第十二届北航程序设计竞赛预赛
https://biancheng.love/contest-ng/index.html#/123/problems
题目链接
A、C看懂题意就好了。
G题，贪心，最大的数肯定要越高位越好，所以尽量放1，剩3就放7，次大就调过来。特判下4没了。
D题，求出每个点需要推到的概率然后加起来。
M题，贪心可得，大乘小对应起来，然后求次数，就用类似求一个个环，假如不对应的环就需要环内点个数-1次来交换。因为假如环内有x个点，你交换x-1次，最后一个也会排好序了
L题，用几个数组维护一下每个点四个方向最远能到达的点，然后求T就枚举中间那个点，L就枚举左下角那个点，求S就枚举最上面的两个点，n^3
F题，一个多边形，它夹角对应的都要放在整数点上，那只能是正方形了，多边形面积是一个n·[(a^2)/4]·cot(π/n)，然后cot好像只有几个特殊点才是有理数吧，如果坐标都在整数点上，那面积肯定可以割割割，反正是个有理数，大概是这样证明的。所以问题就变成从n个点选4个能否组成正方形，把全部点hash起来，然后枚举正方形任意两个点，再判断另外两个点是否存在就行了，复杂度是n^2，光看数据以为会T就加了个读入挂，不知道有没有其他做法。
K题，我们先把这个东西的类似层次遍历的图画一画，就会发现，其实答案会是某层状态最多的方案数量，然后题目就转化成了将若干个数分成n堆，每一堆都有不同的限制di。然后就是dp搞，dp[i][j]表示前i堆分了j个的方案数，然后dp[i][j] = sum(dp[i-1][k])(0<=k<=j&&j-k<di)了为什么小于，因为每一堆上原本就有一个1的，然后求max(dp[n][k])(0<k<若干个数)就是答案了。
B题，首先我瞎做的时候是毫无思路的，于是就自己做起了小学加法题，然后发现每进位一次，原本的数位和就会-9，好了，然后就开始搞了，从L+到R，进位M次，我们需要先能快速求出0-x之间所有数的数位和，这个我们可以用类似拆位来递归下去，先预处理出0-(10^k - 1)之间的数位和，这个比较简单
sum[0] = 0,sum[i] = sum[i-1]*10 + 45*10^(i-1);
那这样我们就可以拆位算下去了，比如求434
我们先算
0 - 99 = sum[2]
100 - 199 = 1 * 10^2 + sum[2]
200 - 299 = 2 * 10^2 + sum[2]
300 - 399 = 3 * 10^2 + sum[2]
400 - 434 我们可以把最前面那个4的贡献单独求出来 = 4 * 35
然后再 + 递归(34)
会求这个之后，我们先暴力求一下最高上界会是多少。。算出来发现挺小的，于是我就把上界设为3e7了，
二分一下R
变成（Cnt(R) - Cnt(L-1) - 暴力求数位和((L+R)*(R-L+1)/2) ）/ 9这个就是进位次数了，然后把R逼近上界就行了
#include <cstdio> #include <cstring> #include <cmath> #include <queue> #include <cstring> #include <vector> #include <string> #include <stack> #include <set> #include <map> #include <iostream> #include <algorithm> using namespace std; #define MP make_pair #define PB push_back typedef long long LL; typedef pair<int, int> Pii; const int inf = 0x3f3f3f3f; const LL INF = (1uLL << 63) - 1; const LL mod = 1000000007; const int N = 1e5 + 5; const double Pi = acos(-1.0); const int maxn = 2e5 + 5; int main() { #ifdef local freopen("in", "r", stdin); #endif int T; cin>>T; while(T--){ unsigned long long x,n; cin>>x>>n; for(int i = 0 ;i < n ; i++){ x<<=1; x|=1; } cout<<x<<endl; } }
#include <cstdio> #include <cstring> #include <cmath> #include <queue> #include <cstring> #include <vector> #include <string> #include <stack> #include <set> #include <map> #include <iostream> #include <algorithm> using namespace std; #define MP make_pair #define PB push_back typedef long long LL; typedef pair<int, int> Pii; const int inf = 0x3f3f3f3f; const LL INF = (1uLL << 63) - 1; const LL mod = 1000000007; const int N = 1e5 + 5; const double Pi = acos(-1.0); const int maxn = 2e5 + 5; int c[10]; struct node { int point; bool flag; } now[10]; void init() { c[1] = 4; c[2] = 3; c[3] = 5; c[4] = 6; c[5] = 4; c[6] = 6; c[7] = 5; c[8] = 4; c[9] = 3; } char s[105]; int main() { #ifdef local freopen("in", "r", stdin); #endif init(); int T; cin >> T; while(T--) { int res = 0 ; for(int i = 1 ; i <= 9 ; i++) { for(int j = 0 ; j < 9; j++) { now[j].flag = 1; } for(int j = 0 ; j < c[i]; j++) { scanf("%d", &now[j].point); } for(int z = 0 ; z < 2 ; z++) for(int j = 0 ; j < c[i]; j++) { scanf("%s", s); if(s[0] - '0' < 3) { now[j].flag = 0; } } for(int j = 0 ; j < c[i]; j++) { if(now[j].flag){ res += now[j].point; } } } cout<<res<<endl; } }
#include <cstdio> #include <cstring> #include <cmath> #include <queue> #include <cstring> #include <vector> #include <string> #include <stack> #include <set> #include <map> #include <iostream> #include <algorithm> using namespace std; #define MP make_pair #define PB push_back typedef long long LL; typedef pair<int, int> Pii; const int inf = 0x3f3f3f3f; const LL INF = (1uLL << 63) - 1; const LL mod = 1000000007; const int N = 1e5 + 5; const double Pi = acos(-1.0); const int maxn = 2e5 + 5; int main() { #ifdef local freopen("in", "r", stdin); #endif int T; cin>>T; while(T--){ int n; cin>>n; if(n==4){ puts("11 4"); continue; } string big = ""; while(n > 6){ big =big + "1"; n -= 2; } if(n==6){ printf("111"); cout<<big<<" "; printf("77"); cout<<big<<endl; } else if(n==5){ printf("71"); cout<<big<<" "; printf("17"); cout<<big<<endl; } } }
#include <cstdio> #include <cstring> #include <cmath> #include <queue> #include <cstring> #include <vector> #include <string> #include <stack> #include <set> #include <map> #include <iostream> #include <algorithm> using namespace std; #define MP make_pair #define PB push_back typedef long long LL; typedef pair<int, int> Pii; const int inf = 0x3f3f3f3f; const LL INF = (1uLL << 63) - 1; const LL mod = 1000000007; const int N = 1e5 + 5; const double Pi = acos(-1.0); const int maxn = 1e5 + 5; namespace IO { const int MT = 5e7; //1e711000kb char buf[MT]; int c, sz; void begin() { c = 0; sz = fread(buf, 1, MT, stdin); } inline bool read(int &t) { while(c < sz && buf[c] != '-' && (buf[c] < '0' || buf[c] > '9')) c++; if(c >= sz) return false; bool flag = 0; if( buf[c] == '-')flag = 1, c++; for(t = 0; c < sz && '0' <= buf[c] && buf[c] <= '9'; c++) t = t * 10 + buf[c] - '0'; if(flag) t = -t; return true; } inline bool read(char s[]) { while(c < sz && (buf[c] == ' ' || buf[c] == '\n')) c++; if(c >= sz) return false; int len = 0; while(c < sz && buf[c] != ' ' && buf[c] != '\n') s[len++] = buf[c] , c++; s[len] = 0; return true; } } using namespace IO; int fa[maxn]; bool vis[maxn]; int n; struct node { int val, id; bool operator < (const node & a)const { return val < a.val; } } X[maxn], Y[maxn]; int main() { #ifdef local freopen("in", "r", stdin); #endif begin(); int T; read(T); while(T--) { int n; read(n); for(int i = 1; i <= n ; i++) { read(X[i].val); X[i].id = i; } for(int i = 1 ; i <= n ; i++) { read(Y[i].val); Y[i].id = i; } sort(X + 1, X + n + 1); sort(Y + 1, Y + n + 1); LL res = 0; for(int i = 1; i <= n; i++) { res += 1LL * X[i].val * Y[n - i + 1].val; } for(int i = 1; i <= n; i++) { int uid = X[i].id; int vid = Y[n - i + 1].id; fa[uid] = vid; } int cnt = 0; for(int i = 1 ; i <= n; i++) { if(!vis[i]) { int len = 0; int u = i; while(!vis[u]) { vis[u] = 1; u = fa[u]; len++; } cnt += len - 1; } } cout << res << " " << cnt << endl; memset(vis, 0, sizeof vis); } }
#include <cstdio> #include <cstring> #include <cmath> #include <queue> #include <cstring> #include <vector> #include <string> #include <stack> #include <set> #include <map> #include <iostream> #include <algorithm> using namespace std; #define MP make_pair #define PB push_back typedef long long LL; typedef pair<int, int> Pii; const int inf = 0x3f3f3f3f; const LL INF = (1uLL << 63) - 1; const LL mod = 1000000007; const int N = 1e5 + 5; const double Pi = acos(-1.0); const int maxn = 200 + 5; int L[maxn][maxn]; int R[maxn][maxn]; int U[maxn][maxn]; int D[maxn][maxn]; char s[maxn][maxn]; int n , m; void gao() { for(int i = 1; i <= n; i++) { s[i][0] = '#'; for(int j = 1; j <= m; j++) { s[0][j] = '#'; if(s[i][j] != '#') { if(s[i][j - 1] != '#') L[i][j] = L[i][j - 1]; if(s[i - 1][j] != '#') U[i][j] = U[i - 1][j]; } } } for(int i = n; i >= 1; i--) { s[i][m + 1] = '#'; for(int j = m; j >= 1; j--) { s[n + 1][j] = '#'; if(s[i][j] != '#') { if(s[i][j + 1] != '#') R[i][j] = R[i][j + 1]; if(s[i + 1][j] != '#') D[i][j] = D[i + 1][j]; } } } } void init() { cin >> n >> m; for(int i = 0; i <= 105; i++) { for(int j = 0 ; j <= 105; j++) { L[i][j] = j; R[i][j] = j; U[i][j] = i; D[i][j] = i; } } } int main() { #ifdef local freopen("in", "r", stdin); #endif int cas; cin >> cas; while(cas--) { init(); for(int i = 1; i <= n; i++) { scanf("%s", s[i] + 1); } gao(); int _T = 0, _L = 0, _S = 0; for(int i = 1 ; i <= n ; i++) { for(int j = 1; j <= m ; j++) { if(s[i][j] != '#') { int _l = j - L[i][j] + 1; int _r = R[i][j] - j + 1; int _d = D[i][j] - i + 1; int _u = i - U[i][j] + 1; int _k = (min(_l, _r) << 1) - 1; if(min(_l, _r) >= 2 && _d >= 3) { if(_k <= _d) _T += min(_l, _r) - 1; else { _T += (_d - 1)/ 2; } } if(min(_u, _r) >= 2) { _L += min(_u, _r) - 1; } for(int z = j + 2; z <= R[i][j]; z++) { int l = z - j + 1; if(_d < l)break; int ni = l + i - 1; int nr = R[ni][j] - j + 1; if(nr < l)continue; int _ni = ni, _nj = z; int _nd = D[_ni][_nj] - _ni + 1; if(_nd < l)continue; int __ni = _ni + l - 1, __nj = _nj; int __k = __nj - L[__ni][__nj] + 1; if(__k >= l) { _S++; // cout<<"--------"<<endl; // cout<<i<<" "<<j<<endl; // cout<<z<<endl; // cout<<_ni<<" "<<_nj<<endl; // cout<<__ni<<" "<<__nj<<endl; // cout<<"--------"<<endl; } } } } } cout << _T << " " << _L << " " << _S << endl; } }
#include <cstdio> #include <cstring> #include <cmath> #include <queue> #include <cstring> #include <vector> #include <string> #include <stack> #include <set> #include <map> #include <iostream> #include <algorithm> using namespace std; #define MP make_pair #define PB push_back typedef long long LL; typedef pair<int, int> Pii; const int inf = 0x3f3f3f3f; const LL INF = (1uLL << 63) - 1; const LL mod = 1000000007; const int N = 1e5 + 5; const double Pi = acos(-1.0); const int maxn = 200 + 5; namespace IO { const int MT = 5e7; //1e711000kb char buf[MT]; int c, sz; void begin() { c = 0; sz = fread(buf, 1, MT, stdin); } inline bool read(int &t) { while(c < sz && buf[c] != '-' && (buf[c] < '0' || buf[c] > '9')) c++; if(c >= sz) return false; bool flag = 0; if( buf[c] == '-')flag = 1, c++; for(t = 0; c < sz && '0' <= buf[c] && buf[c] <= '9'; c++) t = t * 10 + buf[c] - '0'; if(flag) t = -t; return true; } inline bool read(char s[]) { while(c < sz && (buf[c] == ' ' || buf[c] == '\n')) c++; if(c >= sz) return false; int len = 0; while(c < sz && buf[c] != ' ' && buf[c] != '\n') s[len++] = buf[c] , c++; s[len] = 0; return true; } } using namespace IO; struct point { int x, y; }points[maxn]; struct node { int x, y; int next; } T[maxn]; int head[maxn]; int top; void build(point p) { int sum = (1LL * p.x * p.x + 1LL * p.y * p.y) % maxn; T[top].x = p.x; T[top].y = p.y; T[top].next = head[sum]; head[sum] = top++; } bool query(point p) { int sum = (1LL * p.x * p.x + 1LL * p.y * p.y) % maxn; int q = head[sum]; while(q != -1) { if( T[q].x == p.x && T[q].y == p.y ) { return 1; } q = T[q].next; } return 0; } int main() { #ifdef local freopen("in", "r", stdin); #endif begin(); int T; read(T); while(T--) { int n; read(n); top = 0; int x, y; memset(head, -1, sizeof head); for(int i = 0; i < n; i++) { read(x); read(y); points[i].x = x << 1; points[i].y = y << 1; build(points[i]); } if(n < 4) { puts("-1"); continue; } int g, h, u, v; point a, b; bool flag = 0; for(int i = 0 ; i < n && !flag; i++) { for(int j = i + 1; j < n ; j++) { g = (points[i].x + points[j].x); h = (points[i].y + points[j].y); u = (points[j].x - points[i].x); v = (points[i].y - points[j].y); a.x = (g - v) / 2; a.y = (h - u) / 2; b.x = (v + g) / 2; b.y = (h + u) / 2; if(query(a) && query(b)) { flag = 1; break; } } } if(flag)puts("4"); else puts("-1"); } }
#include <cstdio> #include <cstring> #include <cmath> #include <queue> #include <cstring> #include <vector> #include <string> #include <stack> #include <set> #include <map> #include <iostream> #include <algorithm> using namespace std; #define MP make_pair #define PB push_back typedef long long LL; typedef pair<int, int> Pii; const int inf = 0x3f3f3f3f; const LL INF = (1uLL << 63) - 1; const LL mod = 1000000007; const int N = 1e5 + 5; const double Pi = acos(-1.0); const int maxn = 2e6 + 5; int dp[25][maxn]; int sum[25][maxn]; int d[25]; int n , m; int gao() { dp[0][0] = 1; sum[0][0] = 1; for(int i = 1; i <= m; i++)sum[0][i] = 1; for(int i = 1; i <= n; i++){ for(int j = 0; j <= m; j++){ if(j < d[i]){ dp[i][j] = sum[i-1][j]; } else dp[i][j] = sum[i-1][j] - sum[i-1][j-d[i]]; sum[i][j] = (j?sum[i][j-1]:0) + dp[i][j]; } } int res = 0; for(int i = 0; i <= m; i++){ res = max(dp[n][i],res); } return res; } int main() { #ifdef local freopen("in", "r", stdin); #endif int cas; cin >> cas; while(cas--) { cin>>n; m = - n; for(int i = 1 ; i <= n ; i++){ scanf("%d",&d[i]); m += d[i]; } cout<<gao()<<endl; } }
#include <cstdio> #include <cstring> #include <cmath> #include <queue> #include <cstring> #include <vector> #include <string> #include <stack> #include <set> #include <map> #include <iostream> #include <algorithm> using namespace std; #define MP make_pair #define PB push_back typedef long long LL; typedef pair<int, int> Pii; const int inf = 0x3f3f3f3f; const LL INF = (1uLL << 63) - 1; const LL mod = 1000000007; const int N = 1e5 + 5; const double Pi = acos(-1.0); const int maxn = 2e6 + 5; LL sum[15]; int gao(LL a) { int res = 0; while(a) { res += a % 10; a /= 10; } return res; } int Cnt(int n) { if(n < 10)return n * (n + 1) / 2; int d = log10(n); int p = ceil(pow(10, d)); int tst = n / p; return tst * sum[d] + (tst * (tst - 1) / 2) * p + tst * (1 + n % p) + Cnt(n % p); } int upcnt(LL &res , LL b) { LL c = res; res += b; int up = 0; int d = 0; while(b || c) { if( (d = d + b % 10 + c % 10) > 9 )up++; d /= 10; b /= 10; c /= 10; } return up; } LL pai(LL l, LL m) { LL res = 0; int g = 0; for(LL i = l ; ; i++) { g += upcnt(res, i); if(g > m) { return res - i; //return i-1; } } } int main() { #ifdef local freopen("in", "r", stdin); #endif for(int i = 1; i <= 10; i++) { sum[i] = sum[i - 1] * 10 + 45 * ceil(pow(10, i - 1)); } int T; cin >> T; while(T--) { LL L, M; cin >> L >> M; int d = Cnt(L - 1); int l = L , r = L + 2e7; LL res = 0; while(l <= r ) { LL mid = ( l + r ) >> 1; // cout<<(mid + L) * (mid - L + 1) / 2<<endl; int now = gao((mid + L) * (mid - L + 1) / 2); int diff = Cnt(mid) - d - now; diff /= 9; if(diff <= M) { l = mid + 1; res = (mid + L) * (mid - L + 1) / 2; } else r = mid - 1; } cout << res << endl; } }
