[51NOD]BSG白山极客挑战赛

2022-11-18 10:05:12

比赛链接：http://www.51nod.com/contest/problemList.html#!contestId=21

 /*

 ━━━━━┒ギリギリ♂ eye！

 ┓┏┓┏┓┃キリキリ♂ mind！

 ┛┗┛┗┛┃＼○／

 ┓┏┓┏┓┃ /

 ┛┗┛┗┛┃ノ)

 ┓┏┓┏┓┃

 ┛┗┛┗┛┃

 ┓┏┓┏┓┃

 ┛┗┛┗┛┃

 ┓┏┓┏┓┃

 ┛┗┛┗┛┃

 ┓┏┓┏┓┃

 ┃┃┃┃┃┃

 ┻┻┻┻┻┻

 */

 #include <algorithm>

 #include <iostream>

 #include <iomanip>

 #include <cstring>

 #include <climits>

 #include <complex>

 #include <fstream>

 #include <cassert>

 #include <cstdio>

 #include <bitset>

 #include <vector>

 #include <deque>

 #include <queue>

 #include <stack>

 #include <ctime>

 #include <set>

 #include <map>

 #include <cmath>

 using namespace std;

 #define fr first

 #define sc second

 #define cl clear

 #define BUG puts("here!!!")

 #define W(a) while(a--)

 #define pb(a) push_back(a)

 #define Rint(a) scanf("%d", &a)

 #define Rll(a) scanf("%lld", &a)

 #define Rs(a) scanf("%s", a)

 #define Cin(a) cin >> a

 #define FRead() freopen("in", "r", stdin)

 #define FWrite() freopen("out", "w", stdout)

 #define Rep(i, len) for(int i = 0; i < (len); i++)

 #define For(i, a, len) for(int i = (a); i < (len); i++)

 #define Cls(a) memset((a), 0, sizeof(a))

 #define Clr(a, x) memset((a), (x), sizeof(a))

 #define Full(a) memset((a), 0x7f7f, sizeof(a))

 #define lrt rt << 1

 #define rrt rt << 1 | 1

 #define pi 3.14159265359

 #define RT return

 typedef long long LL;

 typedef long double LD;

 typedef unsigned long long ULL;

 typedef pair<int, int> pii;

 typedef pair<string, int> psi;

 typedef map<string, int> msi;

 typedef vector<LL> vl;

 typedef vector<vl> vvl;

 typedef vector<bool> vb;

 LL p[];

 int a,b,d,n;

 int main() {

     // FRead();

     int T;

     Rint(T);

     W(T) {

         Cls(p);

         Rint(a); Rint(b); Rint(d); Rint(n);

         if(n==) {

             if(a*b >= ) p[(a*b)/]++;

             p[(a*b)%]++;

             cout << p[d] << endl;

         }

         else {

             int k = a*b;

             int t = k / ;

             int x = k % ;

             int y = (x + t) / ;

             int g = (x +t) % ;

             int j = (x + y + t) % ;

             p[j] += n-;

             p[g] += ;

             p[x] += ;

             if(k >= ) p[y+t] += ;

             cout << p[d] << endl;

         }

     }

     RT ;

 }

A

 /*

 ━━━━━┒ギリギリ♂ eye！

 ┓┏┓┏┓┃キリキリ♂ mind！

 ┛┗┛┗┛┃＼○／

 ┓┏┓┏┓┃ /

 ┛┗┛┗┛┃ノ)

 ┓┏┓┏┓┃

 ┛┗┛┗┛┃

 ┓┏┓┏┓┃

 ┛┗┛┗┛┃

 ┓┏┓┏┓┃

 ┛┗┛┗┛┃

 ┓┏┓┏┓┃

 ┃┃┃┃┃┃

 ┻┻┻┻┻┻

 */

 #include <algorithm>

 #include <iostream>

 #include <iomanip>

 #include <cstring>

 #include <climits>

 #include <complex>

 #include <fstream>

 #include <cassert>

 #include <cstdio>

 #include <bitset>

 #include <vector>

 #include <deque>

 #include <queue>

 #include <stack>

 #include <ctime>

 #include <set>

 #include <map>

 #include <cmath>

 using namespace std;

 #define fr first

 #define sc second

 #define cl clear

 #define BUG puts("here!!!")

 #define W(a) while(a--)

 #define pb(a) push_back(a)

 #define Rint(a) scanf("%d", &a)

 #define Rll(a) scanf("%lld", &a)

 #define Rs(a) scanf("%s", a)

 #define Cin(a) cin >> a

 #define FRead() freopen("in", "r", stdin)

 #define FWrite() freopen("out", "w", stdout)

 #define Rep(i, len) for(int i = 0; i < (len); i++)

 #define For(i, a, len) for(int i = (a); i < (len); i++)

 #define Cls(a) memset((a), 0, sizeof(a))

 #define Clr(a, x) memset((a), (x), sizeof(a))

 #define Full(a) memset((a), 0x7f7f, sizeof(a))

 #define lrt rt << 1

 #define rrt rt << 1 | 1

 #define pi 3.14159265359

 #define RT return

 typedef long long LL;

 typedef long double LD;

 typedef unsigned long long ULL;

 typedef pair<int, int> pii;

 typedef pair<string, int> psi;

 typedef map<string, int> msi;

 typedef vector<LL> vl;

 typedef vector<vl> vvl;

 typedef vector<bool> vb;

 const int maxn = ;

 const int mod = ;

 LL dp[maxn][maxn];

 LL ans;

 int n;

 int main() {

     // FRead();

     while(~Rint(n)) {

         Cls(dp);

         dp[][] = dp[][] = ; dp[][] = ;

         For(i, , n+) {

             Rep(j, i) {

                 For(k, , ) {

                     dp[i][k] += (dp[j][k-] * dp[i-j-][k-]) % mod;

                     if(dp[i][k] >= mod) dp[i][k] %= mod;

                     if(k >= ) {

                         dp[i][k] += (dp[j][k-] * dp[i-j-][k-]) % mod;

                         if(dp[i][k] >= mod) dp[i][k] %= mod;

                     }

                     dp[i][k] += (dp[j][k-] * dp[i-j-][k-]) % mod;

                     if(dp[i][k] >= mod) dp[i][k] %= mod;

                 }

             }

         }

         ans = ;

         Rep(i, ) {

             ans += dp[n][i];

             ans %= mod;

         }

         cout << ans << endl;

     }

     RT ;

 }

B

 /*

 ━━━━━┒ギリギリ♂ eye！

 ┓┏┓┏┓┃キリキリ♂ mind！

 ┛┗┛┗┛┃＼○／

 ┓┏┓┏┓┃ /

 ┛┗┛┗┛┃ノ)

 ┓┏┓┏┓┃

 ┛┗┛┗┛┃

 ┓┏┓┏┓┃

 ┛┗┛┗┛┃

 ┓┏┓┏┓┃

 ┛┗┛┗┛┃

 ┓┏┓┏┓┃

 ┃┃┃┃┃┃

 ┻┻┻┻┻┻

 */

 #include <algorithm>

 #include <iostream>

 #include <iomanip>

 #include <cstring>

 #include <climits>

 #include <complex>

 #include <fstream>

 #include <cassert>

 #include <cstdio>

 #include <bitset>

 #include <vector>

 #include <deque>

 #include <queue>

 #include <stack>

 #include <ctime>

 #include <set>

 #include <map>

 #include <cmath>

 using namespace std;

 #define fr first

 #define sc second

 #define cl clear

 #define BUG puts("here!!!")

 #define W(a) while(a--)

 #define pb(a) push_back(a)

 #define Rint(a) scanf("%d", &a)

 #define Rll(a) scanf("%lld", &a)

 #define Rs(a) scanf("%s", a)

 #define Cin(a) cin >> a

 #define FRead() freopen("in", "r", stdin)

 #define FWrite() freopen("out", "w", stdout)

 #define Rep(i, len) for(int i = 0; i < (len); i++)

 #define For(i, a, len) for(int i = (a); i < (len); i++)

 #define Cls(a) memset((a), 0, sizeof(a))

 #define Clr(a, x) memset((a), (x), sizeof(a))

 #define Full(a) memset((a), 0x7f7f, sizeof(a))

 #define lrt rt << 1

 #define rrt rt << 1 | 1

 #define pi 3.14159265359

 #define RT return

 typedef long long LL;

 typedef long double LD;

 typedef unsigned long long ULL;

 typedef pair<int, int> pii;

 typedef pair<string, int> psi;

 typedef map<string, int> msi;

 typedef vector<LL> vl;

 typedef vector<vl> vvl;

 typedef vector<bool> vb;

 // const int maxn = ;

 int n;

 int main() {

     // FRead();

     double r, R, s, v;

     cin >> s;

     r = sqrt(s / pi) / ;

     R = s / (pi * r) - r;

     v = pi * r * r * sqrt(R * R - r * r) / ;

     printf("%.6lf\n", v);;

     RT ;

 }

C

 /*

 ━━━━━┒ギリギリ♂ eye！

 ┓┏┓┏┓┃キリキリ♂ mind！

 ┛┗┛┗┛┃＼○／

 ┓┏┓┏┓┃ /

 ┛┗┛┗┛┃ノ)

 ┓┏┓┏┓┃

 ┛┗┛┗┛┃

 ┓┏┓┏┓┃

 ┛┗┛┗┛┃

 ┓┏┓┏┓┃

 ┛┗┛┗┛┃

 ┓┏┓┏┓┃

 ┃┃┃┃┃┃

 ┻┻┻┻┻┻

 */

 #include <algorithm>

 #include <iostream>

 #include <iomanip>

 #include <cstring>

 #include <climits>

 #include <complex>

 #include <fstream>

 #include <cassert>

 #include <cstdio>

 #include <bitset>

 #include <vector>

 #include <deque>

 #include <queue>

 #include <stack>

 #include <ctime>

 #include <set>

 #include <map>

 #include <cmath>

 using namespace std;

 #define fr first

 #define sc second

 #define cl clear

 #define BUG puts("here!!!")

 #define W(a) while(a--)

 #define pb(a) push_back(a)

 #define Rint(a) scanf("%d", &a)

 #define Rll(a) scanf("%lld", &a)

 #define Rs(a) scanf("%s", a)

 #define Cin(a) cin >> a

 #define FRead() freopen("in", "r", stdin)

 #define FWrite() freopen("out", "w", stdout)

 #define Rep(i, len) for(int i = 0; i < (len); i++)

 #define For(i, a, len) for(int i = (a); i < (len); i++)

 #define Cls(a) memset((a), 0, sizeof(a))

 #define Clr(a, x) memset((a), (x), sizeof(a))

 #define Full(a) memset((a), 0x7f7f, sizeof(a))

 #define lp p << 1

 #define rp p << 1 | 1

 #define pi 3.14159265359

 #define RT return

 #define lowbit(x) x & (-x)

 #define onenum(x) __builtin_popcount(x)

 typedef long long LL;

 typedef long double LD;

 typedef unsigned long long ULL;

 typedef pair<int, int> pii;

 typedef pair<string, int> psi;

 typedef map<string, int> msi;

 typedef vector<int> vi;

 typedef vector<LL> vl;

 typedef vector<vl> vvl;

 typedef vector<bool> vb;

 const int maxn = ;

 int n;

 LL k;

 int bit[maxn<<][];

 int t[maxn], dp[maxn];

 void add(int i, int x, int j) {

     while(i <= maxn) {

         bit[i][j] += x;

         i += lowbit(i);

     }

 }

 int sum(int i, int j) {

     int s = ;

     while(i) {

         s += bit[i][j];

         i -= lowbit(i);

     }

     return s;

 }

 bool ok(int x) {

     Cls(dp); Cls(bit);

     Rep(i, n+) {

         if(t[i] >= x) dp[i] = dp[i-] + ;

         else dp[i] = dp[i-];

     }

     Rep(i, n+) dp[i] =  * dp[i] - i + ;

     LL ret = ;

     Rep(i, n+) {

         ret += sum(dp[i]-, !(i&));

         add(dp[i], , i&);

     }

     if(ret >= k) return ;

     return ;

 }

 int main() {

     // FRead();

     while(~Rint(n) && ~Rll(k)) {

         int l = , r = ;

         For(i, , n+) {

             Rint(t[i]);

             r = max(r, t[i]);

         }

         while(l <= r) {

             int m = (l + r) >> ;

             if(ok(m)) l = m + ;

             else r = m - ;

         }

         printf("%d\n", r);

     }

     RT ;

 }

E

E题：

二分中位数x，dp(i)维护[1,i]区间内大于等于x的数量。注意到长为奇数的区间[l,r]，l和r奇偶一定不同，这一点非常重要。

如果区间[l,r]内的中位数大于等于x的话，那么(dp(r)-dp(l))*2>r-l+1，即2*dp[r]-r>2*dp(l)-l+1。

更新dp，使dp(i)-2*dp(i)-i，统计有多少个dp(j)<dp(i) j<i 且i,j奇偶不同。

有一个问题，就是2*dp[i]-i<0，解决方法就是加一个数，并且不至于让dp[i]计算后溢出的数。

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