Codeforces Round #645 (Div. 2)
还是视频题解。
昨晚比赛没打，就看了看题，ABD基本就是贪心+模拟，C感受一下算一下公式就行，E的话有点像交互，分情况讨论一下，\(x\leq 0\)的情况最简单，枚举一下后缀就行；\(x>0\)的时候利用到了倍增的思想，就刚好符合题目给出的条件。感觉这种将题目条件运用到极致的题目挺像交互了2333。F细节是真的多，各种判断，一不小心就卡半天。。不过思路还是有借鉴性，考虑逆操作和前缀和的一些性质，还有最后\(n=2\)时操作类似于欧几里得算法这里也很巧妙。。
补充一下E题思路：
后面\(\lfloor\frac{n}{2}\rfloor\)个数，假设都为\(x\)。
考虑\(x\leq 0\)的情况：注意到最后的答案\(k>\lfloor\frac{n}{2}\rfloor\)，否则\([n-k+1,n]\)这段区间和非正，不满足条件。那么可以直接枚举所有区间最后一个左端点的位置\(i\)，当前会新产生\([i,n]\)这段区间，显然其区间和可以直接计算；对于之前的区间，区间右端点都会左移一位，也就是之前所有的区间都会减少一个相同的数\(x\)。我们要考察所有区间和的最小值，那么只需对所有区间维护一个最小值，当区间端点移动时，最小值减去\(x\)即可，之后再与当前新产生的区间取\(min\)即可。
当\(x>0\)时，答案\(k\)没有明确的限制，我们可以发现若存在一个\(k>\lfloor\frac{n}{2}\rfloor\)合法，那么直接让\(k=n\)也是合法的；接下来就考虑\(k\leq \lfloor\frac{n}{2}\rfloor\)的情况，此时假设存在一个\(k\)合法，容易发现\(2k\)也是合法的答案。也就是说我们能够将\(k\)倍增至大于\(\lfloor\frac{n}{2}\rfloor\)的某个位置。归纳一下\(x>0\)直接取\(k=n\)即可。
代码如下：
A. Park Lighting
/*
* Author: heyuhhh
* Created Time: 2020/5/27 9:52:38
*/
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#include <functional>
#include <numeric>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
#define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
void err() { std::cout << std::endl; }
template<typename T, typename...Args>
void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A>
void err(const T <t> &arg, const A&... args) {
for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
#define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e5 + 5;
void run() {
int n, m; cin >> n >> m;
int ans = n * (m / 2);
if (m & 1) {
ans += n / 2;
if (n & 1) ++ans;
}
cout << ans << '\n';
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(20);
int T; cin >> T; while(T--)
run();
return 0;
}
B. Maria Breaks the Self-isolation
/*
* Author: heyuhhh
* Created Time: 2020/5/27 9:35:36
*/
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#include <functional>
#include <numeric>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
#define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
void err() { std::cout << std::endl; }
template<typename T, typename...Args>
void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A>
void err(const T <t> &arg, const A&... args) {
for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
#define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e5 + 5;
void run() {
int n; cin >> n;
vector <int> a(n);
for (int i = 0; i < n; i++) {
cin >> a[i];
}
sort(all(a));
int r = 1;
for (int i = 0, j; i < n; i = j + 1) {
int fur = -1;
for (j = i; j < n; j++) {
if (j - i + r >= a[j]) fur = j;
}
if (fur == -1) break;
j = fur;
r += j - i + 1;
}
cout << r << '\n';
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(20);
int T; cin >> T; while(T--)
run();
return 0;
}
C. Celex Update
/*
* Author: heyuhhh
* Created Time: 2020/5/27 9:25:12
*/
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#include <functional>
#include <numeric>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
#define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
void err() { std::cout << std::endl; }
template<typename T, typename...Args>
void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A>
void err(const T <t> &arg, const A&... args) {
for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
#define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e5 + 5;
void run() {
int sx, sy, ex, ey;
cin >> sx >> sy >> ex >> ey;
int n = ex - sx + 1, m = ey - sy + 1;
if (n > m) swap(n, m);
ll ans = 1ll * n * (n - 1);
ll r = n + m - 3;
r -= 2 * (n - 1);
ans += r * (n - 1);
++ans;
cout << ans << '\n';
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(20);
int T; cin >> T; while(T--)
run();
return 0;
}
D. The Best Vacation
/*
* Author: heyuhhh
* Created Time: 2020/5/26 23:06:52
*/
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#include <functional>
#include <numeric>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
#define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
void err() { std::cout << std::endl; }
template<typename T, typename...Args>
void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A>
void err(const T <t> &arg, const A&... args) {
for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
#define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e5 + 5;
void run() {
ll n, x; cin >> n >> x;
vector <ll> a(n << 1);
for (int i = 0; i < n; i++) {
cin >> a[i];
a[i + n] = a[i];
}
a.pb(a[0]);
auto calc = [&] (int l, int r) {
return 1ll * (r - l + 1) * (l + r) / 2;
};
vector <ll> sum(n << 1), sum2(n << 1);
for (int i = 0; i < n << 1; i++) {
if (i == 0) sum[i] = a[i];
else sum[i] = sum[i - 1] + a[i];
}
for (int i = 0; i < n << 1; i++) {
if (i == 0) sum2[i] = calc(1, a[i]);
else sum2[i] = sum2[i - 1] + calc(1, a[i]);
}
auto chk = [&] (int i, int j) {
return sum[j] - (i == 0 ? 0 : sum[i - 1]);
};
ll ans = 0;
for (int i = 0; i < n; i++) {
int l = i + 1, r = 2 * n, mid;
while (l < r) {
mid = (l + r) >> 1;
if (chk(i, mid) <= x) l = mid + 1;
else r = mid;
}
int j = l - 1;
ll s = x - chk(i, j);
if (s > 0) {
ll k = min(a[i] - 1, a[j + 1] - s);
ans = max(ans, calc(1 + k, a[i]) + calc(1, s + k) + sum2[j] - sum2[i]);
} else if (s == 0) {
ans = max(ans, sum2[j] - (i == 0 ? 0 : sum2[i - 1]));
} else {
ans = max(ans, calc(a[i] - x + 1, a[i]));
}
}
cout << ans << '\n';
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(20);
run();
return 0;
}
E. Are You Fired?
/*
* Author: heyuhhh
* Created Time: 2020/5/26 23:50:38
*/
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#include <functional>
#include <numeric>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
#define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
void err() { std::cout << std::endl; }
template<typename T, typename...Args>
void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A>
void err(const T <t> &arg, const A&... args) {
for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
#define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 5e5 + 5;
int n;
int a[N];
ll sum[N];
void run() {
cin >> n;
int k = (n + 1) / 2;
for (int i = 1; i <= k; i++) {
cin >> a[i];
sum[i] = sum[i - 1] + a[i];
}
int x; cin >> x;
auto calc = [&] (ll t) {
return sum[k] - sum[t - 1];
};
ll Min = 1e18;
int ans = -1;
for (int i = 1; i <= k; i++) {
ll res = calc(i) + 1ll * (n / 2) * x;
if (Min == 1e18) {
Min = res;
} else {
Min -= x;
Min = min(Min, res);
}
if (Min > 0) ans = n - i + 1;
}
cout << ans << '\n';
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(20);
run();
return 0;
}
F. Tasty Cookie
/*
* Author: heyuhhh
* Created Time: 2020/5/27 15:17:12
*/
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#include <functional>
#include <numeric>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
#define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
void err() { std::cout << std::endl; }
template<typename T, typename...Args>
void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A>
void err(const T <t> &arg, const A&... args) {
for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
#define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e5 + 5;
bool operator == (vector <ll>& A, vector <ll>& B) {
for (int i = 0; i < sz(A); i++) {
if (A[i] != B[i]) return false;
}
return true;
}
vector <ll> rev(vector <ll>& A) {
vector <ll> B = A;
reverse(all(B));
return B;
}
void D(vector <ll>& A) {
int n = sz(A);
for (int i = n - 1; i > 0; i--) {
A[i] -= A[i - 1];
}
}
void out(ll cntp, ll cntr, vector <char>& ans) {
reverse(all(ans));
if (cntp > 2e5) {
cout << "BIG" << '\n';
cout << cntp << '\n';
} else {
cout << "SMALL" << '\n';
cout << sz(ans) << '\n';
for (auto it : ans) cout << it;
cout << '\n';
}
}
void run() {
int n; cin >> n;
vector <ll> a(n), b(n);
for (int i = 0; i < n; i++) {
cin >> a[i];
}
for (int i = 0; i < n; i++) {
cin >> b[i];
}
if (n == 1) {
if (a[0] == b[0]) {
cout << "SMALL" << '\n';
cout << 0 << '\n' << '\n';
} else {
cout << "IMPOSSIBLE" << '\n';
}
return;
}
ll cntr = 0, cntp = 0;
vector <char> ans;
bool BIG = false, f = false;
if (n > 2) {
while (!(a == b || a == rev(b))) {
for (int i = 1; i < n; i++) {
if (b[i] <= b[i - 1]) {
b = rev(b), ++cntr;
ans.push_back('R');
break;
}
}
D(b), ++cntp;
if (cntp > 2e5) BIG = true;
if (!BIG) ans.push_back('P');
for (int i = 0; i < n; i++) {
if (b[i] < 0) {
cout << "IMPOSSIBLE" << '\n';
return;
}
}
}
if (a == rev(b)) f = true;
} else {
while (1) {
if (b[0] == a[1]) {
swap(a[0], a[1]);
f = true;
}
if (b[0] == a[0]) {
if (b[1] < a[1]) {
cout << "IMPOSSIBLE" << '\n';
return;
}
ll r = (b[1] - a[1]) % b[0];
if (r == 0) {
ll now = ((b[1] - a[1]) / b[0]);
cntp += now;
if (cntp > 2e5) BIG = true;
if (!BIG) for (int i = 0; i < now; i++) {
ans.push_back('P');
}
} else {
cout << "IMPOSSIBLE" << '\n';
return;
}
break;
}
if (b[0] < a[0]) {
cout << "IMPOSSIBLE" << '\n';
return;
}
ll& x = b[0], &y = b[1];
ll now = (y - y % x) / x;
y %= x;
cntp += now;
if (cntp > 2e5) BIG = true;
if (!BIG) for (int i = 0; i < now; i++) {
ans.push_back('P');
}
swap(x, y), ++cntr;
ans.push_back('R');
}
}
if (f) {
++cntr;
ans.push_back('R');
}
out(cntp, cntr, ans);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(20);
run();
return 0;
}
重要的是自信，一旦有了自信，人就会赢得一切。
