From 28712e116062e6b784f357fd62efda832e0d5379 Mon Sep 17 00:00:00 2001 From: Toulik Das Date: Tue, 6 Oct 2020 13:59:43 +0530 Subject: [PATCH] Polygon Chain Problem --- Polygon Chain/POLCHAIN.py | 27 +++++++++++++++++++++++++++ Polygon Chain/Polygon Chain.pdf | Bin 0 -> 206404 bytes 2 files changed, 27 insertions(+) create mode 100644 Polygon Chain/POLCHAIN.py create mode 100644 Polygon Chain/Polygon Chain.pdf diff --git a/Polygon Chain/POLCHAIN.py b/Polygon Chain/POLCHAIN.py new file mode 100644 index 0000000..2865a7b --- /dev/null +++ b/Polygon Chain/POLCHAIN.py @@ -0,0 +1,27 @@ +from scipy.optimize import linprog + +n=int(input()) +polys = [[[int(x) for x in input().split()] for _ in range(int(input()))] for _ in range(n)] +polys.sort(key=lambda p: sum(p1[0]*p2[1] - p1[1]*p2[0] for p1,p2 in zip(p, p[1:] + [p[0]]))) + +ninc = n*4 +a = [] +b = [] +c = [1]*ninc +for i in range(len(polys)-1): + poly = polys[i+1] + for p in polys[i]: + for i1 in range(len(poly)): + p0, p1 = poly[i1], poly[(i1+1)%len(poly)] + dx, dy = p1[0]-p0[0], p1[1]-p0[1] + eq = [0]*ninc + eq[4*i ] = dy; eq[4*i+1] = -dy + eq[4*i+2] = -dx; eq[4*i+3] = dx + eq[4*i+4] = -dy; eq[4*i+5] = dy + eq[4*i+6] = dx; eq[4*i+7] = -dx + a.append(eq) + b.append(dx*(p[1]-p0[1]) - dy*(p[0]-p0[0])) + +res = linprog(c, a, b, method='simplex', options={'maxiter':100000, 'tol':1e-7}) +assert res.status == 0 or res.status == 2 +print(res.fun if res.status == 0 else -1) diff --git a/Polygon Chain/Polygon Chain.pdf b/Polygon Chain/Polygon Chain.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7b9193866221c5d728730456ffbe918413f7ea8d GIT binary patch literal 206404 zcmb@t1#BEm^RH{>HO0&jGt-)xVrFJ$rkI&IW{hKIW`>xVdCkle$9(g?U;gJiI=a%; zm5#Jh&vZXkQ@`r!QSZzyg`$`Q0}CT3fMR!VdLDqlO2SOyU~CQG<6{ywadwb!aJD1i z_|vD%q-bPe=0d{$@3E?QH$}gGP5$XFf#+0Ioa7bSm~IVss4OunEs_4oT**RtWAv=O&shdAw zSC^PF3D>_WB&^JAOK{!0P>O9|WCJGi>&u(ELe!;-MFaQ~-eW%=9wqwr5Z>%ZCg z)BfdH|8i`9IkvwX+h30DFUR(mWB<#s|K-^Ka_oOO_P-p*UykE1$MKir_{(wp<+%Rk 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