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web-flow authored Mar 6, 2024
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132 changes: 132 additions & 0 deletions geometry_shojin/Symmetric_Boundary.cpp.md
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---
data:
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_extendedRequiredBy: []
_extendedVerifiedWith: []
_isVerificationFailed: false
_pathExtension: cpp
_verificationStatusIcon: ':warning:'
attributes:
links: []
bundledCode: "#line 1 \"geometry_shojin/Symmetric_Boundary.cpp\"\n#include<bits/stdc++.h>\n\
#define all(v) (v).begin(),(v).end()\nusing namespace std;\nusing ld = long double;\n\
using vec = complex<ld>;\nconst ld eps = 1e-10;\n \nint sgn(ld a){\n return\
\ (a > eps ? 1 : a < -eps ? -1 : 0);\n}\nld dot(vec a, vec b){\n return (conj(a)\
\ * b).real();\n}\nld cross(vec a, vec b){\n return (conj(a) * b).imag();\n\
}\n \nstruct line {\n vec p, q;\n};\n \nbool is_parallel(line a, line b){\n\
\ vec va = a.q - a.p;\n vec vb = b.q - b.p;\n return sgn(cross(va,vb))\
\ == 0;\n}\n \nvec cross_point(line a, line b){\n assert(!is_parallel(a,b));\n\
\ return a.p + (a.q - a.p) * cross(b.p - a.p, b.q - b.p) / cross(a.q - a.p,\
\ b.q - b.p);\n}\n \nbool is_on_line(vec a, line l){\n return sgn(cross(l.p-a,l.q-a))\
\ == 0;\n}\n \nld area_if_convex(vector<vec> a){\n int n = a.size();\n sort(all(a),[&](vec\
\ l, vec r){\n if (sgn(l.real() - r.real()) == 0){\n return\
\ l.imag() < r.imag();\n }\n return l.real() < r.real();\n });\n\
\ stack<int> uid, did;\n vec ri = a[n-1];\n auto make_half = [&](bool\
\ isupper){\n auto &id = (isupper ? uid : did);\n id.push(0);\n\
\ for (int i = 1; i < n-1; i++){\n vec le = a[id.top()];\n \
\ auto cr = cross(ri - le, a[i] - le);\n if ((cr > 0 && isupper)\
\ || (cr < 0 && !isupper)){\n while ((int)(id.size()) >= 2){\n\
\ int test = id.top(); id.pop();\n vec from\
\ = a[id.top()];\n auto cr2 = cross(a[i] - from, a[test] -\
\ from);\n if ((cr2 > 0 && isupper) || (cr2 < 0 && !isupper)){\n\
\ id.push(test);\n break;\n \
\ }\n }\n id.push(i);\n \
\ }\n }\n };\n make_half(true);\n make_half(false);\n vector<int>\
\ ids(1,n-1);\n while (!did.empty()) ids.emplace_back(did.top()), did.pop();\n\
\ reverse(all(ids));\n while (!uid.empty()) ids.emplace_back(uid.top()),\
\ uid.pop();\n ids.pop_back();\n vector<vec> ans(ids.size());\n for (int\
\ i = 0; auto id : ids){\n ans[i++] = a[id];\n }\n // check\n \
\ int sz = ans.size();\n for (int i = 0; i < n; i++){\n bool ok = is_on_line(a[i],line{ans[sz-1],ans[0]});\n\
\ for (int j = 0; j < sz-1; j++){\n if (ok) break;\n \
\ ok = is_on_line(a[i],line{ans[j],ans[j+1]});\n }\n if (!ok){\n\
\ return 1e30;\n }\n }\n // area\n ld area = 0;\n \
\ for (int i = 1; i < sz-1; i++){\n area += abs(cross(ans[i]-ans[0],ans[i+1]-ans[0]));\n\
\ }\n area /= 2;\n // cout << area << endl;\n return area;\n}\n \n\
vector<vec> compressed(vector<vec> a){\n auto comp = [&](vec l, vec r){\n \
\ if (sgn(l.real() - r.real()) == 0){\n return l.imag() < r.imag();\n\
\ }\n return l.real() < r.real();\n };\n sort(all(a),comp);\n\
\ vector<vec> ans;\n int sz = a.size();\n for (int l = 0, r = 0; l <\
\ sz; l = r){\n while (r < sz && sgn(abs(a[l]-a[r])) == 0) r++;\n \
\ ans.emplace_back(a[l]);\n }\n return ans;\n}\n \nvoid solve(){\n \
\ int n; cin >> n;\n vector<vec> a(n);\n for (auto &v : a){\n ld\
\ x, y; cin >> x >> y;\n v = vec(x,y);\n }\n vector<line> ls;\n \
\ for (int i = 0; i < n; i++) for (int j = 0; j < n; j++){\n vec m0 =\
\ (a[i] + a[j]) * 0.5L;\n vec m1 = (a[i] + a[(j == n-1 ? 0 : j+1)]) * 0.5L;\n\
\ ls.push_back(line{m0,m1});\n }\n ld area_min = 1e30;\n vector<vec>\
\ ctrs;\n for (auto l1 : ls) for (auto l2 : ls){\n if (!is_parallel(l1,l2)){\n\
\ ctrs.emplace_back(cross_point(l1,l2));\n }\n }\n ctrs\
\ = compressed(ctrs);\n for (auto ctr : ctrs){\n vector<vec> ps(n+n);\n\
\ for (int i = 0; i < n; i++){\n ps[i] = a[i];\n \
\ ps[n+i] = ctr * 2.L - a[i];\n }\n area_min = min(area_min, area_if_convex(ps));\n\
\ }\n if (area_min > 1e29){\n cout << -1 << endl;\n }\n else\
\ {\n cout << area_min << endl;\n }\n}\n \nint main(){\n cin.tie(0)->sync_with_stdio(0);\n\
\ cout << fixed << setprecision(15);\n int t = 1; // cin >> t;\n while\
\ (t--){\n solve();\n }\n}\n"
code: "#include<bits/stdc++.h>\n#define all(v) (v).begin(),(v).end()\nusing namespace\
\ std;\nusing ld = long double;\nusing vec = complex<ld>;\nconst ld eps = 1e-10;\n\
\ \nint sgn(ld a){\n return (a > eps ? 1 : a < -eps ? -1 : 0);\n}\nld dot(vec\
\ a, vec b){\n return (conj(a) * b).real();\n}\nld cross(vec a, vec b){\n \
\ return (conj(a) * b).imag();\n}\n \nstruct line {\n vec p, q;\n};\n \n\
bool is_parallel(line a, line b){\n vec va = a.q - a.p;\n vec vb = b.q -\
\ b.p;\n return sgn(cross(va,vb)) == 0;\n}\n \nvec cross_point(line a, line\
\ b){\n assert(!is_parallel(a,b));\n return a.p + (a.q - a.p) * cross(b.p\
\ - a.p, b.q - b.p) / cross(a.q - a.p, b.q - b.p);\n}\n \nbool is_on_line(vec\
\ a, line l){\n return sgn(cross(l.p-a,l.q-a)) == 0;\n}\n \nld area_if_convex(vector<vec>\
\ a){\n int n = a.size();\n sort(all(a),[&](vec l, vec r){\n if (sgn(l.real()\
\ - r.real()) == 0){\n return l.imag() < r.imag();\n }\n \
\ return l.real() < r.real();\n });\n stack<int> uid, did;\n vec\
\ ri = a[n-1];\n auto make_half = [&](bool isupper){\n auto &id = (isupper\
\ ? uid : did);\n id.push(0);\n for (int i = 1; i < n-1; i++){\n\
\ vec le = a[id.top()];\n auto cr = cross(ri - le, a[i]\
\ - le);\n if ((cr > 0 && isupper) || (cr < 0 && !isupper)){\n \
\ while ((int)(id.size()) >= 2){\n int test = id.top();\
\ id.pop();\n vec from = a[id.top()];\n \
\ auto cr2 = cross(a[i] - from, a[test] - from);\n if ((cr2\
\ > 0 && isupper) || (cr2 < 0 && !isupper)){\n id.push(test);\n\
\ break;\n }\n }\n \
\ id.push(i);\n }\n }\n };\n make_half(true);\n\
\ make_half(false);\n vector<int> ids(1,n-1);\n while (!did.empty())\
\ ids.emplace_back(did.top()), did.pop();\n reverse(all(ids));\n while (!uid.empty())\
\ ids.emplace_back(uid.top()), uid.pop();\n ids.pop_back();\n vector<vec>\
\ ans(ids.size());\n for (int i = 0; auto id : ids){\n ans[i++] = a[id];\n\
\ }\n // check\n int sz = ans.size();\n for (int i = 0; i < n; i++){\n\
\ bool ok = is_on_line(a[i],line{ans[sz-1],ans[0]});\n for (int\
\ j = 0; j < sz-1; j++){\n if (ok) break;\n ok = is_on_line(a[i],line{ans[j],ans[j+1]});\n\
\ }\n if (!ok){\n return 1e30;\n }\n }\n \
\ // area\n ld area = 0;\n for (int i = 1; i < sz-1; i++){\n area\
\ += abs(cross(ans[i]-ans[0],ans[i+1]-ans[0]));\n }\n area /= 2;\n //\
\ cout << area << endl;\n return area;\n}\n \nvector<vec> compressed(vector<vec>\
\ a){\n auto comp = [&](vec l, vec r){\n if (sgn(l.real() - r.real())\
\ == 0){\n return l.imag() < r.imag();\n }\n return l.real()\
\ < r.real();\n };\n sort(all(a),comp);\n vector<vec> ans;\n int sz\
\ = a.size();\n for (int l = 0, r = 0; l < sz; l = r){\n while (r <\
\ sz && sgn(abs(a[l]-a[r])) == 0) r++;\n ans.emplace_back(a[l]);\n }\n\
\ return ans;\n}\n \nvoid solve(){\n int n; cin >> n;\n vector<vec> a(n);\n\
\ for (auto &v : a){\n ld x, y; cin >> x >> y;\n v = vec(x,y);\n\
\ }\n vector<line> ls;\n for (int i = 0; i < n; i++) for (int j = 0;\
\ j < n; j++){\n vec m0 = (a[i] + a[j]) * 0.5L;\n vec m1 = (a[i]\
\ + a[(j == n-1 ? 0 : j+1)]) * 0.5L;\n ls.push_back(line{m0,m1});\n \
\ }\n ld area_min = 1e30;\n vector<vec> ctrs;\n for (auto l1 : ls) for\
\ (auto l2 : ls){\n if (!is_parallel(l1,l2)){\n ctrs.emplace_back(cross_point(l1,l2));\n\
\ }\n }\n ctrs = compressed(ctrs);\n for (auto ctr : ctrs){\n\
\ vector<vec> ps(n+n);\n for (int i = 0; i < n; i++){\n \
\ ps[i] = a[i];\n ps[n+i] = ctr * 2.L - a[i];\n }\n \
\ area_min = min(area_min, area_if_convex(ps));\n }\n if (area_min > 1e29){\n\
\ cout << -1 << endl;\n }\n else {\n cout << area_min << endl;\n\
\ }\n}\n \nint main(){\n cin.tie(0)->sync_with_stdio(0);\n cout << fixed\
\ << setprecision(15);\n int t = 1; // cin >> t;\n while (t--){\n \
\ solve();\n }\n}"
dependsOn: []
isVerificationFile: false
path: geometry_shojin/Symmetric_Boundary.cpp
requiredBy: []
timestamp: '2024-03-06 14:43:23+09:00'
verificationStatus: LIBRARY_NO_TESTS
verifiedWith: []
documentation_of: geometry_shojin/Symmetric_Boundary.cpp
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redirect_from:
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title: geometry_shojin/Symmetric_Boundary.cpp
---
5 changes: 5 additions & 0 deletions index.md
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- icon: ':heavy_check_mark:'
path: geometry/partition_by_circle.hpp
title: geometry/partition_by_circle.hpp
- name: geometry_shojin
pages:
- icon: ':warning:'
path: geometry_shojin/Symmetric_Boundary.cpp
title: geometry_shojin/Symmetric_Boundary.cpp
- name: graph
pages:
- icon: ':heavy_check_mark:'
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