push(temp);
		}

		temp = A;
		temp[0] = A[0] + A[1];
		temp[1] = 0;
		if(map[temp] == 0) {
			map[temp] = map[A] + 1;
			if(check(temp)) {
				std::cout << map[temp] - 1 << '\n';
				return 1;
			}
			q.push(temp);
		}

		temp = A;
		temp[2] = std::min(M,A[0] + A[2]);
		temp[0] = std::max(0,A[0] + A[2] - M);
		if(map[temp] == 0) {
			map[temp] = map[A] + 1;
			if(check(temp)) {
				std::cout << map[temp] - 1 << '\n';
				return 1;
			}
			q.push(temp);
		}

		temp = A;
		temp[0] = A[0] + A[2];
		temp[2] = 0;
		if(map[temp] == 0) {
			map[temp] = map[A] + 1;
			if(check(temp)) {
				std::cout << map[temp] - 1 << '\n';
				return 1;
			}
			q.push(temp);
		}

		temp = A;
		temp[2] = std::min(M,A[1] + A[2]);
		temp[1] = std::max(0,A[1] + A[2] - M);
		if(map[temp] == 0) {
			map[temp] = map[A] + 1;
			if(check(temp)) {
				std::cout << map[temp] - 1 << '\n';
				return 1;
			}
			q.push(temp);
		}

		temp = A;
		temp[1] = std::min(N,A[1] + A[2]);
		temp[2] = std::max(0,A[1] + A[2] - N);
		if(map[temp] == 0) {
			map[temp] = map[A] + 1;
			if(check(temp)) {
				std::cout << map[temp] - 1 << '\n';
				return 1;
			}
			q.push(temp);
		}
	}
	std::cout << "NO\n";
	return 1;
}

AcWing 4227 找路

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void solve(int n,int m) {
	std::vector<std::string> map(n);
	for(int i = 0; i < n; i++) {
		std::cin >> map[i];
	}

	auto bfs = [&](int sx,int sy) {
		std::vector f(n,std::vector<int> (m,1e9));
		std::array<std::array<int,2>,4> nxt = {{{1,0},{-1,0},{0,1},{0,-1}}};
		std::queue<std::pair<int,int>> q;

		f[sx][sy] = 0;
		q.push(std::pair<int,int> (sx,sy));
		
		while(!q.empty()) {
			int x = q.front().first, y = q.front().second;
			q.pop();
			for(int i = 0; i < 4; i++) {
				int tx = x + nxt[i][0], ty = y + nxt[i][1];
				if(tx < 0 || tx >= n || ty < 0 || ty >= m) continue;
				if(map[tx][ty] == '#') continue;
				if(f[tx][ty] != 1e9) continue;
				f[tx][ty] = f[x][y] + 11;
				q.push(std::pair<int,int> (tx,ty));
			}
		}

		return f;
	};

	std::vector Y(n,std::vector<int> (m)),M(n,std::vector<int> (m));
	for(int i = 0; i < n; i++) {
		for(int j = 0; j < m; j++) {
			if(map[i][j] == 'Y') Y = bfs(i,j);
			if(map[i][j] == 'M') M = bfs(i,j);
		}
	}

	int res = 1e9;
	for(int i = 0; i < n; i++) {
		for(int j = 0; j < m; j++) {
			if(map[i][j] == '@') {
				res = std::min(res, Y[i][j] + M[i][j]);
			}
		}
	}
	std::cout << res << '\n';
}
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  14. AcWing 4227 找路