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#include <bits/stdc++.h> using namespace std; const int M = 200005; int A[M]; double B[M]; int n; double check(double x) { for (int i = 1, i_END_ = n + 1; i < i_END_; ++i) B[i] = A[i] - x; double mx = -1e60, mi = 1e60, s1 = 0, s2 = 0; for (int i = 1, i_END_ = n + 1; i < i_END_; ++i) { s1 += B[i]; mx = max(s1, mx); if (s1 < 0) s1 = 0; s2 += B[i]; mi = min(mi, s2); if (s2 > 0) s2 = 0; } return max(mx, -mi); } int main() { scanf("%d", &n); for (int i = 1, i_END_ = n + 1; i < i_END_; ++i) scanf("%d", &A[i]); double L = -10000, R = 10000, res = -10001; double ans = 1e60; for (int i = 0, i_END_ = 100; i < i_END_; ++i) { double del = (R - L) / 3; double m1 = L + del, m2 = R - del; double r1 = check(m1), r2 = check(m2); ans = min(ans, min(r1, r2)); if (r2 < r1) L = m1; else R = m2; } printf("%.12f\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 200005; const double inf = 0x3f3f3f3f; int n; double a[maxn], mmin, mmax, tmin, tmax; double weakness(double pos) { mmin = 0; mmax = 0; tmin = 0; tmax = 0; for (int i = 0; i < n; i++) { tmin += a[i] - pos; if (tmin > 0) tmin = 0; tmax += a[i] - pos; if (tmax < 0) tmax = 0; mmin = min(mmin, tmin); mmax = max(mmax, tmax); } return max(-mmin, mmax); } int main() { scanf("%d", &n); for (int i = 0; i < n; i++) scanf("%lf", &a[i]); int cnt = 0; double left = -10000, right = 10000; while (cnt++ < 300) { double mid = (left + right) / 2; double mmid = (mid + right) / 2; if (weakness(mid) < weakness(mmid)) right = mmid; else left = mid; } printf("%.9lf\n", weakness(left)); return 0; }
#include <bits/stdc++.h> using namespace std; double cal(int n, int *a, double x) { double ret = 0, t1 = 0, t2 = 0; for (int i = 0; i < n; i++) { t1 += a[i] - x; t2 += a[i] - x; t1 = max(0., t1); t2 = min(0., t2); ret = max(ret, t1); ret = max(ret, -t2); } return ret; } int main() { int n; scanf("%d", &n); static int a[200000]; for (int i = 0; i < n; i++) { scanf("%d", a + i); } double l = -10001, r = 10001, ans; for (int t = 0; t < 100; t++) { double d1 = (2 * l + r) / 3, d2 = (l + 2 * r) / 3; double e1 = cal(n, a, d1), e2 = cal(n, a, d2); if (e1 <= e2) { r = d2; ans = e1; } else { l = d1; ans = e2; } } printf("%.9lf\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 5; const double eps = 1e-12; int a[N]; int main() { int n; scanf("%d", &n); for (int i = 0; i < n; i++) scanf("%d", &a[i]); double Max, Min, now; double l = -1e4, r = 1e4; while (r - l > eps) { double m = (l + r) / 2; now = 0; Max = -1e9; for (int i = 0; i < n; i++) { now += a[i] - m; if (now > Max) Max = now; if (now < 0) now = 0; } now = 0; Min = 1e9; for (int i = 0; i < n; i++) { now += a[i] - m; if (now < Min) Min = now; if (now > 0) now = 0; } if (Max + Min > 0) l = m; else r = m; } printf("%.10f", Max); return 0; }
#include <bits/stdc++.h> const double eps = 1e-10; const int MaxN = 200005; double a[MaxN]; int n; double sol(double x) { double s = 0, mx = 0, mn = 0, res = -1e20; for (int i = 0; i < n; i++) { s += a[i] - x; res = std::max(res, fabs(s - mn)); res = std::max(res, fabs(s - mx)); mx = std::max(mx, s); mn = std::min(mn, s); } return res; } int main() { while (scanf("%d", &n) == 1) { for (int i = 0; i < n; i++) { scanf("%lf", &a[i]); } double l = -1e20, r = 1e20, mid1, mid2, res1, res2; for (int i = 0; i < 200; i++) { mid1 = (2 * l + r) / 3.0; mid2 = (l + 2 * r) / 3.0; res1 = sol(mid1); res2 = sol(mid2); if (res1 < res2 + eps) { r = mid2; } else { l = mid1; } } printf("%.12f\n", sol((l + r) / 2.0)); } return 0; }
#include <bits/stdc++.h> using namespace std; int t[200005]; int n, k; double cal(double x) { double maxx = 0, minn = 0; for (int i = 1; i <= n; i++) { double val = -x * i + t[i]; maxx = max(maxx, val); minn = min(minn, val); } return maxx - minn; } int main() { ios_base::sync_with_stdio(0); cin >> n; t[0] = 0; for (int i = 1; i <= n; i++) cin >> k, t[i] = t[i - 1] + k; double l = -30000, h = 30000; int cc = 0; for (int i = 1; i <= 100; i++) { cc++; double r1 = l + (h - l) / 3; double r2 = l + (h - l) * 2 / 3; double R1 = cal(r1); double R2 = cal(r2); if (R1 < R2 + 1e-8) h = r2; else l = r1; } printf("%.9lf", cal((l + h) / 2)); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 200000 + 10; const int INF = 10000 + 10; const double eps = 1e-11; int n, k = 100; double a[maxn], dp1[maxn], dp2[maxn]; double get_max(double x, double y) { return x > y ? x : y; } double get_min(double x, double y) { return x < y ? x : y; } double f(double x) { int i; double max = 0, b[maxn]; for (i = 0; i < n; i++) b[i] = a[i] - x; dp1[0] = b[0]; for (i = 1; i < n; i++) dp1[i] = get_max(dp1[i - 1] + b[i], b[i]); dp2[0] = b[0]; for (i = 1; i < n; i++) dp2[i] = get_min(dp2[i - 1] + b[i], b[i]); for (i = 0; i < n; i++) { max = get_max(max, abs(dp1[i])); max = get_max(max, abs(dp2[i])); } return max; } double divide(double &l, double &r) { double mid, mmid, fmid, fmmid; if (r - l < eps) return (l + r) / 2; mid = (r + 2 * l) / 3; mmid = (l + 2 * r) / 3; fmid = f(mid); fmmid = f(mmid); if (fmid <= fmmid) r = mmid; else if (fmid > fmmid) l = mid; return divide(l, r); } int main() { int i; double ans, max = -INF, min = INF; scanf("%d", &n); for (i = 0; i < n; i++) scanf("%lf", &a[i]); for (i = 0; i < n; i++) { if (a[i] > max) max = a[i]; if (a[i] < min) min = a[i]; } while (k--) { divide(min, max); } ans = divide(min, max); printf("%.6lf\n", f(ans)); return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> bool uin(T &a, T b) { return a > b ? (a = b, true) : false; } template <class T> bool uax(T &a, T b) { return a < b ? (a = b, true) : false; } double f(const vector<int> &a, double x) { double s = 0.0, mins = 0, maxs = 0; for (int i = 0; i < (int)(a.size()); ++i) { s += a[i] + x; uin(mins, s); uax(maxs, s); } return maxs - mins; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout.precision(10); cout << fixed; int N; cin >> N; vector<int> a(N); for (int i = 0; i < (int)(N); ++i) cin >> a[i]; double l = -1e9, r = 1e9; int A = 11, B = 10; for (int its = 0; its < (int)(100); ++its) { double m1 = (A * l + B * r) / (A + B); double m2 = (B * l + A * r) / (A + B); double f1 = f(a, m1), f2 = f(a, m2); if (f1 < f2) r = m2; else l = m1; } cout << f(a, l) << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 200100; int n; int a[N]; double b[N], sum[N]; double cal(double x) { sum[0] = 0; for (int i = 1; i <= n; i++) b[i] = 1.0 * a[i] - x; double mneg, mpos; mneg = mpos = 0; double gtmax = 0; for (int i = 1; i <= n; i++) { sum[i] = sum[i - 1] + b[i]; gtmax = max(gtmax, abs(b[i])); gtmax = max(gtmax, max(abs(sum[i] - mneg), abs(sum[i] - mpos))); mneg = min(mneg, sum[i]); mpos = max(mpos, sum[i]); } return gtmax; } bool cp(double x, double y) { double t = abs(x - y); return (t > 0.000000000001); } int main() { ios_base::sync_with_stdio(0); cin >> n; for (int i = 1; i <= n; i++) cin >> a[i]; double L = -1000001; double R = 1000001; double ML = (L + L + R) / 3; double MR = (L + R + R) / 3; while (cp(L, ML) && cp(ML, MR) && cp(MR, R)) { double x = cal(ML); double y = cal(MR); if (x > y) L = ML; else R = MR; ML = (L + L + R) / 3; MR = (L + R + R) / 3; } double ans = cal((L + R) / 2); printf("%0.7f", ans); return 0; }
#include <bits/stdc++.h> using namespace std; double b[300001], sum[300001]; int a[300001]; int n; double check(double x) { for (int i = 1; i <= n; i++) b[i] = a[i] * 1.0 - x; for (int i = 1; i <= n; i++) sum[i] = sum[i - 1] + b[i]; double Min = 0.0, Max = 0.0; double ans = 0.0; for (int i = 1; i <= n; i++) { ans = max(ans, fabs(sum[i] - Min)); ans = max(ans, fabs(sum[i] - Max)); Min = min(Min, sum[i]); Max = max(Max, sum[i]); } return ans; } int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) scanf("%d", &a[i]); double l = -999999.0, r = 999999.0; double ans = 9999999999999.0; bool flag = false; for (int i = 1; i <= 200; i++) { double mid1 = l + (r - l) / 3.0, mid2 = r - (r - l) / 3.0; double tmpx = check(mid1), tmpy = check(mid2); if (tmpx > tmpy) l = mid1; else r = mid2; if (flag == false) { flag = true; ans = tmpx; } else ans = min(ans, tmpx); ans = min(ans, tmpy); } ans = min(ans, check(l)); printf("%.9f\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxN = 2e5 + 100; int n, k, x; int a[maxN]; double s[maxN]; double tim() { double res = s[1], sum = 0; for (int i = 1; i <= n; i++) { sum += s[i]; res = max(res, sum); if (sum < 0) sum = 0; } return res; } int main() { cin >> n; for (int i = 1; i <= n; i++) scanf("%i", &a[i]); double res = 1e18; double l = 1e9, r = -1e9; for (int i = 1; i <= n; i++) l = min(l, double(a[i])), r = max(r, double(a[i])); int dem = 100; while (dem--) { double mid = (l + r) / 2; for (int i = 1; i <= n; i++) s[i] = double(a[i]) - mid; double s1 = tim(); for (int i = 1; i <= n; i++) s[i] = -s[i]; double s2 = tim(); res = min(max(abs(s1), abs(s2)), res); if (abs(s1) > abs(s2)) l = mid; else r = mid; } printf("%.9f", res); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 5e5 + 256; const char nxt = '\n'; const double eps = 1e-12; inline bool Pal(const string& s) { return equal(s.begin(), s.end(), s.rbegin()); } inline int readint() { bool neg = false; int ret = 0; char ch; ch = getchar(); while (true) { if (ch == '-') { neg = true; break; } if (ch >= '0' && ch <= '9') break; ch = getchar(); } if (!neg) ret = ch - '0'; while (true) { ch = getchar(); if (ch < '0' || ch > '9') break; ret = ret * 10 + ch - '0'; } return neg ? -ret : ret; } int n; double arr[MAXN]; double ans; inline double calc() { double ans = 0; double sum = 0; for (int i = 1; i <= n; ++i) { sum += arr[i]; if (sum > ans) ans = sum; if (sum < 0) sum = 0; } return ans; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout << setprecision(10) << fixed; cin >> n; for (int i = 1; i <= n; ++i) { cin >> arr[i]; } double l = -1000000.0000, r = 1000000.00000; for (int i = 1; i <= 300; ++i) { double mid = (l + r) / 2.000; for (int j = 1; j <= n; ++j) arr[j] -= mid; double cur1 = calc(); for (int j = 1; j <= n; ++j) arr[j] = -arr[j]; double cur2 = calc(); for (int j = 1; j <= n; ++j) arr[j] = -arr[j], arr[j] += mid; if (cur1 >= cur2) { l = mid; ans = cur1; } else r = mid; } cout << ans; return 0; }
#include <bits/stdc++.h> using namespace std; int N; double a[200010], sum[200010]; double cal(double X) { double hsgs = 0.0, Mn = 0.0, Mx = 0.0; for (int i = 1; i <= N; i++) { sum[i] = sum[i - 1] + a[i] - X; hsgs = max(max(fabs(sum[i] - Mn), fabs(sum[i] - Mx)), hsgs); Mn = min(Mn, sum[i]); Mx = max(Mx, sum[i]); } return hsgs; } int main() { scanf("%d", &N); for (int i = 1; i <= N; i++) scanf("%lf", &a[i]); double l = -1e9, r = 1e9; for (int i = 1; i <= 500; i++) if (cal((2 * l + r) / 3) < cal((l + 2 * r) / 3)) r = (l + 2 * r) / 3; else l = (2 * l + r) / 3; printf("%.15lf", cal(l)); }
#include <bits/stdc++.h> using namespace std; int n; double a[200010], l, r, ml, mr; void nhap() { cin >> n; for (int i = 1; i <= n; ++i) cin >> a[i]; } double func(double x) { double ma = 0, mi = 0, sum = 0; for (int i = 1; i <= n; ++i) { sum += a[i] - x; ma = max(ma, sum); mi = min(mi, sum); } return abs(ma - mi); } int main() { nhap(); l = -20000, r = 20000; for (int i = 1; i <= 100; ++i) { ml = (l + l + r) / 3; mr = (r + r + l) / 3; if (func(ml) > func(mr)) l = ml; else r = mr; } printf("%.10f", func(l)); return 0; }
#include <bits/stdc++.h> using namespace std; double a[200010], sum, mx, mn; int n, x; char c; bool b; double f(double x) { sum = 0, mx = 0, mn = 0; for (int i = 0; i < n; i++) { sum += a[i] - x; if (mx < sum) mx = sum; if (mn > sum) mn = sum; } return (mx - mn); } int qin() { b = false, x = 0; c = getchar(); if (c == '-') { b = true; c = '0'; } while (c != ' ') { x = x * 10 + (c - '0'); c = getchar(); } if (b) return -x; return x; } int qin2() { b = false, x = 0; c = getchar(); if (c == '-') { b = true; c = '0'; } else x = c - '0'; while ((c = getchar()) != EOF && c >= '0' && c <= '9') x = x * 10 + (c - '0'); if (b) return -x; return x; } int main() { n = qin2(); for (int i = 0; i < n - 1; i++) a[i] = qin(); a[n - 1] = qin2(); double l = -10001, r = 10001, ml, mr, z1, z2; int x = 0; while (r - l >= 0.00000000001) { ml = (l + r) / 2.0; mr = (ml + r) / 2.0; z1 = f(mr), z2 = f(ml); if (z1 < z2) l = ml; else r = mr; x++; } l = (l + r) / 2.0; printf("%.15lf", f(l)); return 0; }
#include <bits/stdc++.h> using namespace std; int main() { ios::sync_with_stdio(false); cin.tie(0); int n; cin >> n; vector<int> a(n); for (int i = 0; i < n; i++) { cin >> a[i]; } auto f = [&](double x) { double Min = 0, Max = 0, sm = 0; for (int i = 0; i < n; i++) { sm += a[i] - x; Min = min(Min, sm); Max = max(Max, sm); } return abs(Max - Min); }; double low = -1e6, high = 1e6; for (int i = 0; i < 200; i++) { double m1 = (2 * low + high) / 3; double m2 = (low + 2 * high) / 3; if (f(m1) < f(m2)) { high = m2; } else { low = m1; } } cout << setprecision(6) << fixed; cout << f(low) << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; int n; vector<long double> cum, cumt; long double weakness() { long double mx = 0, mxc = 0, mn = INT_MAX, mnc = INT_MAX; mx = mxc = cum[0]; for (int i = 1; i < n; i++) { mxc = max(cum[i], mxc + cum[i]); mx = max(mx, mxc); } mn = mnc = cum[0]; for (int i = 1; i < n; i++) { mnc = min(cum[i], mnc + cum[i]); mn = min(mn, mnc); } return max(abs(mx), abs(mn)); } long double calc(long double x) { for (double i = 0; i < n; i++) cum[i] = cumt[i] - x; return weakness(); } int main() { ios::sync_with_stdio(false), cin.tie(0); cin >> n; cum.resize(n), cumt.resize(n); for (int i = 0; i < n; i++) cin >> cum[i]; cumt = cum; long double a = -10000, d = 10000, b = (2 * a + d) / 3, c = (a + 2 * d) / 3; while (c - b > 0.000000000001) { if (calc(b) > calc(c)) a = b; else d = c; b = (2 * a + d) / 3, c = (a + 2 * d) / 3; } cout << fixed << setprecision(7) << calc(b) << endl; cin.ignore(), cin.get(); }
#include <bits/stdc++.h> using namespace std; int N, a[200000 + 3]; double prefix[200000 + 3]; pair<double, double> getWeakness(double x) { prefix[0] = 0; for (int i = 1; i <= N; i++) prefix[i] = prefix[i - 1] + (a[i] - x); double minPrefix = 0, maxPrefix = 0; double maxF = -1e10, maxG = -1e10; for (int j = 1; j <= N; j++) { double F = prefix[j] - minPrefix; double G = -prefix[j] + maxPrefix; maxF = max(maxF, F); maxG = max(maxG, G); minPrefix = min(minPrefix, prefix[j]); maxPrefix = max(maxPrefix, prefix[j]); } return {maxF, maxG}; } int main() { scanf("%d", &N); for (int i = 1; i <= N; i++) scanf("%d", &a[i]); double lo = -10000, hi = 10000, mid; for (int rep = 1; rep <= 100; rep++) { mid = (lo + hi) / 2.0; auto weakness = getWeakness(mid); if (weakness.first > weakness.second) lo = mid; else hi = mid; } auto weakness = getWeakness(lo); printf("%.10lf\n", max(weakness.first, weakness.second)); }
#include <bits/stdc++.h> using namespace std; double a[222222], b[222222]; int n; double f(double x) { for (int i = 0; i < n; i++) b[i] = a[i] - x; double MAX = -0x3f3f3f3f, ans = 0; for (int i = 0; i < n; i++) { ans += b[i]; MAX = max(ans, MAX); if (ans < 0) ans = 0; } double MIN = 0x3f3f3f3f; ans = 0; for (int i = 0; i < n; i++) { ans += b[i]; MIN = min(ans, MIN); if (ans > 0) ans = 0; } return max(fabs(MIN), fabs(MAX)); } int main() { scanf("%d", &n); double l = 0x3f3f3f3f, r = -0x3f3f3f3f; for (int i = 0; i < n; i++) { scanf("%lf", &a[i]); l = min(a[i], l); r = max(a[i], r); } while (1) { if (r - l <= 1e-11) break; double mid = (l + r) / 2; double mmid = (mid + r) / 2; if (f(mid) <= f(mmid)) r = mmid; else l = mid; } double goal = (l + r) / 2; printf("%.15f\n", f(goal)); return 0; }
#include <bits/stdc++.h> using namespace std; int n; int a[200000 + 10], ans = -0x7fffffff; double l[200000 + 10]; void Read(int &x) { char c; bool f = 0; while (c = getchar(), c != EOF) { if (c == '-') f = 1; if (c >= '0' && c <= '9') { x = c - '0'; while (c = getchar(), c >= '0' && c <= '9') x = x * 10 + c - '0'; if (f) x = -x; ungetc(c, stdin); return; } } } double get_poor(double x) { int i; double sum = 0, ret = 0; for (i = 1; i <= n; i++) l[i] = a[i] - x; for (i = 1; i <= n; i++) { sum += l[i]; if (sum < 0) sum = 0; ret = max(sum, ret); l[i] = -l[i]; } sum = 0; for (i = 1; i <= n; i++) { sum += l[i]; if (sum < 0) sum = 0; ret = max(sum, ret); } return ret; } int main() { Read(n); int i; for (i = 1; i <= n; i++) Read(a[i]); double l = -1e4, r = 1e4, m1, m2, v1, v2; i = 100; while (i--) { m1 = l + (r - l) / 3; m2 = r - (r - l) / 3; v1 = get_poor(m1); v2 = get_poor(m2); if (v1 > v2) l = m1; else r = m2; } printf("%.15lf\n", get_poor(l)); }
#include <bits/stdc++.h> using namespace std; const int INF = 2147483647, MOD = 1000 * 1000 * 1000 + 7; const double eps = 1e-8; void Error(string err) { cout << err; cerr << "_" << err << "_"; exit(0); } int gcd(int a, int b) { return (b == 0) ? a : gcd(b, a % b); } const int sz = 222 * 1000; int arr[sz], arr2[sz]; double sum[sz]; int n; double f(double x) { double ret = 0; double sm = 0; for (int i = 0; i < (n); i++) { if (sm + arr[i] - x > arr[i] - x) sm += arr[i] - x; else sm = arr[i] - x; ret = max(ret, abs(sm)); } sm = 0; for (int i = 0; i < (n); i++) { if (sm + arr[i] - x < arr[i] - x) sm += arr[i] - x; else sm = arr[i] - x; ret = max(ret, abs(sm)); } return ret; } int main() { cin >> n; for (int i = 0; i < (n); i++) cin >> arr[i]; sum[0] = arr[0]; for (int i = 1; i <= (n - 1); i++) sum[i] = sum[i - 1] + arr[i]; for (int i = 0; i < (n); i++) arr2[i] = arr[i]; sort(arr2, arr2 + n); double a = arr2[n / 2]; double wa = f(a); double inc = (arr2[n - 1] - arr2[0]); while (true) { wa = f(a); double nwai = f(a + inc), nwad = f(a - inc); if (wa > nwai && wa < nwad) a += inc; else if (wa > nwad && wa < nwai) a -= inc; else inc /= 2; double x = wa - nwai; double y = wa - nwad; double z = nwai - nwad; x = abs(x) + abs(y) + abs(z); if (x < 1e-9) break; } cout.setf(ios::fixed); cout.precision(8); cout << wa << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const double e = exp(1.0); const double INF = 1e9; const double eps = 1e-11; double maxX = -INF; double minX = INF; const int N = 200000 + 10; double a[N]; double fx(double v, int n) { double tmp = a[0] - v; double neg_tmp = a[0] - v; bool flag = false; if (a[0] < v) flag = true; for (int i = 1; i < n; i++) { if (a[i] < v) flag = true; tmp += a[i] - v; if (tmp < a[i] - v) tmp = a[i] - v; neg_tmp = max(tmp, neg_tmp); } if (flag) { maxX = v - a[0]; tmp = v - a[0]; for (int i = 1; i < n; i++) { tmp += v - a[i]; if (tmp < v - a[i]) tmp = v - a[i]; maxX = max(tmp, maxX); } } return max(neg_tmp, maxX); } int main() { int n; cin >> n; double xi = 0; for (int i = 0; i < n; i++) { cin >> a[i]; maxX = max(a[i], maxX); maxX = max(-a[i], maxX); minX = min(a[i], minX); } double L = -INF; double R = INF; while (L + eps < R) { double mid_L = (2 * L + R) / 3; double mid_R = (L + 2 * R) / 3; double res_L = fx(mid_L, n); double res_R = fx(mid_R, n); if (res_L > res_R) L = mid_L; else R = mid_R; } double answer = (L + R) / 2; cout << fixed << setprecision(7) << fx(answer, n); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 7; const int M = 4; const int inf = 1e9 + 7; const long long base = 1e18; const double pi = acos(-1); const double ep = 1e-9; int n; int a[N]; double F[N]; double f(double x) { F[0] = 0; double mn = 0, mx = 0; double ans = 0; for (int i = 1; i <= n; i++) { F[i] = F[i - 1] + a[i] - x; ans = max(ans, max(abs(F[i] - mn), abs(F[i] - mx))); mn = min(mn, F[i]); mx = max(mx, F[i]); } return ans; } int main() { cin >> n; for (int i = (int)1; i < (int)n + 1; i++) scanf("%d", a + i); double lo = -10000, hi = 10000, g, res; for (int t = (int)0; t < (int)100; t++) { double g1 = (2 * lo + hi) / 3; double g2 = (lo + 2 * hi) / 3; if (f(g1) < f(g2)) hi = g2; else lo = g1; } printf("%.9lf", f(lo)); }
#include <bits/stdc++.h> using namespace std; double EPS = 1e-9; int INF = 0x7FFFFFFF; long long INFF = 0x7FFFFFFFFFFFFFFF; double PI = acos(-1.0); int dirx[8] = {-1, 0, 0, 1, -1, -1, 1, 1}; int diry[8] = {0, 1, -1, 0, -1, 1, -1, 1}; inline void scanf(int &d1) { scanf("%d", &d1); } inline void scanf(int &d1, int &d2) { scanf("%d%d", &d1, &d2); } inline void scanf(int &d1, int &d2, int &d3) { scanf("%d%d%d", &d1, &d2, &d3); } inline void scanf(long long &d1) { scanf("%I64d", &d1); } inline void scanf(long long &d1, long long &d2) { scanf("%I64d%I64d", &d1, &d2); } inline void scanf(long long &d1, long long &d2, long long &d3) { scanf("%I64d%I64d%I64d", &d1, &d2, &d3); } inline void scanf(char *temp) { scanf("%s", temp); } inline void printf(int d1) { printf("%d\n", d1); } inline void printf(int d1, int d2) { printf("%d %d\n", d1, d2); } inline void printf(double f1) { printf("%.17g\n", f1); } inline void printf(long long l1) { printf("%I64d\n", l1); } inline void printf(long long l1, long long l2) { printf("%I64d %I64d\n", l1, l2); } inline string tostring(int a) { char x[100]; sprintf(x, "%d", a); string s = x; return s; } inline void toupperstring(string &s) { for (int(i) = (0); (i) < ((int)s.size()); ++(i)) { if (s[i] >= 'a' && s[i] <= 'z') { s[i] = s[i] - 'a' + 'A'; } } } inline void tolowerstring(string &s) { for (int(i) = (0); (i) < ((int)s.size()); ++(i)) { if (s[i] >= 'A' && s[i] <= 'Z') { s[i] = s[i] - 'A' + 'a'; } } } inline int toint(string a) { char x[100]; int res; strcpy(x, a.c_str()); sscanf(x, "%d", &res); return res; } inline void gopen(string s) { freopen((s + ".in").c_str(), "r", stdin); freopen((s + ".out").c_str(), "w", stdout); } inline void gcase(int id) { printf("Case #%d:", id); } template <typename T1, typename T2, typename T> inline typename T::iterator findorinsert(T &m, const T1 &t1, const T2 &t2) { typename T::iterator iter = m.find(t1); if (iter == m.end()) { m.insert(make_pair(t1, t2)); return m.find(t1); } else { return iter; } } template <typename T> inline T gcd(T u, T v) { while (v != 0) { T r = u % v; u = v; v = r; } return u; } template <typename T, int n> struct Vector { T data[n]; void read() { for (int(i) = (0); (i) < (n); ++(i)) { cin >> data[i]; } } inline T operator*(const Vector<T, n> &v) const { T res = 0; for (int(i) = (0); (i) < (n); ++(i)) { res += data[i] * v[i]; } return res; } inline bool operator<(const Vector<T, n> &v) const { for (int(i) = (0); (i) < (n); ++(i)) { if (data[i] != v[i]) { return data[i] < v[i]; } } return false; } inline bool operator==(const Vector<T, n> &v) const { for (int(i) = (0); (i) < (n); ++(i)) { if (data[i] != v[i]) { return false; } } return true; } inline T &operator[](int id) { return data[id]; } inline T operator[](int id) const { return data[id]; } inline int size() const { return n; } }; template <typename T> inline Vector<T, 2> make_vector(const T &t1, const T &t2) { Vector<T, 2> res = {t1, t2}; return res; } template <typename T, int n> struct Matrix { Vector<T, n> data[n]; inline Vector<T, n> operator*(const Vector<T, n> &v) const { Vector<T, n> res; for (int(i) = (0); (i) < (n); ++(i)) { res[i] = data[i] * v; } return res; } inline Matrix<T, n> operator*(const Matrix<T, n> &m) const { Matrix<T, n> res; for (int(i) = (0); (i) < (n); ++(i)) { Vector<T, n> temp; for (int(j) = (0); (j) < (n); ++(j)) { temp[j] = m[j][i]; } for (int(j) = (0); (j) < (n); ++(j)) { res[j][i] = data[j] * temp; } } return res; } static inline Matrix<T, n> identity() { Matrix<T, n> res; for (int(i) = (0); (i) < (n); ++(i)) { memset(res[i].data, 0, sizeof(T) * n); } for (int(i) = (0); (i) < (n); ++(i)) { res[i][i] = 1; } return res; } Vector<T, n> &operator[](int id) { return data[id]; } Vector<T, n> operator[](int id) const { return data[id]; } int size() const { return n; } }; template <typename T, int n> class BIT { public: BIT(int size = n) { memset(bit, 0, sizeof(bit)); this->size = size; } BIT(T *data, int size = n) { this->size = size; for (int i = 1; i <= size; i++) { bit[i] = data[i - 1]; for (int j = i - 1; j > i - lowbit(i); j--) { bit[i] += bit[j]; } } } void edit(int i, T delta) { for (int j = i + 1; j <= size; j += lowbit(j)) { bit[j] += delta; } } T sum(int k) { T ans = 0; for (int i = k + 1; i > 0; i -= lowbit(i)) { ans += bit[i]; } return ans; } private: T bit[n + 1]; int size; inline int lowbit(int x) const { return x & (-x); } }; class Prime { public: Prime(int num) { bits.resize(num + 1, true); sieve(); collect(); } bool is_prime(int num) const { return bits[num]; } int find1factor(int num) const { for (int(i) = (0); (i) < ((int)results.size()); ++(i)) { if (num % results[i] == 0) { return results[i]; } } return num; } private: vector<bool> bits; vector<int> results; void sieve() { bits[0] = false; bits[1] = false; for (int i = 2; i < (int)bits.size(); ++i) { if (bits[i] == true) { for (int j = 2;; ++j) { int v2 = j * i; if (v2 >= (int)bits.size()) { break; } bits[v2] = false; } } } } void collect() { for (int i = 0; i < (int)bits.size(); ++i) { if (bits[i]) { results.push_back(i); } } } }; template <int n, int m> struct Graph { int head[n], edge_id; struct { int to, next; } edges[m]; void init(int num = n) { edge_id = 0; memset(head, -1, sizeof(int) * num); } int add(int from, int to) { edges[edge_id].next = head[from]; edges[edge_id].to = to; head[from] = edge_id; edge_id++; return head[from]; } inline int next(int edge) const { return edges[edge].next; } inline int to(int edge) const { return edges[edge].to; } }; template <class T> inline void hash_combine(std::size_t &seed, const T &v) { std::hash<T> hasher; seed ^= hasher(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2); } template <typename T, int n> struct VectorHash { inline std::size_t operator()(const Vector<T, n> &v) const { std::size_t seed = 0; for (int(i) = (0); (i) < (n); ++(i)) { hash_combine(seed, v[i]); } return seed; } }; const int max_n = 200000; int a[max_n]; double b[max_n]; int n; double maxSum(double A[]) { double ans = 0, tmp = 0; for (int i = 0; i < n; i++) { tmp += A[i]; if (tmp < 0) tmp = 0; ans = max(ans, tmp); } return ans; } double calc(double x) { for (int i = 0; i < n; i++) b[i] = a[i] - x; double ans1 = maxSum(b); for (int i = 0; i < n; i++) b[i] = -b[i]; double ans2 = maxSum(b); return max(ans1, ans2); } int main() { double vmax = -INF, vmin = INF; scanf(n); for (int(i) = (0); (i) < (n); ++(i)) { scanf(a[i]); vmax = max(vmax, (double)a[i]); vmin = min(vmin, (double)a[i]); } double v1, v2, c1, c2; while (true) { v1 = (2 * vmin + vmax) / 3; v2 = (vmin + 2 * vmax) / 3; c1 = calc(v1); c2 = calc(v2); if (c1 < c2) { vmax = v2; } else { vmin = v1; } if (abs(vmax - vmin) < 1e-11) { break; } } printf(c1); return 0; }
#include <bits/stdc++.h> using namespace std; double a[220005]; double b[220005]; int n; double check(double x) { double q1 = 0.0, q2 = 0.0, q3 = 0.0; for (int i = 1; i <= n; i++) b[i] = a[i] - x; for (int i = 1; i <= n; i++) q1 = max(b[i], b[i] + q1), q3 = max(q1, q3); for (int i = 1; i <= n; i++) b[i] = (-1.0) * b[i]; for (int i = 1; i <= n; i++) q2 = max(b[i], b[i] + q2), q3 = max(q3, q2); return q3; } int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) scanf("%lf", &a[i]); double l, r; l = -30000.0, r = 30000.0; while (r - l > 1e-11) { double mid1 = (l + r) / 2.0; double mid2 = (mid1 + r) / 2.0; if (check(mid1) >= check(mid2)) l = mid1; else r = mid2; } printf("%.13lf\n", check((l + r) / (2.0))); return 0; }
#include <bits/stdc++.h> using namespace std; const int X = 100000 + 5; long double foo1(vector<long double> &v) { long double s = 0, mx = 0; for (int i = 0; i < (int)v.size(); i++) { s += v[i]; mx = max(mx, s); if (s < 1e-10) s = 0; } return mx; } long double foo(long double x, vector<long double> v) { for (int i = 0; i < (int)v.size(); i++) v[i] = v[i] - x; long double s = foo1(v); for (int i = 0; i < (int)v.size(); i++) v[i] *= -1; s = max(s, foo1(v)); for (int i = 0; i < (int)v.size(); i++) v[i] *= -1; for (int i = 0; i < (int)v.size(); i++) v[i] = v[i] + x; return s; } long double calc(vector<long double> &v) { long double lo = -1e5, hi = 1e5; for (int it = 1; it < 100; it++) { long double ml = lo + (hi - lo) / 3.0, mr = hi - (hi - lo) / 3.0; if (foo(ml, v) <= foo(mr, v)) hi = mr; else lo = ml; } return foo(lo, v); } void MAIN() { int n; long double x; cin >> n; vector<long double> v; for (int i = 0; i < n; i++) { cin >> x; v.push_back(x); } cout << calc(v); } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout << setprecision(12); MAIN(); return 0; }
#include <bits/stdc++.h> using namespace std; int dx[] = {0, 0, 1, -1}; int dy[] = {1, -1, 0, 0}; int dx8[] = {0, 0, 1, 1, 1, -1, -1, -1}; int dy8[] = {1, -1, -1, 0, 1, -1, 0, 1}; int kx8[] = {1, 1, 2, 2, -1, -1, -2, -2}; int ky8[] = {2, -2, 1, -1, 2, -2, 1, -1}; long long bigmod(long long a, long long b, long long c) { if (b == 0) return 1 % c; long long x = bigmod(a, b / 2, c); x = x * x % c; if (b % 2 == 1) x = x * a % c; return x; } long long mod_inverse(long long a, long long mod) { return bigmod(a, mod - 2, mod); } double a[2 * 100005]; double b[2 * 100005]; double fun(int n) { double mx = -1e15; double sum = 0; int ptr = 0; for (int i = 0; i < (n); i++) { sum += b[i]; while (sum < 0 && ptr <= i) { sum -= b[ptr++]; } mx = max(sum, mx); } return mx; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); int n, k; cin >> n; for (int i = 0; i < (n); i++) cin >> a[i]; double lw = -100000, hi = 100000, ans = 0, mid, midd; double res = 1e15; for (int i = 0; i < (200); i++) { mid = (lw + lw + hi) / 3.0; midd = (lw + hi + hi) / 3.0; for (int i = 0; i < (n); i++) { b[i] = a[i] - mid; } double d1 = fun(n); for (int i = 0; i < (n); i++) { b[i] *= -1.0; } double d2 = fun(n); double mx = max(d1, d2); for (int i = 0; i < (n); i++) { b[i] = a[i] - midd; } d1 = fun(n); for (int i = 0; i < (n); i++) { b[i] *= -1.0; } d2 = fun(n); double mxx = max(d1, d2); if (mx < mxx) { hi = midd; ans = mid; res = mx; } else { lw = mid; ans = midd; res = mxx; } } cout << fixed << setprecision(10) << res << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int IN() { int c, f, x; while (!isdigit(c = getchar()) && c != '-') ; c == '-' ? (f = 1, x = 0) : (f = 0, x = c - '0'); while (isdigit(c = getchar())) x = (x << 1) + (x << 3) + c - '0'; return !f ? x : -x; } const int N = 200000 + 19; int A[N], n; double B[N], l, r, res, tmp; double calc(double x) { res = 0; for (int i = 1; i < n + 1; i++) B[i] = A[i] - x; tmp = 0; for (int i = 1; i < n + 1; i++) { tmp = max(tmp, 0.0) + B[i]; res = max(res, abs(tmp)); } tmp = 0; for (int i = 1; i < n + 1; i++) { tmp = min(tmp, 0.0) + B[i]; res = max(res, abs(tmp)); } return res; } int main() { n = IN(); for (int i = 1; i < n + 1; i++) A[i] = IN(); l = -10000, r = 10000; for (int i = 0; i < 100; i++) { double t = (r - l) / 3.0; double t1 = l + t, t2 = r - t; if (calc(t1) > calc(t2)) l = t1; else r = t2; } printf("%.10lf\n", calc(l)); }
#include <bits/stdc++.h> using namespace std; inline int Get() { int x = 0, f = 1; char ch = getchar(); while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); } while ('0' <= ch && ch <= '9') { x = (x << 1) + (x << 3) + ch - '0'; ch = getchar(); } return x * f; } int n; double w[200005]; double mx[200005], mn[200005]; double ans = 1e16; double cal(double x) { mx[0] = mn[0] = 0; double ans = 0; for (int i = 1; i <= n; i++) { mx[i] = max(0.0, mx[i - 1]) + w[i] - x; mn[i] = min(0.0, mn[i - 1]) + w[i] - x; ans = max(ans, max(fabs(mx[i]), fabs(mn[i]))); } return ans; } int main() { n = Get(); for (int i = 1; i <= n; i++) { scanf("%lf", &w[i]); } long double l = -10001, r = 10001, mid, rmid; while (l + 1e-13 < r) { mid = (l + r) / 2; rmid = (mid + r) / 2; double lx = cal(mid), rx = cal(rmid); if (lx + 1e-13 > rx) { ans = min(ans, rx); l = mid + 1e-13; } else { ans = min(ans, lx); r = rmid - 1e-13; } } printf("%.6lf", ans); return 0; }
#include <bits/stdc++.h> using namespace std; int a[200005]; int n; double cal(double x) { double t1 = 0, t2 = 0, maxsum = -1320, minsum = 1320; for (int i = 1; i <= n; i++) { if (t1 >= 0) { t1 += a[i] - x; } else { t1 = a[i] - x; } if (t2 <= 0) { t2 += a[i] - x; } else { t2 = a[i] - x; } maxsum = max(maxsum, t1); minsum = min(minsum, t2); } return max(fabs(maxsum), fabs(minsum)); } double triple(double L, double R) { int t = 100; while (t--) { double mid = L + (R - L) / 3.0; double mmid = R - (R - L) / 3.0; if (cal(mid) > cal(mmid)) L = mid; else R = mmid; } return cal(L) > cal(R) ? L : R; } int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) { scanf("%d", &a[i]); } printf("%.7lf\n", cal(triple(-10005, 10005))); }
#include <bits/stdc++.h> using namespace std; void fio() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); } double solve(double mid, vector<double> vec, double n) { for (int i = 0; i < n; i++) { vec[i] = vec[i] - mid; } double cur_sum = vec[0], max_sum = vec[0]; double cur_min = vec[0], min_sum = vec[0]; for (int i = 1; i < n; i++) { cur_sum = max(cur_sum + vec[i], vec[i]); max_sum = max(max_sum, cur_sum); cur_min = min(cur_min + vec[i], vec[i]); min_sum = min(cur_min, min_sum); } return max(max_sum, abs(min_sum)); } int main() { fio(); cout << fixed << setprecision(14); double n; cin >> n; vector<double> vec(n); for (int i = 0; i < n; i++) { cin >> vec[i]; } double l = -(1e4 + 7), r = 1e4 + 7; for (int i = 0; i < 300; i++) { double m1 = l + (r - l) / 3; double m2 = r - (r - l) / 3; double f1 = solve(m1, vec, n); double f2 = solve(m2, vec, n); if (f1 < f2) r = m2; else l = m1; } double mid = r; for (int i = 0; i < n; i++) { vec[i] = vec[i] - mid; } double cur_sum = vec[0], max_sum = vec[0]; double cur_min = vec[0], min_sum = vec[0]; for (int i = 1; i < n; i++) { cur_sum = max(cur_sum + vec[i], vec[i]); max_sum = max(max_sum, cur_sum); cur_min = min(cur_min + vec[i], vec[i]); min_sum = min(cur_min, min_sum); } cout << max(max_sum, abs(min_sum)) << endl; return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("Ofast") using namespace std; ; long long max(long long a, long long b) { if (a > b) return a; else return b; } long long min(long long a, long long b) { if (a > b) return b; else return a; } long long gcd(long long a, long long b) { return (b == 0) ? a : gcd(b, a % b); } inline long long lcm(long long a, long long b) { return a / gcd(a, b) * b; } inline long long normalize(long long x, long long mod) { x %= mod; if (x < 0) x += mod; return x; } long long dx[4] = {0, 0, 1, -1}; long long dy[4] = {1, -1, 0, 0}; string abc = "abcdefghijklmnopqrstuvwxyz"; const double PI = acosl(-1); const long long mod = 998244353; const long long inf = 1e18 + 5; inline long long add(long long a, long long b, long long p = mod) { long long c = a + b; if (c >= p) c -= p; return c; } inline long long sub(long long a, long long b, long long p = mod) { long long c = a - b; if (c < 0) c += p; return c; } inline long long mul(long long a, long long b, long long p = mod) { return (a * 1ll * b) % p; } long long floor1(long long n, long long k) { if (n % k == 0 || n >= 0) return n / k; return (n / k) - 1; } long long ceil1(long long n, long long k) { return floor1(n + k - 1, k); } long long powm(long long a, long long b) { long long res = 1; while (b) { if (b & 1) res = (res * a) % mod; a = (a * a) % mod; b >>= 1; } return res; } const long long N = 2e5 + 5; long long n, m, k; long long a[N], b[N]; long double cache[N]; long double dp() { long double mx = 0.0; long double cur = 0.0; for (long long i = (1); i < (n + 1); ++i) { if (cur + cache[i] > cache[i]) cur = cur + cache[i]; else cur = cache[i]; if (cur > mx) mx = cur; } return mx; } long double f(long double x) { long double ans = 0.0; for (long long i = (1); i < (n + 1); ++i) cache[i] = a[i] - x; ans = max(ans, dp()); for (long long i = (1); i < (n + 1); ++i) cache[i] = -cache[i]; ans = max(ans, dp()); return ans; } long double ternary_search(long double l, long double r) { long double eps = 1e-12; while (r - l > eps) { long double m1 = l + (r - l) / 3.00; long double m2 = r - (r - l) / 3.00; long double f1 = f(m1); long double f2 = f(m2); if (f1 > f2) l = m1; else r = m2; } return f(l); } void solve() { cin >> n; for (long long i = (1); i < (n + 1); ++i) cin >> a[i]; cout << ternary_search(-20005, 20005) << "\n"; } signed main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); cout << fixed << setprecision(10); long long t = 1; while (t--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; int n; double v[200010]; double func(double x) { double mn = 0, mx = 0, a = 0, b = 0; for (int i = 0; i < n; i++) { a += v[i] - x; b += v[i] - x; mn = min(mn, a); mx = max(mx, b); if (a > 0) a = 0; if (b < 0) b = 0; } return max(mx, -mn); } int main() { scanf("%d", &n); for (int i = 0; i < n; i++) scanf("%lf", &v[i]); double st, ed; st = -10000; ed = 10000; for (int i = 0; i < 100; i++) { double p1 = st + (ed - st) / 3.0; double p2 = ed - (ed - st) / 3.0; if (func(p1) >= func(p2)) st = p1; else ed = p2; } printf("%.7lf\n", func(st)); return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T1, typename T2> std::istream& operator>>(std::istream& in, pair<T1, T2>& a) { in >> a.first >> a.second; return in; } template <typename T1, typename T2> std::ostream& operator<<(std::ostream& out, pair<T1, T2>& a) { out << a.first << " " << a.second; return out; } const long long N = 2e5 + 5; long long a[N]; double b[N]; long long n; double calc(double x) { for (long long i = 0; i < n; i++) b[i + 1] = a[i] - x; double s = 0, ans = 0; b[0] = 0; for (long long i = 1; i < n + 1; i++) { b[i] += b[i - 1]; } double l = 0, u = 0; for (long long i = 1; i < n + 1; i++) { ans = max(ans, abs(b[i] - l)); ans = max(ans, abs(b[i] - u)); l = min(l, b[i]); u = max(u, b[i]); } return ans; } void solve() { cin >> n; for (long long i = 0; i < n; i++) cin >> a[i]; double L = -10002, U = 10002; for (long long i = 0; i < 90; i++) { double d = (U - L) / 3; if (calc(L + d) > calc(L + 2 * d)) { L = L + d; } else { U = U - d; } } cout << calc(L); } signed main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cout << setprecision(9); cout << fixed; long long t = 1; while (t--) solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const int dr[] = {1, 0, -1, 0, 1, 1, -1, -1}; const int dc[] = {0, 1, 0, -1, 1, -1, -1, 1}; const double eps = 1e-9; const int INF = 0x7FFFFFFF; const long long INFLL = 0x7FFFFFFFFFFFFFFFLL; const double pi = acos(-1); template <class T> T take(queue<T> &O) { T tmp = O.front(); O.pop(); return tmp; } template <class T> T take(stack<T> &O) { T tmp = O.top(); O.pop(); return tmp; } template <class T> T take(priority_queue<T> &O) { T tmp = O.top(); O.pop(); return tmp; } template <class T> inline void getint(T &num) { bool neg = 0; num = 0; char c; while ((c = getchar_unlocked()) && (!isdigit(c) && c != '-')) ; if (c == '-') { neg = 1; c = getchar_unlocked(); } do num = num * 10 + c - '0'; while ((c = getchar_unlocked()) && isdigit(c)); if (neg) num = -num; } template <class T> inline bool inRange(T z, T a, T b) { return a <= z && z <= b; } void OPEN(string in = "input.txt", string out = "output.txt") { freopen(in.c_str(), "r", stdin); freopen(out.c_str(), "w", stdout); return; } int arr[200005]; int n; vector<int> vc; inline double cek(double x) { double tmp = 0.0, ansz = 0.0; for (int(i) = (0), _t = (n); i < (_t); ++(i)) { tmp = max(tmp + arr[i] - x, 0.0); ansz = max(ansz, tmp); } tmp = 0.0; for (int(i) = (0), _t = (n); i < (_t); ++(i)) { tmp = max(tmp + -(arr[i] - x), 0.0); ansz = max(ansz, tmp); } return ansz; } int main(int argc, const char *argv[]) { ios::sync_with_stdio(false); cin.tie(0); cin >> n; for (int(i) = (0), _t = (n); i < (_t); ++(i)) cin >> arr[i]; double lo = -10000.0, hi = 10000.0, le, ri; for (int(i) = (0), _t = (120); i < (_t); ++(i)) { le = lo + (hi - lo) / 3.; ri = lo + (hi - lo) * 2. / 3.; double cle = cek(le), cri = cek(ri); if (cle < cri) hi = ri; else if (cle > cri) lo = le; else { lo = le; hi = ri; } } cout << fixed << setprecision(10) << cek(lo) << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 9; int a[N], n; double ans(double x) { double arr[N]; for (int i = 0; i < n; i++) arr[i] = a[i] - x; double neg = 0; double pos = 0; double ans = 0; for (int i = 0; i < n; i++) { if (neg > 0) neg = 0; if (pos < 0) pos = 0; neg += arr[i]; pos += arr[i]; ans = max(ans, max(-neg, pos)); } return ans; } int main() { cin >> n; for (int i = 0; i < n; i++) cin >> a[i]; double l = -1e5 - 9, r = 1e5 + 9; for (int i = 0; i < 100; i++) { double m1 = l + (r - l) / 3, m2 = r - (r - l) / 3; if (ans(m1) > ans(m2)) l = m1; else r = m2; } cout << setprecision(12) << fixed << ans(l) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; double n, a[200005], sum[200005]; const double EPS = 0.000000000005; double f(double x) { double ans = -999999999, t_sum = 0, max_sum = -999999999, min_sum = 999999999, temp; for (int i = 0; i < n; i++) { t_sum += a[i] - x; sum[i] = t_sum; } for (int i = 0; i < n; i++) { ans = max(ans, abs(sum[i])); if (i != 0) { if (sum[i] < 0) { temp = sum[i] - max_sum; ans = max(ans, abs(temp)); } else { temp = sum[i] - min_sum; ans = max(ans, abs(temp)); } } if (sum[i] > max_sum) { max_sum = sum[i]; } if (sum[i] < min_sum) { min_sum = sum[i]; } } return ans; } double solve() { double l = -10000, r = 10000, m1, m2; while (r - l > EPS) { m1 = l + (r - l) / 3; m2 = r - (r - l) / 3; if (f(m1) < f(m2)) { r = m2; } else { l = m1; } } return r; } int main() { cin >> n; for (int i = 0; i < n; i++) { cin >> a[i]; } cout << fixed << setprecision(7) << f(solve()); return 0; }
#include <bits/stdc++.h> using namespace std; bool compare(int a, int b) { return a > b; } class Compare { public: bool operator()(int a, int b) { return a > b; } }; int mod(int a, int b) { return ((a % b) + b) % b; } int n, a[200009]; double f(double x) { double g_mx = -100000000000, l_mx = 0, l_mn = 0; for (int i = 0; i < n; i++) { double q = a[i] - x, p1 = l_mx + q, p2 = l_mn + q; l_mx = max(q, p1), l_mn = min(q, p2); g_mx = max(g_mx, max(fabs(l_mn), fabs(l_mx))); } return g_mx; } int main() { scanf("%d", &n); for (int i = 0; i < n; i++) scanf("%d", &a[i]); double l = -100000.0, r = 100000.0, m1, m2; for (int i = 0; i < 250; i++) { m1 = l + (r - l) / 3.0; m2 = r - (r - l) / 3.0; if (f(m1) > f(m2)) l = m1; else r = m2; } printf("%.12lf\n", f(m1)); return 0; }
#include <bits/stdc++.h> using namespace std; int a[300005]; int n; long double ans = 10000000000; long double test(long double x) { long double sum = 0; long double mn = 0; long double mx = 0; long double ret = 0; for (int i = 0; i < n; i++) { sum += (a[i] - x); ret = max(ret, abs(sum - mn)); ret = max(ret, abs(sum - mx)); mn = min(mn, sum); mx = max(mx, sum); } ans = min(ans, ret); return ret; } int main() { cin >> n; for (int i = 0; i < n; i++) cin >> a[i]; long double s = -10000000, e = 10000000; while (e - s > 1e-12) { long double t1 = s + (e - s) / 3; long double t2 = s + (e - s) * 2 / 3; long double v1 = test(t1); long double v2 = test(t2); if (v1 < v2) { e = t2; } else { s = t1; } } printf("%.9Lf", ans); }
#include <bits/stdc++.h> using namespace std; int n; double a[200005], b[200005], r = -10005, l = 10005, midl, midr, sum, ans; double weakn(double m) { ans = 0; sum = 0; for (int i = 0; i < n; i++) { sum += a[i] - m; if (sum < 0) sum = 0; ans = max(ans, sum); } sum = 0; for (int i = 0; i < n; i++) { sum += m - a[i]; if (sum < 0) sum = 0; ans = max(ans, sum); } return ans; } int main() { scanf("%d", &n); for (int i = 0; i < n; i++) { scanf("%lf", &a[i]); if (a[i] > r) r = a[i]; if (a[i] < l) l = a[i]; } while (r - l > 2e-12) { midl = (l + r) / 2; midr = (midl + r) / 2; if (weakn(midl) < weakn(midr)) r = midr; else l = midl; } printf("%lf", weakn(l)); }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 10; int a[N], n; double solve(double x) { double ma = -1, now = 0; for (int i = 0; i < n; i++) ma = max(ma, now = max(0.0, now + a[i] - x)); now = 0; for (int i = 0; i < n; i++) ma = max(ma, now = max(0.0, now + x - a[i])); return ma; } int main() { scanf("%d", &n); for (int i = 0; i < n; i++) scanf("%d", a + i); double l = -1e4, r = 1e4; int T = 200; while (T--) { double m = (l + r) / 2, ml = (l + m) / 2, mr = (r + m) / 2; if (solve(ml) <= solve(mr)) r = mr; else l = ml; } printf("%.15f\n", solve(l)); return 0; }
#include <bits/stdc++.h> int a[200000]; double diff[200000]; double getAns(int n, double x) { for (int i = 0; i < n; i++) { diff[i] = a[i] - x; } double small = 0, big = 0, min = 0, max = 0; for (int i = 0; i < n; i++) { small += diff[i]; min = std::min(min, small); if (small > 0) small = 0; big += diff[i]; max = std::max(max, big); if (big < 0) big = 0; } return std::max(max, -min); } double trinarySearch(int n, double left, double right) { int t = 100; while (t--) { double mid1 = left + (right - left) / 3; double mid2 = left + 2 * (right - left) / 3; double ans1 = getAns(n, mid1); double ans2 = getAns(n, mid2); if (ans1 == ans2) { left = mid1; right = mid2; } else if (ans1 < ans2) { right = mid2; } else { left = mid1; } } return (left + right) / 2; } int main() { int n; scanf("%d", &n); int max = -10000, min = 10000; for (int i = 0; i < n; i++) { scanf("%d", &a[i]); if (max < a[i]) max = a[i]; if (min > a[i]) min = a[i]; } double x = trinarySearch(n, min, max); printf("%.10f\n", getAns(n, x)); return 0; }
#include <bits/stdc++.h> using namespace std; int n, i; int mn; int a[400010]; double mx, sum, l, r, mid, mmid; double d[400010]; double f(double x) { mx = 0; for (i = 1; i <= n; i++) d[i] = a[i] - x; if (d[1] >= 0) sum = d[1]; else sum = 0; for (i = 2; i <= n; i++) { if (sum - mx > 1e-30) mx = sum; if (d[i] + sum >= 0) { sum += d[i]; continue; } sum = 0; } if (sum - mx > 1e-30) mx = sum; for (i = 1; i <= n; i++) d[i] = x - a[i]; if (d[1] >= 0) sum = d[1]; else sum = 0; for (i = 2; i <= n; i++) { if (sum - mx > 1e-30) mx = sum; if (d[i] + sum >= 0) { sum += d[i]; continue; } sum = 0; } if (sum - mx > 1e-30) mx = sum; return mx; } int main() { cin >> n; for (i = 1; i <= n; i++) { scanf("%d", &a[i]); mn = max(mn, a[i]); mn = max(mn, -a[i]); } l = -mn; r = mn; while (l < r - 4e-12) { mid = (l + r) / 2; mmid = (mid + r) / 2; if (f(mid) <= f(mmid)) r = mmid; else l = mid; } printf("%.7f", f(l)); return 0; }
#include <bits/stdc++.h> using namespace std; const double eps = 1e-11; vector<double> a; double okk(double m) { long long n = a.size(); double ans = 0; double tmp[n], pf[n]; for (long long i = 0; i < n; i++) { tmp[i] = a[i] - m; if (i == 0) pf[i] = tmp[i]; else pf[i] = pf[i - 1] + tmp[i]; } double mn = 0; for (long long i = 0; i < n; i++) { ans = max(ans, pf[i] - mn); mn = min(mn, pf[i]); pf[i] *= -1; } mn = 0; for (long long i = 0; i < n; i++) { ans = max(ans, pf[i] - mn); mn = min(mn, pf[i]); } return ans; } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << setprecision(15) << fixed; long long n; cin >> n; a.resize(n); set<long long> st; for (long long i = 0; i < n; i++) { cin >> a[i]; st.insert(a[i]); } if (st.size() == 1) { cout << 0 << '\n'; return 0; } double l = -1e6, r = 1e6, ans = 1e15; while (r - l > eps) { double m1 = l + (r - l) / 3; double m2 = r - (r - l) / 3; double t1 = okk(m1); double t2 = okk(m2); ans = min(ans, t1); ans = min(ans, t2); if (t1 > t2) l = m1; else r = m2; } cout << ans << '\n'; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 5; int n; double a[N]; double max_poor(double x) { int i; double pre, mpre, ret = 0; pre = mpre = 0; for (i = 0; i < n; i++) { pre += a[i] - x; ret = max(ret, abs(pre - mpre)); mpre = min(mpre, pre); } pre = mpre = 0; for (i = 0; i < n; i++) { pre += a[i] - x; ret = max(ret, abs(pre - mpre)); mpre = max(mpre, pre); } return ret; } int main() { cin.tie(0); ios::sync_with_stdio(0); int i; double l = 0.0, h = 0.0, m1, m2; cin >> n; for (i = 0; i < n; h = max(h, abs(a[i])), i++) cin >> a[i]; l = -h; for (i = 0; i < 300; i++) { m1 = l + (h - l) / 3; m2 = h - (h - l) / 3; if (max_poor(m1) > max_poor(m2)) l = m1; else h = m2; } printf("%.17f\n", max_poor(l)); return 0; }
#include <bits/stdc++.h> using namespace std; const double INF = 1e9; vector<int> a; int n; double Solve(double x) { double _max = 0.0; double _temp = 0.0; double sum = 0.0; for (int i = 0; i < n; i++) { sum = max(sum + a[i] - x, a[i] - x); _max = max(_max, sum); } sum = 0.0; for (int i = 0; i < n; i++) { sum = max(sum + x - a[i], x - a[i]); _temp = max(_temp, sum); } return max(_max, _temp); } int main() { cin >> n; for (int i = 0; i < n; i++) { int x; cin >> x; a.emplace_back(x); } double left = -INF; double right = INF; double mid_L, mid_R; double fx, fy; for (int i = 0; i < 300; i++) { mid_L = left + (right - left) / 3; mid_R = right - (right - left) / 3; fx = Solve(mid_L); fy = Solve(mid_R); if (fx < fy) right = mid_R; else left = mid_L; } cout << setprecision(11) << fixed << fx << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; double poorness(vector<int> v, double x) { double total_max = abs(v[0] - x); double max_sum = v[0] - x; double min_sum = v[0] - x; double sum_total_max = max_sum; double sum_total_min = min_sum; for (int i = 1; i < v.size(); i++) { max_sum = max(v[i] - x, v[i] + max_sum - x); min_sum = min(v[i] - x, v[i] + min_sum - x); sum_total_max = max(sum_total_max, max_sum); sum_total_min = min(sum_total_min, min_sum); total_max = max(abs(sum_total_max), abs(sum_total_min)); } return total_max; } double ternary_search(vector<int> v, double left, double right, int step) { if (step == 150) { return poorness(v, (right + left) / 2); } double new_left = left + (right - left) / 3; double new_right = new_left + (right - left) / 3; if (poorness(v, new_left) < poorness(v, new_right)) { return ternary_search(v, left, new_right, step + 1); } else { return ternary_search(v, new_left, right, step + 1); } } int main() { int n; cin >> n; vector<int> v(n, 0); for (int i = 0; i < n; i++) { cin >> v[i]; } cout << fixed << setprecision(15); cout << ternary_search(v, -10001, 10001, 0) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 201010; int N; double arr[MAXN]; double brr[MAXN]; double calc() { double sum = 0; double ans = 0; double curmin = 0; for (int i = 0; i < N; i++) { sum += brr[i]; ans = max(ans, sum - curmin); curmin = min(curmin, sum); } return ans; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> N; for (int i = 0; i < N; i++) cin >> arr[i]; double lb = -22222, rb = 22222; while (rb - lb > 1E-11) { double mb = (lb + rb) / 2; for (int i = 0; i < N; i++) brr[i] = arr[i] + mb; double maxsum = calc(); for (int i = 0; i < N; i++) brr[i] = -arr[i] - mb; double minsum = calc(); if (maxsum > minsum) rb = mb; else lb = mb; } double ans = (lb + rb) / 2; for (int i = 0; i < N; i++) brr[i] = arr[i] + ans; double out = calc(); cout << fixed << setprecision(12) << out << endl; return 0; }
#include <bits/stdc++.h> using namespace std; double eps = 1e-9; long long int n; long double arr[1000000]; long double solve(long double mid) { double maxi = 0.0, sum = 0.0; for (long long int i = 0; i < n; i++) { sum += (arr[i] - mid); if (sum < 0) { sum = 0; } maxi = max(abs(sum), maxi); } sum = 0.0; for (long long int i = 0; i < n; i++) { sum += (arr[i] - mid); if (sum > 0) { sum = 0; } maxi = max(abs(sum), maxi); } return maxi; } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n; for (long long int i = 0; i < n; i++) { cin >> arr[i]; } long double lo = -10000.0, hi = 10000.0, mid1, mid2; for (long long int i = 1; i <= 100; i++) { mid1 = lo + (hi - lo) / 3; mid2 = hi - (hi - lo) / 3; if (solve(mid1) >= solve(mid2)) { lo = mid1; } else { hi = mid2; } } cout << fixed << setprecision(10) << solve(lo) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const double eps = 1e-9; double a[222222]; int n; double check(double x) { double sum = 0; double ans = 0; for (int i = 0; i < n; i++) { if (sum + a[i] - x < a[i] - x) { sum = a[i] - x; } else sum += a[i] - x; ans = max(ans, sum); } sum = 0; for (int i = 0; i < n; i++) { if (sum + (-(a[i] - x)) < (-(a[i] - x))) { sum = (-(a[i] - x)); } else sum += (-(a[i] - x)); ans = max(ans, sum); } return ans; } int main(void) { scanf("%d", &n); for (int i = 0; i < n; i++) { scanf("%lf", &a[i]); } double l = -1e9; double r = 1e9; double ans; double mid; double mmid; for (int i = 0; i < 700; i++) { mid = l + (r - l) / 3.0; mmid = r - (r - l) / 3.0; if (check(mid) <= check(mmid)) r = mmid; else l = mid; } printf("%f\n", check(l)); return 0; }
#include <bits/stdc++.h> using namespace std; const double eps = 3e-12; int n; double a[200005], b[200005]; double maxsum() { double ans = 0, tmp = 0; for (int i = 1; i <= n; i++) { tmp += b[i]; if (tmp < 0) tmp = 0; ans = max(tmp, ans); } return ans; } double cal(double x) { for (int i = 1; i <= n; i++) b[i] = a[i] - x; double ans1 = maxsum(); for (int i = 1; i <= n; i++) b[i] = -b[i]; double ans2 = maxsum(); return max(ans1, ans2); } int main() { while (scanf("%d", &n) != EOF) { for (int i = 1; i <= n; i++) scanf("%lf", &a[i]); double l = -10005, r = 10005; while (r - l > eps) { double m1 = l + (r - l) / 3.0; double m2 = r - (r - l) / 3.0; if (cal(m1) < cal(m2)) r = m2; else l = m1; } printf("%.15f\n", cal(l)); } return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> v1; pair<int, int> p1; double a[1234567]; string s; int dp[1001]; double max1 = 0.0000000000, max2 = 0.00000000; double b[200001]; int n; double check(double b[]) { int i; double max_upto = 0.0000, overall = 0.0000; for (i = 0; i < n; i++) { max_upto += b[i]; if (max_upto > overall) overall = max_upto; if (max_upto < 0) max_upto = 0; } return overall; } int main() { int t; int i, j, k, m; scanf("%d", &n); for (i = 0; i < n; i++) cin >> a[i]; double l = -1000000000.0000; double h = 1000000000, mid; for (j = 0; j < 100; j++) { mid = (l + h) / 2; for (i = 0; i < n; i++) b[i] = a[i] - mid; max1 = check(b); for (i = 0; i < n; i++) b[i] *= (-1); max2 = check(b); if (max1 > max2) l = mid; else h = mid; } printf("%.12lf\n", max(max1, max2)); return 0; }
#include <bits/stdc++.h> using namespace std; double arr[200005]; int n; double solve(double x) { double ans1 = 0, ans2 = 0; double val = 0; for (int i = 0; i < n; i++) { val += (arr[i] - x); if (val > ans1) ans1 = val; if (val < 0) val = 0; } val = 0; for (int i = 0; i < n; i++) { val += (arr[i] - x); if (val < ans2) ans2 = val; if (val > 0) val = 0; } return max(ans1, -ans2); } int main() { cin >> n; for (int i = 0; i < n; i++) { cin >> arr[i]; } double l1 = -100000, l2 = 100000; double mid1, mid2; for (int i = 0; i < 100; i++) { mid1 = (l1 + l2) / 2.0; mid2 = (mid1 + l2) / 2.0; if (solve(mid1) < solve(mid2)) { l2 = mid2; } else { l1 = mid1; } } cout << fixed << setprecision(9) << solve(l2) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int SIZE = 2e5; int a[SIZE], n; double f(double x) { double ma = 0, mi = 0, now = 0; double res = 0; for (int i = 1; i <= n; i++) { now += a[i] - x; res = max(res, fabs(ma - now)); res = max(res, fabs(mi - now)); ma = max(ma, now); mi = min(mi, now); } return res; } int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) scanf("%d", &a[i]); double ll = -10000, rr = 10000; for (int k = 0; k < 100; k++) { double mm1 = ll * 0.54 + rr * 0.46; double mm2 = ll * 0.46 + rr * 0.54; double v1 = f(mm1); double v2 = f(mm2); if (v1 > v2) ll = mm1; else rr = mm2; } printf("%.15f\n", f((ll + rr) * 0.5)); return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T> int len(const T& a) { return a.size(); } using ll = long long; constexpr long double EPS = 1e-7; long double MaxSubarray(const vector<long double>& a) { long double best = -1e8; long double cur = 0.0; for (auto& i : a) { cur = max((long double)0, cur + i); best = max(best, cur); } return best; } long double MinSubarray(const vector<long double>& a) { long double best = 1e8; long double cur = 0.0; for (auto& i : a) { cur = min((long double)0, cur + i); best = min(best, cur); } return best; } long double Check(const vector<long double>& a, long double x) { vector<long double> new_a(a.size()); for (int i = 0; i < len(a); ++i) { new_a[i] = (long double)a[i] - x; } return max(abs(MaxSubarray(new_a)), abs(MinSubarray(new_a))); } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(6); int n; cin >> n; vector<long double> a(n); for (auto& i : a) cin >> i; long double l = -1e4 - 10, r = 1e4 + 10; for (int step = 0; step < 200; ++step) { long double m1 = l + (r - l) / 3.0; long double m2 = r - (r - l) / 3.0; if (Check(a, m1) - Check(a, m2) > EPS) { l = m1; } else { r = m2; } } cout << Check(a, l); return 0; }
#include <bits/stdc++.h> long long mpow(long long a, long long n, long long mod) { long long ret = 1; long long b = a; while (n) { if (n & 1) ret = (ret * b) % mod; b = (b * b) % mod; n >>= 1; } return (long long)ret; } using namespace std; int a[2 * 100000 + 5]; int n; int i, j; double X(double x) { vector<double> v; for (int j = 0; j < n; j++) v.push_back(a[j] - x); double curmax = 0; double sum = 0; for (j = 0; j < n; j++) { sum += v[j]; if (curmax < 0 && sum >= 0) { if (abs(curmax) < abs(sum - curmax)) { double k = curmax; curmax = sum - k; sum = sum - k; } } else if (curmax >= 0 && sum <= 0) { if (abs(curmax) < abs(-curmax + sum)) { double k = curmax; curmax = -k + sum; sum = -k + sum; } } else { if (abs(curmax) < abs(sum)) { curmax = sum; } } } return abs(curmax); } int main() { scanf("%d", &n); for (j = 0; j < n; j++) scanf("%d", &a[j]); double lo = -10001; double hi = 10001; i = 0; while (i != 300) { double g = lo + (hi - lo) / 3.0; double h = hi - (hi - lo) / 3.0; if (X(g) < X(h)) { hi = h; } else lo = g; i++; } cout << fixed << setprecision(10) << X(lo); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 200000 + 24; int n; double a[maxn]; double cal(double x) { double ans1 = 0.0, tmp1 = 0.0, ans2 = 0.0, tmp2 = 0.0; for (int i = 1; i <= n; ++i) { double k = a[i] - x; tmp1 = max(tmp1 + k, 0.0); tmp2 = max(tmp2 - k, 0.0); ans1 = max(ans1, tmp1); ans2 = max(ans2, tmp2); } return max(ans1, ans2); } int main() { scanf("%d", &n); for (int i = 1; i <= n; ++i) scanf("%lf", &a[i]); double eps = 1e-6 / n / 2 * 1.0; double l = -10000.0, r = 10000.0, m1 = 0.0, m2 = 0.0, ans = 0.0; while (r - l > eps) { m1 = l + (r - l) / 3.0; m2 = r - (r - l) / 3.0; if (cal(m1) >= cal(m2)) l = ans = m1; else r = ans = m2; } printf("%.10lf\n", cal(ans)); }
#include <bits/stdc++.h> using namespace std; vector<long long> A; void calc(double x, double& pos, double& neg) { double max_ending_here = (A[0] - x); double max_from_start = (A[0] - x); for (int i = 1; i < A.size(); i++) { if (max_ending_here + (A[i] - x) < (A[i] - x)) { max_ending_here = (A[i] - x); } else { max_ending_here += (A[i] - x); } max_from_start = max(max_from_start, max_ending_here); } pos = max_from_start; max_ending_here = -(A[0] - x); max_from_start = -(A[0] - x); for (int i = 1; i < A.size(); i++) { if (max_ending_here + (-(A[i] - x)) < (-(A[i] - x))) { max_ending_here = (-(A[i] - x)); } else { max_ending_here += (-(A[i] - x)); } max_from_start = max(max_from_start, max_ending_here); } neg = max_from_start; } int main() { int n; cin >> n; for (int i = 0; i < n; i++) { int t; scanf("%d", &t); A.push_back(t); } double lo = -11111, hi = 11111; for (int i = 0; i < 100; i++) { double a = (lo * 2 + hi) / 3; double b = (lo + hi * 2) / 3; double t, s; calc(a, t, s); double aa = max(t, s); calc(b, t, s); double bb = max(t, s); if (aa < bb) { hi = b; } else { lo = a; } } double ans1, ans2; calc((lo + hi) / 2, ans1, ans2); printf("%.8lf\n", max(ans1, ans2)); }
#include <bits/stdc++.h> using namespace std; using ll = long long; const ll llinf = 0x3f3f3f3f3f3f3f3f; const ll inf = 0x3f3f3f3f3f; const double eps = 1e-9; int n; int t[200010]; double now, max_glo, min_glo; double a, b, m1, m2, res; double f(double x) { now = 0; max_glo = -llinf; for (int i = 0; i < n; i++) { if (0 > now) { now = t[i] - x; } else { now += t[i] - x; } if (max_glo < now) { max_glo = now; } } now = 0; min_glo = llinf; for (int i = 0; i < n; i++) { if (0 < now) { now = t[i] - x; } else { now += t[i] - x; } if (min_glo > now) { min_glo = now; } } return max(abs(max_glo), abs(min_glo)); } int main() { cin >> n; for (int i = 0; i < n; i++) cin >> t[i]; int mx = -inf; int mn = inf; for (int i = 0; i < n; i++) { mx = max(mx, t[i]); mn = min(mn, t[i]); } a = mn; b = mx; int cnt = 0; while (cnt++ < 200) { m1 = a + (b - a) / 3; m2 = b - (b - a) / 3; if (f(m1) < f(m2)) { b = m2; } else { a = m1; } } cout << fixed << f(b) << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; double tong(double x, vector<double> a) { double maxt = 0, mint = 0, s = 0; for (int i = 0; i < a.size(); i++) { s += a[i] - x; maxt = max(s, maxt); mint = min(s, mint); } return abs(maxt - mint); } int main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); int n; cin >> n; vector<double> a(n); for (int i = 0; i < n; i++) { cin >> a[i]; } double l = -20000, r = 20000; for (int i = 0; i < 100; i++) { double l1 = (l + l + r) / 3; double r1 = (l + r + r) / 3; if (tong(l1, a) > tong(r1, a)) { l = l1; } else r = r1; } cout << setprecision(6) << fixed << tong(l, a); return 0; }
#include <bits/stdc++.h> double a[2000005]; double f(double x, int n) { int i; double sum[200005] = {0}, maxl = 0, minl = 0; for (i = 1; i <= n; i++) { sum[i] = sum[i - 1] + a[i - 1] - x; if (maxl < sum[i]) maxl = sum[i]; if (minl > sum[i]) minl = sum[i]; } return maxl - minl; } double solve(double l, double r, int n) { double mid, mid2; int t = 200; while (t--) { mid = (l + r) / 2.0; mid2 = (mid + r) / 2.0; if (f(mid, n) < f(mid2, n)) r = mid2; else l = mid; } return l; } int main() { int n, i; double hzb; while (~scanf("%d", &n)) { for (i = 0; i < n; i++) scanf("%lf", &a[i]); hzb = solve(-1e9, 1e9, n); printf("%.15lf\n", f(hzb, n)); } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int n; cin >> n; vector<int> a(n), b(n); for (int i = 0; i < n; i++) cin >> a[i]; double l = *min_element(a.begin(), a.end()); double r = *max_element(a.begin(), a.end()); double mx = 0, mn = 0; while (r - l > 1e-12) { double mid = (l + r) / 2, sum1 = 0, sum2 = 0; mx = mn = 0; for (int i = 0; i < n; i++) { sum1 += a[i] - mid; if (sum1 < 0) sum1 = 0; if (sum1 > mx) mx = sum1; sum2 += a[i] - mid; if (sum2 > 0) sum2 = 0; if (sum2 < mn) mn = sum2; } if (mx + mn > 0) l = mid; else r = mid; } printf("%.12f\n", max(mx, abs(mn))); return 0; }
#include <bits/stdc++.h> using namespace std; const double EPS = 1e-9; double g[200100], f[200100], a[233333]; int n; double equ(double x) { double ans = 0; g[0] = 0; f[0] = 0; double maxn = -1e20, minn = 1e20; for (int i = 1; i <= n; i++) { f[i] = max(f[i - 1] + a[i] - x, a[i] - x); maxn = max(maxn, f[i]); g[i] = min(g[i - 1] + a[i] - x, a[i] - x); minn = min(minn, g[i]); } ans = max(maxn, fabs(minn)); return ans; } double ternarySearch(double l, double r) { for (int i = 1; i <= 233; i++) { double ll = (2 * l + r) / 3; double rr = (l + 2 * r) / 3; double ans1 = equ(ll); double ans2 = equ(rr); if (ans1 > ans2) l = ll; else r = rr; } return l; } int main() { scanf("%d", &n); double maxn = 100000.0; for (int i = 1; i <= n; i++) { scanf("%lf", &a[i]); } double ans = ternarySearch(-maxn, maxn); ans = equ(ans); printf("%.8lf\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; int a[200010], n; double Get_weekness(double x) { double k1 = 0.0, k2 = 0.0, res = 0.0; for (int i = 0; i < n; i++) { k1 += a[i] - x; k2 += a[i] - x; if (k1 < 0) k1 = 0.0; if (k2 > 0) k2 = 0.0; if (k1 > res) res = k1; if (-k2 > res) res = -k2; } return res; } int main() { scanf("%d", &n); for (int i = 0; i < n; i++) scanf("%d", &a[i]); double l = -99999.99, r = 99999.99; for (int i = 0; i < 100; i++) { double k1 = l / 3 * 2 + r / 3; double k2 = l / 3 + r / 3 * 2; if (Get_weekness(k1) > Get_weekness(k2)) l = k1; else r = k2; } printf("%.12f\n", Get_weekness(l)); return 0; }
#include <bits/stdc++.h> using namespace std; inline long long int GCD(long long int x, long long int y) { if (x < y) swap(x, y); if (x == 0) return y; if (y == 0) return x; return GCD(x % y, y); } long long int phi(long long int n) { long long int result = n; for (long long int i = 2; i * i <= n; i++) { if (n % i == 0) { while (n % i == 0) n /= i; result -= result / i; } } if (n > 1) result -= result / n; return result; } long long int power(long long int x, long long int n, long long int mod) { long long int res = 1; x %= mod; while (n) { if (n & 1) { res = ((res * x) % mod + mod) % mod; } x = ((x * x) % mod + mod) % mod; n >>= 1; } return res; } const long double eps = 1e-12; const int MAXN = 200005; long double N, A[MAXN], Al[MAXN]; long double process(long double x) { for (long long int i = 1; i <= N; i++) { Al[i] = A[i] - x; } long double sum = 0; long double mx = -1e18 + 9; for (long long int i = 1; i <= N; i++) { sum += Al[i]; if (sum < 0) sum = 0; mx = max(mx, sum); } for (long long int i = 1; i <= N; i++) { Al[i] = -Al[i]; } sum = 0; for (long long int i = 1; i <= N; i++) { sum += Al[i]; if (sum < 0) sum = 0; mx = max(mx, sum); } return mx; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); ; cin >> N; for (long long int i = 1; i <= N; i++) { cin >> A[i]; } long double l = -10000.0, r = 10000.0; while (r - l > eps) { long double mid1 = l + (long double)(r - l) / (long double)3.0; long double mid2 = r - (long double)(r - l) / (long double)3.0; if (process(mid1) < process(mid2)) { r = mid2; } else { l = mid1; } } long double ans = process(l); cout << setprecision(10) << fixed << ans << endl; }
#include <bits/stdc++.h> using namespace std; using lli = long long int; using ulli = unsigned long long int; using ld = long double; int n; ld a[(int)(2e5 + 5)]; ld f(ld x) { ld ans = 0; ld temp = 0; for (int i = 0; i < n; ++i) { temp += a[i] - x; if (temp < 0) temp = 0; ans = max(ans, temp); } temp = 0; for (int i = 0; i < n; ++i) { temp += a[i] - x; if (temp > 0) temp = 0; ans = max(ans, -temp); } return ans; } int ts(ld l, ld r) { if (r - l <= (long double)(1e-11)) { cout << setprecision(12) << f(r); return 0; } ld m1 = l + (r - l) / 3; ld m2 = r - (r - l) / 3; ld f1 = f(m1), f2 = f(m2); if (f1 < f2) { ts(l, m2); return 0; } if (f2 < f1) { ts(m1, r); return 0; } ts(m1, m2); return 0; } int main() { cin >> n; ld lmax = -(long double)(10000), lmin = (long double)(10000); for (int i = 0; i < n; ++i) { cin >> a[i]; lmax = max(lmax, a[i]); lmin = min(lmin, a[i]); } ts(lmin, lmax); return 0; }
#include <bits/stdc++.h> using namespace std; template <class P, class Q> inline void smin(P &a, Q b) { if (b < a) a = b; } template <class P, class Q> inline void smax(P &a, Q b) { if (a < b) a = b; } const int maxn = 200000 + 100; int n; int a[maxn], s[maxn]; double f(double x) { double mn = 0, mx = 0; for (int i = 0, _n = (int)(n + 1); i < _n; i++) smin(mn, s[i] - i * x), smax(mx, s[i] - i * x); return mx - mn; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cin >> n; for (int i = 0, _n = (int)(n); i < _n; i++) cin >> a[i]; for (int i = 0, _n = (int)(n); i < _n; i++) s[i + 1] = s[i] + a[i]; double lo = -1e5, hi = 1e5; for (int z = 0, _n = (int)(100); z < _n; z++) { double m1 = (2 * lo + hi) / 3; double m2 = (lo + 2 * hi) / 3; if (f(m1) < f(m2)) hi = m2; else lo = m1; } cout.setf(ios::fixed); cout.precision(9); cout << f(lo) << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; double a[200007]; int n; double cal(double x) { double s, maxx, minn; maxx = a[0] - x; s = 0; for (int i = 0; i < n; i++) { if (s < 0) s = a[i] - x; else s = s + a[i] - x; if (s > maxx) maxx = s; } minn = a[0] - x; s = 0; for (int i = 0; i < n; i++) { if (s > 0) s = a[i] - x; else s = s + a[i] - x; if (s < minn) minn = s; } return max(fabs(maxx), fabs(minn)); } int main() { while (scanf("%d", &n) == 1) { double L = 100000, R = -100000, mid, mmid, t1, t2, ans; for (int i = 0; i < n; i++) { scanf("%lf", a + i); L = min(a[i], L); R = max(a[i], R); } for (int i = 0; i < 200; i++) { mid = L + (R - L) / 3; mmid = R - (R - L) / 3; t1 = cal(mid); t2 = cal(mmid); if (t1 < t2) R = mmid, ans = t1; else L = mid, ans = t2; } printf("%.16f\n", ans); } return 0; }
#include <bits/stdc++.h> using namespace std; long long length; vector<double> nums; double kadane(double x) { double currentMax = nums[0] - x; double currentMin = nums[0] - x; double globalMax = nums[0] - x; double globalMin = nums[0] - x; for (unsigned i = 1; i < nums.size(); i++) { currentMax = max(nums[i] - x, nums[i] - x + currentMax); currentMin = min(nums[i] - x, nums[i] - x + currentMin); if (currentMax > globalMax) globalMax = currentMax; if (currentMin < globalMin) globalMin = currentMin; } if (abs(globalMin) < globalMax) return globalMax; else return abs(globalMin); } int main() { ios::sync_with_stdio(0); cin.tie(0); double num; cin >> length; for (int i = 0; i < length; i++) { cin >> num; nums.push_back(num); } double l = -10000, r = 10000; double m1, m2; double resM1, resM2; for (int i = 0; i < 200; i++) { m1 = l + (r - l) / 3; m2 = r - (r - l) / 3; resM1 = kadane(m1); resM2 = kadane(m2); if (resM1 < resM2) r = m2; else l = m1; } cout << fixed << setprecision(7) << resM1 << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 5; double a[N], b[N], pr[N]; int n; double f(double d) { for (int i = 1; i <= n; i++) { b[i] = a[i] - d; pr[i] = b[i] + pr[i - 1]; } double ans = abs(b[n]); int mkmin = n, mkmax = n; for (int i = n - 1; i >= 1; i--) { if (pr[i] > pr[mkmax]) mkmax = i; if (pr[i] < pr[mkmin]) mkmin = i; ans = max(ans, abs(pr[mkmin] - pr[i - 1])); ans = max(ans, abs(pr[mkmax] - pr[i - 1])); } return ans; } int main() { ios_base::sync_with_stdio(0); cin >> n; for (int i = 1; i <= n; i++) cin >> a[i]; double l = -1e5, r = 1e5, mid1, mid2; for (int i = 1; i <= 300; i++) { mid1 = (2 * l + r) / 3; mid2 = (l + 2 * r) / 3; if (f(mid1) > f(mid2)) l = mid1; else r = mid2; } l = (r + l) / 2; cout << fixed << setprecision(6) << f(l); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 100 * 1000 * 2 + 10; int arr[N], n; double solver(double d, bool reverse) { double ret = 0; double curr = 0; for (int i = 0; i < n; i++) { curr += (arr[i] - d) * pow(-1, reverse); if (curr < 0) curr = 0; ret = max(ret, curr); } return ret; } int main() { scanf("%d", &n); for (int i = 0; i < n; i++) { scanf("%d", &arr[i]); } double ini = -200 * 100 - 2; double fim = 200 * 100 + 2; int interacoes = 200; while (interacoes--) { double terco = (fim - ini) / 3.0; double ter1 = ini + terco; double ter2 = fim - terco; double resp1 = max(solver(ter1, false), solver(ter1, true)); double resp2 = max(solver(ter2, false), solver(ter2, true)); if (resp1 < resp2) { fim = ter2; } else { ini = ter1; } } printf("%.10f", max(solver((ini + fim) / 2.0, false), solver((ini + fim) / 2.0, true))); return 0; }
#include <bits/stdc++.h> using namespace std; const long long inf = (1ll << 50); const int mod = inf + 7; const double pi = acos(-1.0); const double eps = 1e-10; double mi[220000], ma[220000], u[220000]; double second[220000]; int n, a[220000]; double first(double x) { for (int i = 1; i <= n; i++) second[i] = second[i - 1] + a[i] - x; mi[n] = second[n]; ma[n] = second[n]; for (int i = n - 1; i >= 1; i--) { ma[i] = max(ma[i + 1], second[i]); mi[i] = min(mi[i + 1], second[i]); } double res = 0, su = 0; for (int i = 1; i <= n; i++) { res = max(ma[i] + su, res); res = max(-(mi[i] + su), res); su += -a[i] + x; } return res; } int main() { scanf("%d", &n); long long e = 0; for (int i = 1; i <= n; i++) { scanf("%d", &a[i]); e += a[i]; } double l = -(1e14); double r = (1e14); for (int i = 0; i <= 300; i++) { double m1 = l + (r - l) / 3.0; double m2 = r - (r - l) / 3.0; if (first(m1) < first(m2)) r = m2; else l = m1; } printf("%.10lf", first(l)); return 0; }
#include <bits/stdc++.h> using namespace std; int A[200005]; int n, k, x; struct node { double l, r; }; inline node check(double v) { double a = 0, b = 0; double mx_a = 0, mx_b = 0; for (int i = 1; i <= n; i++) { a += 1.0 * (A[i] - v); if (a < 0) a = 0; mx_a = max(mx_a, a); } for (int i = 1; i <= n; i++) { b += 1.0 * (v - A[i]); if (b < 0) b = 0; mx_b = max(mx_b, b); } return (node){mx_a, mx_b}; } int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) scanf("%d", &A[i]); double l = -10000, r = 10000; double ans = 0; int num = 100; while (num--) { double mid = 1.0 * (l + r) / 2; node res = check(mid); if (res.r >= res.l) { ans = res.r; r = mid; } else l = mid; } printf("%lf\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; int n; double a[200005], b[200005]; double l = -10001, r = 10001; const double eps = 2e-12; double solve(double x) { for (int i = 1; i <= n; ++i) b[i] = a[i] - x; double res = 0, tmp = 0; for (int i = 1; i <= n; ++i) { if (tmp < 0) tmp = 0; tmp += b[i]; res = max(res, tmp); } tmp = 0; for (int i = 1; i <= n; ++i) { if (tmp < 0) tmp = 0; tmp -= b[i]; res = max(res, tmp); } return res; } int main() { scanf("%d", &n); for (int i = 1; i <= n; ++i) { scanf("%lf", &a[i]); } while (r > eps + l) { double ll = (2 * l + r) / 3, rr = (l + 2 * r) / 3; double lll = solve(ll); double rrr = solve(rr); if (lll < rrr) r = rr; else l = ll; } cout << fixed << setprecision(12) << solve((l + r) / 2) << endl; }
#include <bits/stdc++.h> using namespace std; int n; int a[200002]; pair<double, int> weakness(double x) { double mini = 0, maxi = 0, p = 0, g = 0; for (int i = 1; i < n + 1; i++) { if (mini > a[i] - x * i) { p = i; mini = a[i] - x * i; } if (maxi < a[i] - x * i) { g = i; maxi = a[i] - x * i; } } return make_pair(maxi - mini, g - p); } int main() { scanf("%d", &n); for (int i = 1; i < n + 1; i++) scanf("%d", &a[i]); for (int i = 2; i < n + 2; i++) a[i] += a[i - 1]; double l = -1000000000, r = 1000000000; pair<double, int> wt; for (int i = 0; i < 80; i++) { wt = weakness((l + r) / 2); if (wt.second == 0) { printf("0\n"); return 0; } if (wt.second > 0) l = (l + r) / 2; else r = (l + r) / 2; } printf("%.7lf\n", wt.first); }
#include <bits/stdc++.h> using namespace std; #pragma comment(linker, "/STACK:102400000,102400000") void RI(int& x) { x = 0; char c = getchar(); while (c == ' ' || c == '\n') c = getchar(); bool flag = 1; if (c == '-') { flag = 0; c = getchar(); } while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); } if (!flag) x = -x; } void RII(int& x, int& y) { RI(x), RI(y); } void RIII(int& x, int& y, int& z) { RI(x), RI(y), RI(z); } const int maxn = 1e5 + 1000; const double eps = 1e-11; int n; int a[maxn << 1]; double b[maxn << 1]; double cal(double x) { double res = 0; double now = 0; for (int i = 0; i < n; i++) b[i] = a[i] * 1.0 - x; for (int i = 0; i < n; i++) { now += b[i]; if (now < 0) now = 0; res = max(res, now); b[i] = -b[i]; } now = 0; for (int i = 0; i < n; i++) { now += b[i]; if (now < 0) now = 0; res = max(res, now); } return res; } int main() { RI(n); for (int i = 0; i < n; i++) RI(a[i]); double tmp = 0; double l = -10000, r = 10000, mid1, mid2; double ans1, ans2; int t = 100; while (t--) { mid1 = l + (r - l) / 3; mid2 = r - (r - l) / 3; ans1 = cal(mid1); ans2 = cal(mid2); if (ans1 > ans2) l = mid1; else r = mid2; } printf("%.6f\n", cal(l)); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 200000 + 10; int n; int a[N]; double C(double m) { double mn = 0, mx = 0, ret = 0, sum = 0; for (int i = 0; i < n; i++) { sum += a[i] - m; ret = max(ret, max(abs(sum - mx), sum - mn)); mn = min(mn, sum); mx = max(mx, sum); } return ret; } int main() { scanf("%d", &n); for (int i = 0; i < n; i++) scanf("%d", a + i); double lb = -10005.0, ub = 10005.0; int t = 100; while (t--) { double m1 = (lb + lb + ub) / 3.0, m2 = (lb + ub + ub) / 3.0; if (C(m1) > C(m2)) lb = m1; else ub = m2; } printf("%.10f\n", C(lb)); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 100; const int inf = 1e9; int n, a[N]; double ma(double p) { double sum = a[1] - p, b = a[1] - p; for (int i = 2; i <= n; i++) { if (b > 0) b += a[i] - p; else b = a[i] - p; sum = max(sum, b); } return abs(sum); } double mi(double p) { double sum = a[1] - p, b = a[1] - p; for (int i = 2; i <= n; i++) { if (b < 0) b += a[i] - p; else b = a[i] - p; sum = min(sum, b); } return abs(sum); } double work(double p) { return max(ma(p), mi(p)); } double cal() { double l = -10000, r = -l; double X; int cnt = 300; while (cnt--) { double mid1 = (2 * l + r) / 3.0, mid2 = (2 * r + l) / 3; double x = work(mid1), y = work(mid2); X = min(x, y); if (x <= y) { r = mid2; } else { l = mid1; } } return X; } int main() { while (~scanf("%d", &n)) { for (int i = 1; i <= n; i++) scanf("%d", &a[i]); printf("%.12f\n", cal()); } return 0; }
#include <bits/stdc++.h> using namespace std; const double eps = 1e-8; int read() { int x = 0, f = 1; char c = getchar(); while (c < '0' || c > '9') { if (c == '-') f = -1; c = getchar(); } while ('0' <= c && c <= '9') { x = x * 10 + c - '0'; c = getchar(); } return x * f; } int N; double a[200010], b[200010], f[200010]; double calc(double x) { memset(f, 0, sizeof(f)); for (int i = 1; i <= N; ++i) b[i] = a[i] + x; double ans = 0, res = 0; for (int i = 1; i <= N; ++i) { if (res + b[i] > 0) res += b[i]; else res = 0; ans = max(ans, res); } for (int i = 1; i <= N; ++i) b[i] = -b[i]; res = 0; for (int i = 1; i <= N; ++i) { if (res + b[i] > 0) res += b[i]; else res = 0; ans = max(ans, res); } return ans; } int main() { N = read(); for (int i = 1; i <= N; ++i) a[i] = read(); double l = -20000, r = 20000; for (int cnt = 1; cnt <= 200; ++cnt) { double mid = (l + r) / 2; double q1 = calc(mid - eps), q2 = calc(mid + eps); if (q1 > q2) l = mid; else r = mid; } printf("%.7lf", calc(l)); return 0; }
#include <bits/stdc++.h> using namespace std; int n; int A[200000]; double T[200001]; double weakness(double x) { T[0] = 0; for (int i = 0; i < n; i++) { T[i + 1] = T[i] + A[i] - x; } double mn = T[n], mx = T[n], mxw = 0; for (int i = n - 1; i >= 0; i--) { mxw = max(mxw, max(abs(mx - T[i]), abs(mn - T[i]))); if (T[i] > mx) mx = T[i]; if (T[i] < mn) mn = T[i]; } return mxw; } int main() { ios::sync_with_stdio(0); cin.tie(0); cin >> n; for (int i = 0; i < n; i++) cin >> A[i]; int amn = A[0], amx = A[0]; for (int i = 0; i < n; i++) { if (amn > A[i]) amn = A[i]; if (amx < A[i]) amx = A[i]; } double l = amn, r = amx; for (int i = 0; i < 300; i++) { double step = (r - l) / 3; double m1 = weakness(l + step), m2 = weakness(r - step); if (m1 < m2) r -= step; else l += step; } cout << fixed << setprecision(10) << weakness(l) << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; int n; int arr[200001]; long double cum[200001]; long double EPS = 1e-12; long double f(long double mid) { cum[0] = arr[0] - mid; long double mini = 0; long double maxi = 0; long double ans = 0; for (int i = 0; i < n; i++) { if (i != 0) cum[i] = (arr[i] - mid) + cum[i - 1]; ans = max(ans, abs(cum[i] - maxi)); ans = max(ans, abs(cum[i] - mini)); maxi = max(maxi, cum[i]); mini = min(mini, cum[i]); } return ans; } long double ternarySearch(long double left, long double right) { while (right - left > EPS) { long double g = left + (right - left) / 3, h = left + 2 * (right - left) / 3; if (f(g) < f(h)) right = h; else left = g; } return f((left + right) / 2); } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> n; for (int i = 0; i < n; i++) cin >> arr[i]; cout << fixed << setprecision(10) << ternarySearch(-10000, 10000) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int n; double a[200100], b[200100]; const double eps = 1e-6; double getmax() { double ans = 0, sum = 0; for (int i = 1; i <= n; i++) { sum = sum + b[i]; if (sum < 0) sum = 0; ans = max(ans, sum); } return ans; } double calc(double x) { for (int i = 1; i <= n; i++) b[i] = a[i] - x; double ans = getmax(); for (int i = 1; i <= n; i++) b[i] = -b[i]; ans = max(ans, getmax()); return ans; } int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) scanf("%lf", &a[i]); double l = -10000.0, r = 10000.0, mid; for (int i = 0; i < 100; i++) { double m1 = l + (r - l) / 3; double m2 = r - (r - l) / 3; if (calc(m1) < calc(m2)) r = m2; else l = m1; } printf("%.6f\n", calc(l)); return 0; }
#include <bits/stdc++.h> using namespace std; int n; double getMax(double *arr, double x) { for (int i = 0; i < n; i++) arr[i] -= x; double cur = arr[0], maxm = arr[0]; bool flag = false; for (int i = 0; i < n; i++) { if (arr[i] >= 0) { flag = true; } cur = max(arr[i], maxm); } if (!flag) { for (int i = 0; i < n; i++) arr[i] += x; return maxm; } cur = 0, maxm = arr[0]; for (int i = 0; i < n; i++) { cur += arr[i]; if (cur < 0) cur = 0; maxm = max(cur, maxm); } for (int i = 0; i < n; i++) arr[i] += x; return maxm; } double getMin(double *arr, double x) { for (int i = 0; i < n; i++) arr[i] -= x; double cur = arr[0], minm = arr[0]; bool flag = false; for (int i = 0; i < n; i++) { if (arr[i] <= 0) { flag = true; } cur = min(cur, minm); } if (!flag) { for (int i = 0; i < n; i++) arr[i] += x; return minm; } cur = 0, minm = arr[0]; for (int i = 0; i < n; i++) { cur += arr[i]; if (cur > 0) cur = 0; minm = min(cur, minm); } for (int i = 0; i < n; i++) arr[i] += x; return minm; } double search(double *arr) { double lo = *min_element(arr, arr + n); double hi = *max_element(arr, arr + n); double brr[200200]; for (int i = 0; i < n; i++) brr[i] = arr[i]; int t = 200; while (t--) { double mid = (lo + hi) / 2; double maxmp = abs(getMax(brr, mid)); double maxmn = abs(getMin(brr, mid)); if (maxmp > maxmn) lo = mid; else hi = mid; } return (lo + hi) / 2; } int main() { double arr[200002]; cin >> n; for (int i = 0; i < n; i++) { scanf("%lf", &arr[i]); } double x = search(arr); double ans1 = abs(getMax(arr, x)); double ans2 = abs(getMin(arr, x)); printf("%.12lf\n", max(ans1, ans2)); return 0; }
#include <bits/stdc++.h> using namespace std; int a[200005]; int n; double calc(double x) { double ans1 = 0, sum1 = 0; for (int i = 1; i <= n; i++) { if (sum1 > 0) sum1 += a[i] - x; else sum1 = a[i] - x; ans1 = max(ans1, sum1); } double ans2 = 0, sum2 = 0; for (int i = 1; i <= n; i++) { if (sum2 < 0) sum2 += a[i] - x; else sum2 = a[i] - x; ans2 = min(ans2, sum2); } return max(ans1, abs(ans2)); } int main() { int maxval = 0, minval = 20000; scanf("%d", &n); for (int i = 1; i <= n; i++) { scanf("%d", a + i); maxval = max(maxval, a[i]); minval = min(minval, a[i]); } double l = minval, r = maxval, mid1, mid2; for (int times = 0; times < 100; times++) { mid1 = (2 * l + r) / 3; mid2 = (l + 2 * r) / 3; if (calc(mid1) < calc(mid2)) r = mid2; else l = mid1; } printf("%.7lf\n", calc(mid1)); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 8; int n; double a[N], q, w, ans, x, l = -N, r = N, m1, m2, mn, mx, sum; double c(double x) { mx = 0, mn = 0, ans = 0, sum = 0; for (int i = 0; i < n; i++) { sum += (a[i] - x); ans = max(ans, max(abs(sum - mx), abs(sum - mn))); mn = min(mn, sum); mx = max(mx, sum); } return ans; } int main() { ios::sync_with_stdio(0), cin.tie(0), cout.tie(0); cin >> n; for (int i = 0; i < n; i++) cin >> a[i]; for (int i = 0; i < 500; i++) { m1 = l + (r - l) / 3; m2 = l + (r - l) * 2 / 3; if (c(m1) > c(m2)) l = m1; else r = m2; } cout << fixed << setprecision(15) << c(l); }
#include <bits/stdc++.h> using namespace std; const double eps = 1e-11; int n; int a[200010]; double b[200010]; double l = -20000, r = 20000, ans = 2147483647, w1, w2, v1, v2; double make(double x) { double maxh = -2147483647, tmp = 0, minh = 2147483647; for (int i = 1; i <= n; i++) b[i] = a[i] - x; for (int i = 1; i <= n; i++) { if (tmp < 0) tmp = b[i]; else tmp += b[i]; if (tmp > maxh) maxh = tmp; } tmp = 0; for (int i = 1; i <= n; i++) { if (tmp > 0) tmp = b[i]; else tmp += b[i]; if (tmp < minh) minh = tmp; } return max(maxh, -minh); } int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) scanf("%d", &a[i]); for (int i = 1; i <= 200; i++) { w1 = l + (r - l) / 3; w2 = r - (r - l) / 3; v1 = make(w1); v2 = make(w2); if (v1 < v2) r = w2, ans = min(ans, v1); else l = w1, ans = min(ans, v2); } printf("%.15lf", ans); return 0; }
#include <bits/stdc++.h> using namespace std; double ans = 0; double x = 0; int n; vector<double> v; int32_t main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n; v.resize(n + 1); for (int i = 1; i <= n; i++) cin >> v[i]; double ans = 0.00000000; double L = -100005, R = -L; for (int roda = 0; roda <= 90; roda++) { double mid = (L + R) / 2.000; double mxans = 0.0000000000000, mnans = 0.00000000000; double lxans = 0.000000000000, lyans = 0.00000000000; double sj = 0.00; for (int i = 1; i <= n; i++) { sj += v[i] - mid; double lans = sj, rans = sj; lans = sj - mxans; rans = sj - mnans; if (i == 1) { lxans = sj; lyans = sj; mxans = sj; mnans = sj; } else { lxans = min(lxans, lans); lyans = max(lyans, rans); lxans = min(lxans, sj); lyans = max(lyans, sj); mxans = max(mxans, sj); mnans = min(mnans, sj); } } if (-lxans > lyans) { R = mid; } else L = mid; } double mid = (L + R) / 2.000; double mxans = 0.0000000000000, mnans = 0.00000000000; double lxans = 0.000000000000, lyans = 0.00000000000; double sj = 0.00; for (int i = 1; i <= n; i++) { sj += v[i] - mid; double lans = sj, rans = sj; lans = sj - mxans; rans = sj - mnans; if (i == 1) { lxans = sj; lyans = sj; mxans = sj; mnans = sj; } else { lxans = min(lxans, lans); lyans = max(lyans, rans); lxans = min(lxans, sj); lyans = max(lyans, sj); mxans = max(mxans, sj); mnans = min(mnans, sj); } } ans = max(fabs(lyans), fabs(lxans)); cout << fixed << setprecision(9) << ans << endl; }
#include <bits/stdc++.h> using namespace std; double find_max(int *a, int n, double x) { double min_p = a[0] - x; double max_p = a[0] - x; double maxv = abs(a[0] - x); for (int i = 1; i < n; ++i) { min_p = min(min_p + a[i] - x, a[i] - x); max_p = max(max_p + a[i] - x, a[i] - x); maxv = max(abs(min_p), maxv); maxv = max(abs(max_p), maxv); } return maxv; } int main() { ios_base::sync_with_stdio(false); int a[200000]; int n; cin >> n; for (int i = 0; i < n; ++i) cin >> a[i]; double L = -1e9; double R = 1e9 + 1e-2; while (abs(L - R) > 1e-11) { double x1 = L + (R - L) * 1 / 3; double x2 = L + (R - L) * 2 / 3; double vl = find_max(a, n, x1); double vr = find_max(a, n, x2); if (vl + 1e-9 < vr) { R = x2; } else { L = x1; } } std::cout.precision(8); cout << fixed << find_max(a, n, L) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; using lli = long long int; using ulli = unsigned long long int; using ld = long double; int n; ld a[(int)(2e5 + 5)]; ld f(ld x) { ld ans = 0; ld temp = 0; for (int i = 0; i < n; ++i) { temp += a[i] - x; if (temp < 0) temp = 0; ans = max(ans, temp); } temp = 0; for (int i = 0; i < n; ++i) { temp += a[i] - x; if (temp > 0) temp = 0; ans = max(ans, -temp); } return ans; } int ts(ld l, ld r) { if (r - l <= (long double)(1e-12)) { cout << setprecision(12) << f(r); return 0; } ld m1 = l + (r - l) / 3; ld m2 = r - (r - l) / 3; ld f1 = f(m1), f2 = f(m2); if (f1 < f2) { ts(l, m2); return 0; } if (f2 < f1) { ts(m1, r); return 0; } ts(m1, m2); return 0; } int main() { cin >> n; ld lmax = -(long double)(10000), lmin = (long double)(10000); for (int i = 0; i < n; ++i) { cin >> a[i]; } ts(-(long double)(10000), (long double)(10000)); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1e6 + 10; const int INF = 2000000010; const long long INFLL = 999999999999999999ll; const double eps = 1e-11; int origin[MAXN]; double cop[MAXN]; int n; double f(double x) { for (int i = 1; i <= n; i++) cop[i] = 1.0 * origin[i] - x; double maxx = 0; double cur = 0; for (int i = 1; i <= n; i++) { cur = max(0.0, cur + cop[i]); maxx = max(maxx, cur); } double ret = maxx; maxx = 0; for (int i = 1; i <= n; i++) cop[i] *= -1; cur = 0; for (int i = 1; i <= n; i++) { cur = max(0.0, cur + cop[i]); maxx = max(maxx, cur); } return max(ret, maxx); } double ternary(double left, double right) { if (right - left < eps) return (left + right) / 2.0; double leftThird = (2.0 * left + right) / 3.0; double rightThird = (left + 2.0 * right) / 3.0; if (f(leftThird) > f(rightThird)) return ternary(leftThird, right); else return ternary(left, rightThird); } int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) scanf("%d", &origin[i]); printf("%lf\n", f(ternary(-20000.0, 20000.0))); return 0; }
#include <bits/stdc++.h> using namespace std; int a[200005]; double fmin(double x, int n) { double ans = 0, cur = 0; for (int i = 0; i < n; i++) { cur += (a[i] - x); if (cur > 0) cur = 0; ans = min(ans, cur); } return ((ans) > 0 ? (ans) : (-(ans))); } double fmax(double x, int n) { double ans = 0, cur = 0; for (int i = 0; i < n; i++) { cur += (a[i] - x); if (cur < 0) cur = 0; ans = max(ans, cur); } return ((ans) > 0 ? (ans) : (-(ans))); } int main() { int n; cin >> n; for (int i = 0; i < n; i++) scanf("%d", &a[i]); double lo = -10000, hi = 10000, mid, v1 = -200, v2 = 200; while (((v1 - v2) > 0 ? (v1 - v2) : (-(v1 - v2))) > .4 * 1e-6) { mid = (lo + hi) / 2; v1 = fmin(mid, n); v2 = fmax(mid, n); if (v1 < v2) lo = mid; else hi = mid; } printf("%.9lf\n", v1); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 7; int a[N], n; double f(double x) { double sum = 0, mn = 0, mx = 0, ans = 0; for (int i = 0; i < n; i++) { mn = min(mn, sum); mx = max(mx, sum); sum += a[i] - x; ans = max(ans, abs(sum - mn)); ans = max(ans, abs(sum - mx)); } return ans; } int main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> n; for (int i = 0; i < n; i++) cin >> a[i]; double l = -1e4 - 7, r = 1e4 + 7; int t = 230; while (t--) { double mid1 = (2 * r + l) / 3; double mid2 = (2 * l + r) / 3; if (f(mid1) < f(mid2)) l = mid2; else r = mid1; } cout << setprecision(9) << fixed << f(l) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int n, a[(int)2e5 + 10]; long double WeekNess, mx = -1e18, mn = 1e18, sum; long double Answer(long double Check) { mx = 0, mn = 0, sum = 0, WeekNess = 0; for (int i = 0; i < n; i++) { mx = max(mx, sum); mn = min(mn, sum); sum += a[i] - Check; WeekNess = max(WeekNess, fabs(sum - mx)); WeekNess = max(WeekNess, fabs(sum - mn)); } return WeekNess; } long double BinarySol(long double l, long double r) { long double mid1 = (2 * l + r) / 3; long double mid2 = (2 * r + l) / 3; int c = 0; while (c++ <= 200) { mid1 = (2 * l + r) / 3; mid2 = (2 * r + l) / 3; if (Answer(mid1) >= Answer(mid2)) { l = mid1; } else { r = mid2; } } return l; } int main() { cin >> n; for (int i = 0; i < n && scanf("%d", a + i); i++) ; cout << setprecision(6) << fixed << Answer(BinarySol(-1e10, 1e10)); }
#include <bits/stdc++.h> using namespace std; void DBG() { cerr << "]" << endl; } template <class H, class... T> void DBG(H h, T... t) { cerr << h; if (sizeof...(t)) { cerr << ", "; } DBG(t...); } int n; long double a[200005]; inline long double weakness(long double x) { long double s1 = 0.0, s2 = 0.0; long double mx = 0.0; for (int i = 0; i < n; i++) { long double temp = a[i] - x; s1 += temp; if (s1 < 0) s1 = 0; s2 += temp; if (s2 > 0) s2 = 0; mx = max(mx, max(s1, -s2)); } return mx; } int main() { cin >> n; for (int i = 0; i < n; i++) { cin >> a[i]; } long double l = -10001.0, r = 10001.0; while (r - l > 1e-12) { long double lm = (l * 2 + r) / 3; long double rm = (l + r * 2) / 3; if (weakness(lm) > weakness(rm)) l = lm; else r = rm; } cout << setprecision(9) << weakness(l); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 2e5 + 10; int a[maxn]; double b[maxn]; int n; double maxsum(double a[maxn]) { double mx = 0, now = 0; for (int i = 1; i <= n; ++i) { now += a[i]; if (now > mx) mx = now; if (now < 0) { now = 0; } } return mx; } double f(double x) { for (int i = 1; i <= n; ++i) { b[i] = a[i] - x; } double psum = maxsum(b); for (int i = 1; i <= n; ++i) { b[i] *= -1; } double nsum = maxsum(b); return max(psum, nsum); } double ts(double l, double r) { for (int i = 1; i <= 300; ++i) { double m1 = l + (r - l) / 3; double m2 = r - (r - l) / 3; double f1 = f(m1); double f2 = f(m2); if (f1 > f2) { l = m1; } else { r = m2; } } return f(l); } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cin >> n; for (int i = 1; i <= n; ++i) { cin >> a[i]; } double l = *min_element(a + 1, a + n + 1); double r = *max_element(a + 1, a + n + 1); cout << fixed << setprecision(12) << ts(l, r) << "\n"; return 0; }
#include <bits/stdc++.h> int n; double a[200005]; double f(double x) { int i; double sum[200005] = {0}, max = 0, min = 0; for (i = 1; i <= n; i++) { sum[i] = sum[i - 1] + a[i - 1] - x; if (max < sum[i]) max = sum[i]; if (min > sum[i]) min = sum[i]; } return max - min; } int main() { int i; double l = -1e9, m, mm, r = 1e9; scanf("%d", &n); for (i = 0; i < n; i++) scanf("%lf", &a[i]); for (i = 0; i < 200; i++) { m = l + (r - l) / 3; mm = r - (r - l) / 3; if (f(m) < f(mm)) r = mm; else l = m; } printf("%.15f\n", f(l)); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 200010; const double inf = 1e30; struct point { int x, y; point() : x(0), y(0) {} point(int x_, int y_) : x(x_), y(y_) {} double get_b(double k) { return y - k * x; } } a[maxn], b[maxn]; double get_k(point a, point b) { return 1.0 * (b.y - a.y) / (b.x - a.x); } long long det(point a, point b) { return 1LL * a.x * b.y - 1LL * a.y * b.x; } point operator-(point a, point b) { return point(a.x - b.x, a.y - b.y); } int n, an, bn; int main() { scanf("%d", &n); an = bn = 0, a[1] = b[1] = point(0, 0); for (int i = 1, v, s = 0; i <= n; ++i) scanf("%d", &v), a[i + 1] = b[i + 1] = point(i, s += v); for (int i = 1; i <= n + 1; ++i) { while (an >= 2 && det(a[an] - a[an - 1], a[i] - a[an - 1]) <= 0) --an; while (bn >= 2 && det(b[bn] - b[bn - 1], b[i] - b[bn - 1]) >= 0) --bn; a[++an] = a[i], b[++bn] = b[i]; } double ans = inf, k1, k2; for (int i = 1, j = bn; i < an || j > 1;) { if (i < an) k1 = get_k(a[i], a[i + 1]); else k1 = inf; if (j > 1) k2 = get_k(b[j], b[j - 1]); else k2 = inf; if (k1 < k2) ans = min(ans, b[j].get_b(k1) - a[i++].get_b(k1)); else ans = min(ans, b[j--].get_b(k2) - a[i].get_b(k2)); } printf("%.12f\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; double a[200005], ans; int i, j, k, s, m, n; inline double check(double o) { double ans1 = 0, ans2 = 0, ans = 0; for (int i = 1; i <= n; i++) { ans1 = ans1 + a[i] - o; ans2 = ans2 + a[i] - o; if (ans1 > 0) ans1 = 0; if (ans2 < 0) ans2 = 0; ans = max(ans, max(abs(ans1), abs(ans2))); } return ans; } int main() { scanf("%d", &n); for (i = 1; i <= n; i++) scanf("%lf", &a[i]); ans = n * 10000.0; double l = -10000.0, r = 10000.0; while (l + 1e-12 <= r) { double mid = (r - l) / 3.0 + l, mid1 = r - (r - l) / 3.0; double gt = check(mid), gtw = check(mid1); if (gt < gtw) { ans = min(ans, gt); r = mid1 - 1e-12; } else { ans = min(ans, gtw); l = mid + 1e-12; } } printf("%.9lf", ans); }
#include <bits/stdc++.h> using namespace std; const int N = 200200; double a[N]; int n, m, i, j, k; double l, r, f1, f2, u, v; double solve(double c) { int i; double sum, ans, l, r; l = r = sum = 0; for (i = 1; i <= n; i++) { sum += a[i] - c; l = min(l, sum); r = max(r, sum); } return r - l; } int main() { scanf("%d", &n); l = 1e8; r = -1e8; for (i = 1; i <= n; i++) { scanf("%lf", &a[i]); r = max(r, a[i]); l = min(l, a[i]); } while (1) { u = l + (r - l) / 3; v = l + (r - l) / 3 * 2; f1 = solve(u); f2 = solve(v); if (fabs(f1 - f2) <= 1e-8 && fabs(r - l) <= 1e-11) break; if (f1 <= f2) r = v; else l = u; } printf("%.9lf\n", f1); return 0; }
#include <bits/stdc++.h> using namespace std; long double pref[200500]; int a[200500], n; long double maxx(long double x) { pref[0] = 1.0 * a[0] - x; for (int i = 1; i < n; ++i) { pref[i] = pref[i - 1] + (1.0 * a[i] - x); } double mn = 0, mx = 0, res = 0; for (int i = 0; i < n; ++i) { if (fabs(pref[i] - mn) > res) res = fabs(pref[i] - mn); if (pref[i] < mn) mn = pref[i]; if (fabs(pref[i] - mx) > res) res = fabs(pref[i] - mx); if (pref[i] > mx) mx = pref[i]; } return res; } int main() { cin >> n; for (int i = 0; i < n; ++i) { cin >> a[i]; } long double l = -100000, r = 100000; while (r - l > 0.000000000001) { long double m1 = l + (r - l) / 3.0; long double m2 = r - (r - l) / 3.0; if (maxx(m1) > maxx(m2)) l = m1; else r = m2; } cout << fixed << setprecision(9); cout << maxx(l) << '\n'; return 0; }