Andrew Stankevich's Contest (1)

打一半出门了，回来才补完了。。。各种大数又不能上java。。也是蛋疼无比

A：依据置换循环节非常easy得出要gcd(x, n) = 1而且x <= n / 2，那么把相应几种情况的最大值考虑一下就可以，各自是n % 2 = 1为n / 2, n % 4 = 0为n / 2 - 1，n % 4 = 2为n / 2 - 2

B：限制下限的最大流，建模方法为原来容量变成c - l，然后源点连到每一个点的下限和为正，每一个点下限和为负连到汇点，跑一下最大流，假设源点流出的所有满流就是有解，然后输出的时候仅仅要把相应的自由流加上下限就可以

C：贪心，从叶子结点不断往上推，一有合适就用掉，然后把父结点标记一下用来推断就可以

D：就简单的矩阵相乘，因为要考虑复杂度，所以能够先算出没排的和，然后每一个位置分别乘上相应那排再累加就可以

E：矩阵高速幂，把两两关系确立后，建立矩阵跑一下高速幂就可以

F：几何题，推断有限视角和是否会形成-2pi，利用spfa判负环就可以

G：LIS，先按x从小到大，再按y从大到小排序，这样对y做lis就是答案，因为要输出路径，所以开一个dp数组记录下每一个位置的答案，然后在扫一遍随意输出一种方案就可以

H：高斯消元，和大白书上例题差点儿相同，全然平方数的每一个因子必定是偶数，这样就能够建立异或方程，然后计算出自由便元个数x，那么答案就是2^x - 1

代码：

A:

#include <cstdio>
#include <cstring>
#include <iostream>using namespace std;
typedef long long ll;
const int MAXN = 2005;struct bign {int len;ll num[MAXN];bign () {len = 0;memset(num, 0, sizeof(num));}bign (ll number) {*this = number;}bign (const char* number) {*this = number;}void DelZero ();void Put ();void operator = (ll number);void operator = (char* number);bool operator <  (const bign& b) const;bool operator >  (const bign& b) const { return b < *this; }bool operator <= (const bign& b) const { return !(b < *this); }bool operator >= (const bign& b) const { return !(*this < b); }bool operator != (const bign& b) const { return b < *this || *this < b;}bool operator == (const bign& b) const { return !(b != *this); }void operator ++ ();void operator -- ();bign operator + (const int& b);bign operator + (const bign& b);bign operator - (const int& b);bign operator - (const bign& b);bign operator * (const ll& b);bign operator * (const bign& b);bign operator / (const ll& b);//bign operator / (const bign& b);int operator % (const int& b);
};/*Code*/char str[2005];int main() {while (~scanf("%s", str)) {bign sb;sb = str;bign ans;if (sb % 2) ans = sb / 2;else if (sb % 4 == 0) ans = sb / 2 - 1;else ans = sb / 2 - 2;ans.Put();printf("\n");}return 0;
}/*********************************************/void bign::DelZero () {while (len && num[len-1] == 0)len--;if (len == 0) {num[len++] = 0;}
}void bign::Put () {for (int i = len-1; i >= 0; i--)printf("%lld", num[i]);
}void bign::operator = (char* number) {len = strlen (number);for (int i = 0; i < len; i++)num[i] = number[len-i-1] - '0';DelZero ();
}void bign::operator = (ll number) {len = 0;while (number) {num[len++] = number%10;number /= 10;}DelZero ();
}bool bign::operator < (const bign& b) const {if (len != b.len)return len < b.len;for (int i = len-1; i >= 0; i--)if (num[i] != b.num[i])return num[i] < b.num[i];return false;
}void bign::operator ++ () {int s = 1;for (int i = 0; i < len; i++) {s = s + num[i];num[i] = s % 10;s /= 10;if (!s) break;}while (s) {num[len++] = s%10;s /= 10;}
}void bign::operator -- () {if (num[0] == 0 && len == 1) return;int s = -1;for (int i = 0; i < len; i++) {s = s + num[i];num[i] = (s + 10) % 10;if (s >= 0) break;}DelZero ();
}bign bign::operator + (const int& b) {bign a = b;return *this + a;
}bign bign::operator + (const bign& b) {int bignSum = 0;bign ans;for (int i = 0; i < len || i < b.len; i++) {if (i < len) bignSum += num[i];if (i < b.len) bignSum += b.num[i];ans.num[ans.len++] = bignSum % 10;bignSum /= 10;}while (bignSum) {ans.num[ans.len++] = bignSum % 10;bignSum /= 10;}return ans;
}bign bign::operator - (const int& b) {bign a = b;return *this - a;
}bign bign::operator - (const bign& b) {ll bignSub = 0;bign ans;for (int i = 0; i < len || i < b.len; i++) {bignSub += num[i];if (i < b.len)bignSub -= b.num[i];ans.num[ans.len++] = (bignSub + 10) % 10;if (bignSub < 0) bignSub = -1;else bignSub = 0;}ans.DelZero();return ans;
}bign bign::operator * (const ll& b) {ll bignSum = 0;bign ans;ans.len = len;for (int i = 0; i < len; i++) {bignSum += num[i] * b;ans.num[i] = bignSum % 10;bignSum /= 10;}while (bignSum) {ans.num[ans.len++] = bignSum % 10;bignSum /= 10;}return ans;
}bign bign::operator * (const bign& b) {bign ans;ans.len = 0;for (int i = 0; i < len; i++){ int bignSum = 0; for (int j = 0; j < b.len; j++){ bignSum += num[i] * b.num[j] + ans.num[i+j]; ans.num[i+j] = bignSum % 10; bignSum /= 10;} ans.len = i + b.len; while (bignSum){ ans.num[ans.len++] = bignSum % 10; bignSum /= 10;} } return ans;
}bign bign::operator / (const ll& b) {bign ans;ll s = 0;for (int i = len-1; i >= 0; i--) {s = s * 10 + num[i];ans.num[i] = s/b;s %= b;}ans.len = len;ans.DelZero();return ans;
}int bign::operator % (const int& b) {bign ans;int s = 0;for (int i = len-1; i >= 0; i--) {s = s * 10 + num[i];ans.num[i] = s/b;s %= b;}return s;
}

B:

#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>
using namespace std;const int MAXNODE = 205;
const int MAXEDGE = 210005;typedef int Type;
const Type INF = 0x3f3f3f3f;struct Edge {int u, v;Type cap, flow, low;Edge() {}Edge(int u, int v, Type cap, Type flow, Type low) {this->u = u;this->v = v;this->cap = cap;this->flow = flow;this->low = low;}
};struct Dinic {int n, m, s, t;Edge edges[MAXEDGE];int first[MAXNODE];int next[MAXEDGE];bool vis[MAXNODE];Type d[MAXNODE];int cur[MAXNODE];vector<int> cut;void init(int n) {this->n = n;memset(first, -1, sizeof(first));m = 0;}void add_Edge(int u, int v, Type cap, Type low) {edges[m] = Edge(u, v, cap, 0, low);next[m] = first[u];first[u] = m++;edges[m] = Edge(v, u, 0, 0, low);next[m] = first[v];first[v] = m++;}bool bfs() {memset(vis, false, sizeof(vis));queue<int> Q;Q.push(s);d[s] = 0;vis[s] = true;while (!Q.empty()) {int u = Q.front(); Q.pop();for (int i = first[u]; i != -1; i = next[i]) {Edge& e = edges[i];if (!vis[e.v] && e.cap > e.flow) {vis[e.v] = true;d[e.v] = d[u] + 1;Q.push(e.v);}}}return vis[t];}Type dfs(int u, Type a) {if (u == t || a == 0) return a;Type flow = 0, f;for (int &i = cur[u]; i != -1; i = next[i]) {Edge& e = edges[i];if (d[u] + 1 == d[e.v] && (f = dfs(e.v, min(a, e.cap - e.flow))) > 0) {e.flow += f;edges[i^1].flow -= f;flow += f;a -= f;if (a == 0) break;}}return flow;}Type Maxflow(int s, int t) {this->s = s; this->t = t;Type flow = 0;while (bfs()) {for (int i = 0; i < n; i++)cur[i] = first[i];flow += dfs(s, INF);}return flow;}bool solve(int s, int t, int tot) {Maxflow(s, t); for (int i = first[s]; i + 1; i = next[i]) {if (edges[i].flow != edges[i].cap) return false;}printf("YES\n");for (int i = 0; i < 2 * tot; i += 2)printf("%d\n", edges[i].flow + edges[i].low);return true;}void MinCut() {cut.clear();for (int i = 0; i < m; i += 2) {if (vis[edges[i].u] && !vis[edges[i].v])cut.push_back(i);}}
} gao;const int N = 205;int n, m, M[N];int main() {while (~scanf("%d%d", &n, &m)) {gao.init(n + 2);int u, v, l, c;memset(M, 0, sizeof(M));for (int i = 0; i < m; i++) {scanf("%d%d%d%d", &u, &v, &l, &c);gao.add_Edge(u, v, c - l, l);M[u] -= l;M[v] += l;}for (int i = 1; i <= n; i++) {if (M[i] > 0) gao.add_Edge(0, i, M[i], 0);else if (M[i] < 0) gao.add_Edge(i, n + 1, -M[i], 0);}if (!gao.solve(0, n + 1, m)) printf("NO\n");}return 0;
}

C:

#include <cstdio>
#include <cstring>
#include <queue>
#include <set>
#include <algorithm>
using namespace std;const int N = 500005;int n, fa[N], du[N], vis[N];
int out[N], on;int main() {while (~scanf("%d", &n)) {int f;int ans = 0;memset(du, 0, sizeof(du));memset(vis, 0, sizeof(vis));for (int i = 2; i <= n; i++) {scanf("%d", &f);fa[i] = f;du[f]++;}on = 0;queue<int> Q;for (int i = 1; i <= n; i++) {if (du[i] == 0)Q.push(i);}while (!Q.empty()) {int u = Q.front();if (u == 1) break;Q.pop();if (!vis[u] && !vis[fa[u]]) {vis[fa[u]] = 1;out[on++] = u;ans += 1000;}du[fa[u]]--;if (du[fa[u]] == 0) Q.push(fa[u]);}sort(out, out + on);printf("%d\n", ans);for (int i = 0; i < on; i++)printf("%d%c", out[i], i == on - 1 ? '\n' : ' ');}return 0;
}

D:

#include <cstdio>
#include <cstring>const int N = 10005;
const int M = 100005;int n, m, cnt[N];
int u[M], v[M];int main() {while (~scanf("%d%d", &n, &m)) {long long ans = 0;memset(cnt, 0, sizeof(cnt));for (int i = 0; i < m; i++) {scanf("%d%d", &u[i], &v[i]);cnt[u[i]]++;if (v[i] != u[i]) cnt[v[i]]++;}for (int i = 0; i < m; i++) {ans += cnt[u[i]];if (u[i] != v[i]) ans += cnt[v[i]];}printf("%lld\n", ans);}return 0;
}

E:

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;typedef long long ll;
const ll MOD = 1000000000;
const int NUMLEN = 105;struct Bign {ll num[NUMLEN];int len;void init(char *str) {for (int i = strlen(str) - 1; i >= 0; i--) {if (str[i] == '0') str[i] = '9';else {str[i]--;break;}}if (str[0] == '0') {int ca = strlen(str);for (int i = 0; i < ca; i++)str[i] = str[i + 1];str[ca - 1] = '\0';}len = 0;memset(num, 0, sizeof(num));for (int i = strlen(str) - 1; i >= 0; i -= 9) {for (int j = max(0, i - 8); j <= i; j++) {num[len] = num[len] * 10 + str[j] - '0';}len++;}}ll div2() {ll yu = 0;for (int i = len - 1; i >= 0; i--) {num[i] = num[i] + yu * MOD;yu = num[i] % 2;num[i] /= 2;}while (len > 1 && num[len - 1] == 0) len--;return yu;}bool iszero() {if (len == 1 && num[0] == 0) return true;return false;}void print() {for (int i = len - 1; i >= 0; i--) {if (i != len - 1) printf("%09lld", num[i]);else printf("%lld", num[i]);}}
} n;const int N = 105;char num[N];
int m, p, tot;struct mat {int v[35][35];mat() {memset(v, 0, sizeof(v));}mat operator * (mat c) {mat ans;for (int k = 0; k < tot; k++) {for (int i = 0; i < tot; i++) {if (v[i][k] == 0) continue;for (int j = 0; j < tot; j++) {if (c.v[k][j] == 0) continue;ans.v[i][j] = (ans.v[i][j] + v[i][k] * c.v[k][j]) % p;}}}return ans;}
};mat pow_mod(mat x, Bign k) {mat ans;for (int i = 0; i < tot; i++) ans.v[i][i] = 1;while (!k.iszero()) {ll sb = k.div2();if (sb == 1) ans = ans * x;x = x * x;}return ans;
}int main() {while (~scanf("%s%d%d", num, &m, &p)) {n.init(num);tot = (1<<m);mat A;for (int i = 0; i < tot; i++) {for (int j = 0; j < tot; j++) {int flag = 1;int st = 3;for (int k = 0; k < m - 1; k++) {int sb = (i&st)>>k;if ((sb == 0 || sb == 3) && (i&st) == (j&st)) {flag = 0;break;}st <<= 1;}if (flag == 1) A.v[i][j] = 1;}}A = pow_mod(A, n);ll ans = 0;for (int i = 0; i < tot; i++) {for (int j = 0; j < tot; j++)ans = (ans + A.v[i][j]) % p;}printf("%lld\n", ans);}return 0;
}

F:

#include <cstdio>
#include <cstring>
#include <vector>
#include <cmath>
#include <algorithm>
#include <queue>
using namespace std;typedef double Type;const double eps = 1e-6;
const int MAXNODE = 305;
const int MAXEDGE = 100005;struct Edge {int u, v;Type dist;Edge() {}Edge(int u, int v, Type dist) {this->u = u;this->v = v;this->dist = dist;}
};struct BellmanFrod {int n, m;Edge edges[MAXEDGE];int first[MAXNODE];int next[MAXEDGE];bool inq[MAXNODE];Type d[MAXNODE];int p[MAXNODE];int cnt[MAXNODE];void init(int n) {this->n = n;memset(first, -1, sizeof(first));m = 0;}void add_Edge(int u, int v, Type dist) {edges[m] = Edge(u, v, dist);next[m] = first[u];first[u] = m++;}bool negativeCycle() {queue<int> Q;memset(inq, 0, sizeof(inq));memset(cnt, 0, sizeof(cnt));for (int i = 0; i < n; i++) {d[i] = 0; inq[i] = true; Q.push(i);}while (!Q.empty()) {int u = Q.front();Q.pop();inq[u] = false;for (int i = first[u]; i != -1; i = next[i]) {Edge& e = edges[i];if (d[e.v] > eps + d[u] + e.dist) {d[e.v] = d[u] + e.dist;p[e.v] = i;if (!inq[e.v]) {Q.push(e.v);inq[e.v] = true;if (++cnt[e.v] > n) return true;}}}}return false;}
} gao;const int N = 305;int n;struct Circle {double x, y, r;void read() {scanf("%lf%lf%lf", &x, &y, &r);}
} c[N], cc;double dis(Circle a, Circle b) {double dx = a.x - b.x;double dy = a.y - b.y;return sqrt(dx * dx + dy * dy);
}int main() {while (~scanf("%d", &n)) {for (int i = 0; i < n; i++) c[i].read();cc.read();for (int i = 0; i < n; i++) {c[i].x -= cc.x;c[i].y -= cc.y;c[i].r += cc.r;}cc.x = cc.y = 0;gao.init(n);for (int i = 0; i < n; i++) {for (int j = i + 1; j < n; j++) {if (c[i].r + c[j].r - eps < dis(c[i], c[j])) continue;double tmp = acos((c[i].x * c[j].x + c[i].y * c[j].y) / dis(c[i], cc) / dis(c[j], cc));bool flag = (c[i].x * c[j].y - c[i].y * c[j].x) >= 0;gao.add_Edge(i, j, flag ? tmp : -tmp);gao.add_Edge(j, i, flag ? -tmp : tmp);}}printf("%s\n", !gao.negativeCycle() ? "YES" : "NO");}return 0;
}

G:

#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>
using namespace std;const int N = 100005;
int n;
struct Man {int a, b, id;
} man[N];bool cmp(Man a, Man b) {if (a.a == b.a) return a.b > b.b;return a.a < b.a;
}int dp[N], save[N], sn;bool judge(Man a, Man b) {if (a.a <= b.a && a.b >= b.b) return false;if (a.a >= b.a && a.b <= b.b) return false;return true;
}int main() {while (~scanf("%d", &n)) {for (int i = 1; i <= n; i++) {scanf("%d%d", &man[i].a, &man[i].b);man[i].id = i;}sort(man + 1, man + n + 1, cmp);memset(dp, 0, sizeof(dp));sn = 0;save[sn++] = 0;for (int i = 1; i <= n; i++) {int v = lower_bound(save, save + sn, man[i].b) - save;save[v] = man[i].b;if (v == sn) sn++;dp[i] = v;}int sum = sn - 1;printf("%d\n", sum);int bo = 0;for (int i = n; i >= 1; i--) {if (dp[i] == sum) {if (bo) printf(" ");else bo = 1;printf("%d", man[i].id);sum--;}}printf("\n");}return 0;
}

H:

#include <cstdio>
#include <cstring>
#include <iostream>using namespace std;
typedef long long ll;
const int MAXN = 2005;struct bign {int len;ll num[MAXN];bign () {len = 0;memset(num, 0, sizeof(num));}bign (ll number) {*this = number;}bign (const char* number) {*this = number;}void DelZero ();void Put ();void operator = (ll number);void operator = (char* number);bool operator <  (const bign& b) const;bool operator >  (const bign& b) const { return b < *this; }bool operator <= (const bign& b) const { return !(b < *this); }bool operator >= (const bign& b) const { return !(*this < b); }bool operator != (const bign& b) const { return b < *this || *this < b;}bool operator == (const bign& b) const { return !(b != *this); }void operator ++ ();void operator -- ();bign operator + (const int& b);bign operator + (const bign& b);bign operator - (const int& b);bign operator - (const bign& b);bign operator * (const ll& b);bign operator * (const bign& b);bign operator / (const ll& b);//bign operator / (const bign& b);int operator % (const int& b);
};/*Code*/int prime[10005], pn = 0, vis[10005];void getprime() {for (int i = 2; i < 10000; i++) {if (vis[i]) continue;prime[pn++] = i;for (int j = i * i; j < 10000; j += i)vis[j] = 1;}
}const int N = 105;
int m, n;
int A[N][N];int gauss() {int i = 0, j = 0, k, r, u;while (i < m && j < n) {r = i;for (k = i; k < m; k++)if (A[k][j]) {r = k; break;}if (A[r][j]) {if (r != i) for (int k = 0; k <= n; k++) swap(A[r][k], A[i][k]);for (u = i + 1; u < m; u++) if (A[u][j])for (k = i; k <= n; k++) A[u][k] ^= A[i][k];i++;}j++;}return i;
}int main() {getprime();while (~scanf("%d%d", &m, &n)) {memset(A, 0, sizeof(A));int num;for (int k = 0; k < n; k++) {scanf("%d", &num);for (int i = 0; i < m; i++) {if (num % prime[i] == 0) {int cnt = 0;while (num % prime[i] == 0) {num /= prime[i];cnt++;}if (cnt % 2) A[i][k] = 1;}}}int sb = gauss();bign ans = 1;for (int i = 0; i < n - sb; i++) {ans = ans + ans;}ans = ans - 1;ans.Put();printf("\n");}return 0;
}/*********************************************/void bign::DelZero () {while (len && num[len-1] == 0)len--;if (len == 0) {num[len++] = 0;}
}void bign::Put () {for (int i = len-1; i >= 0; i--) printf("%lld", num[i]);
}void bign::operator = (char* number) {len = strlen (number);for (int i = 0; i < len; i++)num[i] = number[len-i-1] - '0';DelZero ();
}void bign::operator = (ll number) {len = 0;while (number) {num[len++] = number%10;number /= 10;}DelZero ();
}bool bign::operator < (const bign& b) const {if (len != b.len)return len < b.len;for (int i = len-1; i >= 0; i--)if (num[i] != b.num[i])return num[i] < b.num[i];return false;
}void bign::operator ++ () {int s = 1;for (int i = 0; i < len; i++) {s = s + num[i];num[i] = s % 10;s /= 10;if (!s) break;}while (s) {num[len++] = s%10;s /= 10;}
}void bign::operator -- () {if (num[0] == 0 && len == 1) return;int s = -1;for (int i = 0; i < len; i++) {s = s + num[i];num[i] = (s + 10) % 10;if (s >= 0) break;}DelZero ();
}bign bign::operator + (const int& b) {bign a = b;return *this + a;
}bign bign::operator + (const bign& b) {int bignSum = 0;bign ans;for (int i = 0; i < len || i < b.len; i++) {if (i < len) bignSum += num[i];if (i < b.len) bignSum += b.num[i];ans.num[ans.len++] = bignSum % 10;bignSum /= 10;}while (bignSum) {ans.num[ans.len++] = bignSum % 10;bignSum /= 10;}return ans;
}bign bign::operator - (const int& b) {bign a = b;return *this - a;
}bign bign::operator - (const bign& b) {ll bignSub = 0;bign ans;for (int i = 0; i < len || i < b.len; i++) {bignSub += num[i];if (i < b.len)bignSub -= b.num[i];ans.num[ans.len++] = (bignSub + 10) % 10;if (bignSub < 0) bignSub = -1;else bignSub = 0;}ans.DelZero();return ans;
}bign bign::operator * (const ll& b) {ll bignSum = 0;bign ans;ans.len = len;for (int i = 0; i < len; i++) {bignSum += num[i] * b;ans.num[i] = bignSum % 10;bignSum /= 10;}while (bignSum) {ans.num[ans.len++] = bignSum % 10;bignSum /= 10;}return ans;
}bign bign::operator * (const bign& b) {bign ans;ans.len = 0; for (int i = 0; i < len; i++){  int bignSum = 0;  for (int j = 0; j < b.len; j++){  bignSum += num[i] * b.num[j] + ans.num[i+j];  ans.num[i+j] = bignSum % 10;  bignSum /= 10;}  ans.len = i + b.len;  while (bignSum){  ans.num[ans.len++] = bignSum % 10;  bignSum /= 10;}  }  return ans;
}bign bign::operator / (const ll& b) {bign ans;ll s = 0;for (int i = len-1; i >= 0; i--) {s = s * 10 + num[i];ans.num[i] = s/b;s %= b;}ans.len = len;ans.DelZero();return ans;
}int bign::operator % (const int& b) {bign ans;int s = 0;for (int i = len-1; i >= 0; i--) {s = s * 10 + num[i];ans.num[i] = s/b;s %= b;}return s;
}