#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define mp make_pair
#define pii pair<int, int>
#define f first
#define s second
typedef long double T;
typedef complex<T> pt;
#define x real()
#define y imag()
T dot(pt v, pt w) {return (conj(v)*w).x;}
T cross(pt v, pt w) {return (conj(v)*w).y;}
T orient(pt a, pt b, pt c) {return cross(b-a,c-a);} // positive for left, negative for right, 0 for straight
bool half(pt p) {return p.y > 0 || (p.y == 0 && p.x < 0);}
// Warning: polarSort shouldn't contain origin
void polarSort(vector<pt> &v) {sort(v.begin(), v.end(), [](pt v, pt w) {return make_tuple(half(v), 0) < make_tuple(half(w), cross(v,w));});}
bool inDisk(pt a, pt b, pt p) {return dot(a-p, b-p) <= 0;}
bool onSegment(pt a, pt b, pt p) {return orient(a,b,p) == 0 && inDisk(a,b,p);}
bool intersect(pt a, pt b, pt c, pt d) {
if (a == c || a == d || b == c || b == d) return false;
if (onSegment(a, b, c)) return true;
if (onSegment(a, b, d)) return true;
if (onSegment(c, d, a)) return true;
if (onSegment(c, d, b)) return true;
T oa = orient(c, d, a), ob = orient(c, d, b), oc = orient(a, b, c), od = orient(a, b, d);
return ((oa > 0 && ob < 0) || (oa < 0 && ob > 0)) && ((oc > 0 && od < 0) || (oc < 0 && od > 0));
}
T area(vector<pt> polygon) {
int n = polygon.size();
T res = 0;
for (int i=0; i<n; i++) res += polygon[i].x * polygon[(i+1)%n].y - polygon[i].y * polygon[(i+1)%n].x;
return abs(res) / 2;
}
int contains(vector<pt> polygon, pt p) {
// Return 0 if outside, 1 if inside, 2 if on boundary
int n = polygon.size(), res = 0;
for (int i=0; i<n; i++) {
if (onSegment(polygon[i], polygon[(i+1)%n], p)) return 2;
res ^= ((p.y>=polygon[(i+1)%n].y)-(p.y>=polygon[i].y)) * orient(p, polygon[i], polygon[(i+1)%n]) > 0;
}
return res;
}
vector<vector<pt>> shapes;
void output(vector<pt> polygon) {
printf("%d", polygon.size());
for (pt p : polygon) printf(" %.12Lf %.12Lf", p.x, p.y);
printf("\n");
}
vector<int> scissors(int original, vector<vector<pt>> pieces) {
printf("scissors\n%d %d\n", original, pieces.size());
vector<int> res;
for (vector<pt>& piece : pieces) {
res.push_back(shapes.size());
shapes.push_back(piece);
output(piece);
}
return res;
}
int tape(vector<int> pieces, vector<pt> combined) {
printf("tape\n%d", pieces.size());
for (int i : pieces) printf(" %d", i);
printf("\n");
for (int i : pieces) output(shapes[i]);
output(combined);
shapes.push_back(combined);
return shapes.size()-1;
}
int move(int shape, vector<pt> loc, int rotatenum = 0) {
printf("tape\n1 %d\n", shape);
vector<pt> pts;
for (int i=rotatenum; i<loc.size(); i++) pts.push_back(loc[i]);
for (int i=0; i<rotatenum; i++) pts.push_back(loc[i]);
output(pts);
output(loc);
shapes.push_back(loc);
return shapes.size()-1;
}
vector<pt> read() {
int n, a, b;
scanf("%d", &n);
vector<pt> polygon;
for (int i=0; i<n; i++) {
scanf("%d%d", &a, &b);
polygon.emplace_back(a, b);
}
return polygon;
}
vector<pt> genrect(T lx, T rx, T ly, T ry) {
return {{lx, ly}, {rx, ly}, {rx, ry}, {lx, ry}};
}
int resize(int rectangle, T newwidth) {
T newheight = area(shapes[rectangle]) / newwidth;
T curwidth = shapes[rectangle][1].x, curheight = shapes[rectangle][2].y;
if (abs(newwidth-curwidth) <= 1e-11) return rectangle;
if (newwidth > newheight + 1e-11) {
int res = resize(rectangle, newheight);
return move(res, genrect(0, newwidth, 0, newheight), 1);
}
if (curheight >= 2 * newheight) {
vector<int> halves = scissors(rectangle, {genrect(0, curwidth, 0, curheight/2), genrect(0, curwidth, curheight/2, curheight)});
int h2 = move(halves[1], genrect(curwidth, curwidth*2, 0, curheight/2));
int res = tape({halves[0], h2}, genrect(0, 2*curwidth, 0, curheight/2));
return resize(res, newwidth);
}
if (curwidth >= 2 * newwidth) {
vector<int> halves = scissors(rectangle, {genrect(0, curwidth/2, 0, curheight), genrect(curwidth/2, curwidth, 0, curheight)});
int h2 = move(halves[1], genrect(0, curwidth/2, curheight, curheight*2));
int res = tape({halves[0], h2}, genrect(0, curwidth/2, 0, curheight*2));
return resize(res, newwidth);
}
if (curwidth < newwidth) {
int res = move(rectangle, genrect(0, curheight, 0, curwidth), 1);
return resize(res, newwidth);
}
vector<int> pieces = scissors(rectangle, {
{{0, 0}, {newwidth, 0}, {newwidth, newheight-curheight}, {curwidth-newwidth, curheight}, {0, curheight}},
{{newwidth, 0}, {curwidth, 0}, {newwidth, newheight-curheight}},
{{curwidth, 0}, {curwidth, curheight}, {curwidth-newwidth, curheight}}
});
int a = pieces[0];
int b2 = move(pieces[1], {{0, curheight}, {curwidth-newwidth, curheight}, {0, newheight}});
int c2 = move(pieces[2], {{newwidth, newheight-curheight}, {newwidth, newheight}, {0, newheight}});
return tape({a, b2, c2}, genrect(0, newwidth, 0, newheight));
}
pt calc(vector<pt> triangle) {
// If point 0 is at (0, 0) and point 1 is on the positive x axis, where is point 2?
// dot(p2-p1, p3-p1) = dot(answer, new p1)
T x2 = dot(triangle[2]-triangle[0], (triangle[1]-triangle[0])/abs(triangle[1]-triangle[0]));
T y2 = sqrt(dot(triangle[2]-triangle[0], triangle[2]-triangle[0]) - x2 * x2);
return pt{x2, y2};
}
int rotate(int triangle) {
// Make longest side between the first two points
T a = abs(shapes[triangle][0] - shapes[triangle][1]), b = abs(shapes[triangle][1] - shapes[triangle][2]), c = abs(shapes[triangle][0] - shapes[triangle][2]);
if (a >= b && a >= c) return triangle;
if (b >= a && b >= c) return move(triangle, {shapes[triangle][1], shapes[triangle][2], shapes[triangle][0]}, 2);
return move(triangle, {shapes[triangle][2], shapes[triangle][0], shapes[triangle][1]}, 1);
}
int tritorect(int triangle, int newwidth) {
triangle = rotate(triangle);
pt top = calc(shapes[triangle]);
triangle = move(triangle, {{0, 0}, {abs(shapes[triangle][0]-shapes[triangle][1]), 0}, top});
pt a = {top.x/2, top.y/2}, b = {(top.x+shapes[triangle][1].x)/2, top.y/2}, c = {top.x, top.y/2};
vector<int> pieces = scissors(triangle, {
{{0, 0}, {shapes[triangle][1].x, 0}, b, a},
{a, c, top},
{c, b, top}
});
int A = pieces[0];
int B = move(pieces[1], {a, {0, top.y/2}, {0, 0}});
int C = move(pieces[2], {{shapes[triangle][1].x, top.y/2}, b, {shapes[triangle][1].x, 0}});
int rect = tape({A, B, C}, genrect(0, shapes[triangle][1].x, 0, top.y/2));
return resize(rect, newwidth);
}
int recttotri(int rectangle, vector<pt> triangle) {
T a = abs(triangle[0] - triangle[1]), b = abs(triangle[1] - triangle[2]), c = abs(triangle[0] - triangle[2]);
if (b > a && b > c) return move(recttotri(rectangle, {triangle[1], triangle[2], triangle[0]}), triangle, 1);
if (c > a && c > b) return move(recttotri(rectangle, {triangle[2], triangle[0], triangle[1]}), triangle, 2);
pt top = calc(triangle);
rectangle = resize(rectangle, a);
pt A = {top.x/2, top.y/2}, B = {(top.x+a)/2, top.y/2}, C = {top.x, top.y/2};
vector<int> pieces = scissors(rectangle, {
{{0, 0}, {a, 0}, B, A},
{A, {0, top.y/2}, {0, 0}},
{{a, top.y/2}, B, {a, 0}}
});
int p1 = pieces[0];
int p2 = move(pieces[1], {A, C, top});
int p3 = move(pieces[2], {C, B, top});
int tri = tape({p1, p2, p3}, {{0, 0}, {a, 0}, top});
return move(tri, triangle);
}
vector<vector<pt>> triangulate(vector<pt> polygon) {
vector<vector<pt>> res;
while (polygon.size() > 3) {
int n = polygon.size();
for (int i=0; i<n; i++) {
if (orient(polygon[i], polygon[(i+1)%n], polygon[(i+2)%n]) < 0) continue;
bool ok = true;
for (int j=0; j<n; j++) {
if (j == i || j == (i+1)%n || j == (i+2)%n) continue;
ok = ok && contains({polygon[i], polygon[(i+1)%n], polygon[(i+2)%n]}, polygon[j]) == 0;
}
if (ok) {
res.push_back({polygon[i], polygon[(i+1)%n], polygon[(i+2)%n]});
polygon.erase(polygon.begin()+(i+1)%n);
break;
}
}
}
res.push_back(polygon);
return res;
}
int main() {
vector<pt> s = read(), t = read();
shapes = {s};
T width = sqrt(area(s)), curheight = 0;
vector<int> rectpieces;
for (int triangle : scissors(0, triangulate(s))) {
int rect = tritorect(triangle, width);
rectpieces.push_back(move(rect, genrect(0, width, curheight, curheight + shapes[rect][2].y)));
curheight += shapes[rect][2].y;
}
int combined = tape(rectpieces, genrect(0, width, 0, width));
curheight = 0;
vector<vector<pt>> rectpieces2, triangulation = triangulate(t);
for (auto triangle : triangulation) {
rectpieces2.push_back(genrect(0, width, curheight, curheight+area(triangle)/width));
curheight += area(triangle)/width;
}
vector<int> rects = scissors(combined, rectpieces2), finalpieces;
for (int i=0; i<rects.size(); i++) {
int rect = move(rects[i], genrect(0, width, 0, rectpieces2[i][2].y-rectpieces2[i][1].y));
finalpieces.push_back(recttotri(rect, triangulation[i]));
}
tape(finalpieces, t);
}
Compilation message
scissors.cpp: In function 'void output(std::vector<std::complex<long double> >)':
scissors.cpp:55:14: warning: format '%d' expects argument of type 'int', but argument 2 has type 'std::vector<std::complex<long double> >::size_type' {aka 'long unsigned int'} [-Wformat=]
55 | printf("%d", polygon.size());
| ~^ ~~~~~~~~~~~~~~
| | |
| int std::vector<std::complex<long double> >::size_type {aka long unsigned int}
| %ld
scissors.cpp: In function 'std::vector<int> scissors(int, std::vector<std::vector<std::complex<long double> > >)':
scissors.cpp:61:27: warning: format '%d' expects argument of type 'int', but argument 3 has type 'std::vector<std::vector<std::complex<long double> > >::size_type' {aka 'long unsigned int'} [-Wformat=]
61 | printf("scissors\n%d %d\n", original, pieces.size());
| ~^ ~~~~~~~~~~~~~
| | |
| int std::vector<std::vector<std::complex<long double> > >::size_type {aka long unsigned int}
| %ld
scissors.cpp: In function 'int tape(std::vector<int>, std::vector<std::complex<long double> >)':
scissors.cpp:72:20: warning: format '%d' expects argument of type 'int', but argument 2 has type 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wformat=]
72 | printf("tape\n%d", pieces.size());
| ~^ ~~~~~~~~~~~~~
| | |
| int std::vector<int>::size_type {aka long unsigned int}
| %ld
scissors.cpp: In function 'int move(int, std::vector<std::complex<long double> >, int)':
scissors.cpp:84:28: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::complex<long double> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
84 | for (int i=rotatenum; i<loc.size(); i++) pts.push_back(loc[i]);
| ~^~~~~~~~~~~
scissors.cpp: In function 'int main()':
scissors.cpp:235:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
235 | for (int i=0; i<rects.size(); i++) {
| ~^~~~~~~~~~~~~
scissors.cpp: In function 'std::vector<std::complex<long double> > read()':
scissors.cpp:94:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
94 | scanf("%d", &n);
| ~~~~~^~~~~~~~~~
scissors.cpp:97:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
97 | scanf("%d%d", &a, &b);
| ~~~~~^~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
212 KB |
Operation 16 (tape), polygon 0: Equivalent polygons must not change their area by more than 0.001000, got '12.000000' vs '14.696938', error '0.224745' |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
used 550 vertices, largest error was 0.00000008064320 |
| 2 |
Correct |
1 ms |
340 KB |
used 662 vertices, largest error was 0.00000307399580 |
| 3 |
Correct |
1 ms |
340 KB |
used 606 vertices, largest error was 0.00000057650166 |
| 4 |
Correct |
1 ms |
340 KB |
used 550 vertices, largest error was 0.00000004347702 |
| 5 |
Correct |
1 ms |
324 KB |
used 550 vertices, largest error was 0.00000004800000 |
| 6 |
Correct |
1 ms |
316 KB |
used 550 vertices, largest error was 0.00000013150701 |
| 7 |
Correct |
1 ms |
212 KB |
used 550 vertices, largest error was 0.00000003200000 |
| 8 |
Correct |
1 ms |
340 KB |
used 550 vertices, largest error was 0.00000006374210 |
| 9 |
Correct |
1 ms |
340 KB |
used 550 vertices, largest error was 0.00000006275000 |
| 10 |
Correct |
1 ms |
212 KB |
used 550 vertices, largest error was 0.00000011081120 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
212 KB |
Operation 16 (tape), polygon 0: Equivalent polygons must not change their area by more than 0.001000, got '12.000000' vs '14.696938', error '0.224745' |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
used 410 vertices, largest error was 0.00000003200000 |
| 2 |
Correct |
1 ms |
212 KB |
used 410 vertices, largest error was 0.00000002052869 |
| 3 |
Correct |
1 ms |
212 KB |
used 410 vertices, largest error was 0.00000008454028 |
| 4 |
Correct |
1 ms |
212 KB |
used 410 vertices, largest error was 0.00000004347702 |
| 5 |
Correct |
1 ms |
212 KB |
used 404 vertices, largest error was 0.00000009938108 |
| 6 |
Correct |
1 ms |
212 KB |
used 404 vertices, largest error was 0.00000003390678 |
| 7 |
Correct |
1 ms |
212 KB |
used 410 vertices, largest error was 0.00000036020208 |
| 8 |
Correct |
1 ms |
212 KB |
used 410 vertices, largest error was 0.00000008637088 |
| 9 |
Correct |
1 ms |
212 KB |
used 438 vertices, largest error was 0.00000004298278 |
| 10 |
Correct |
1 ms |
212 KB |
used 404 vertices, largest error was 0.00000003200000 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
used 250 vertices, largest error was 0.00000301744246 |
| 2 |
Correct |
1 ms |
212 KB |
used 272 vertices, largest error was 0.00000038701441 |
| 3 |
Correct |
1 ms |
212 KB |
used 272 vertices, largest error was 0.00000233666220 |
| 4 |
Correct |
1 ms |
212 KB |
used 306 vertices, largest error was 0.00000116407378 |
| 5 |
Correct |
1 ms |
212 KB |
used 334 vertices, largest error was 0.00000205185540 |
| 6 |
Correct |
1 ms |
212 KB |
used 278 vertices, largest error was 0.00000080655399 |
| 7 |
Correct |
1 ms |
212 KB |
used 334 vertices, largest error was 0.00000156601947 |
| 8 |
Correct |
1 ms |
300 KB |
used 300 vertices, largest error was 0.00000127375671 |
| 9 |
Correct |
1 ms |
212 KB |
used 278 vertices, largest error was 0.00000014525383 |
| 10 |
Correct |
1 ms |
212 KB |
used 278 vertices, largest error was 0.00000034127538 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
212 KB |
Operation 16 (tape), polygon 0: Equivalent polygons must not change their area by more than 0.001000, got '12.000000' vs '14.696938', error '0.224745' |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
212 KB |
Operation 16 (tape), polygon 0: Equivalent polygons must not change their area by more than 0.001000, got '12.000000' vs '14.696938', error '0.224745' |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
212 KB |
Operation 16 (tape), polygon 0: Equivalent polygons must not change their area by more than 0.001000, got '12.000000' vs '14.696938', error '0.224745' |
| 2 |
Halted |
0 ms |
0 KB |
- |
