[Codeforces1017E] The Supersonic Rocket (凸包, KMP)

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链接：http://codeforces.com/contest/1017/problem/E

给你两组点，问你这两组点的凸包是不是同构的。

先分别跑出两组点的凸包，判断一下点数是否相等，然后依次按照凸包的长度和拐点的角度记录下数列，然后可以用最小表示法都调成最小表示，或者对其中一个数列扩大两倍作匹配串，另一个作模式串跑KMP。

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#include <bits/stdc++.h>
using namespace std;

using LL = long long;
const LL maxn = 1500500;
typedef struct Point { LL x, y; }Point;
Point point[maxn];
LL st[maxn], top;

LL cross(Point p0, Point p1, Point p2) {
  return (p1.x-p0.x)*(p2.y-p0.y)-(p1.y-p0.y)*(p2.x-p0.x);
}

LL dis(Point p1, Point p2) {
  return (p2.x-p1.x)*(p2.x-p1.x)+(p2.y-p1.y)*(p2.y-p1.y);  
}

bool cmp(Point p1, Point p2) {
  LL tmp = cross(point[0], p1, p2);
  if(tmp > 0) return 1;
  if(tmp == 0) return dis(point[0], p1) < dis(point[0], p2);
  return 0;
}

void graham(LL n, vector<Point> &ret) {
  ret.clear();
  for(LL i = 0; i < n; i++) {
    if(point[0].y >= point[i].y) {
      if(point[0].y == point[i].y) {
        if(point[0].x > point[i].x) swap(point[i], point[i]);
      }
      else swap(point[0], point[i]);
    }
  }
  sort(point+1, point+n, cmp);
  top = 0;
  st[top++] = 0, st[top++] = 1;
  for(LL i = 0; i < n; i++) {
    while(top-2 >= 0 && cross(point[st[top-2]], point[st[top-1]], point[i]) <= 0) --top;
    st[top++] = i;
  }
  for(LL i = 0; i < top; i++) ret.emplace_back(point[st[i]]);
}

Point a[maxn], b[maxn];
vector<Point> conv1, conv2;
LL n, m;

LL na, nb;
LL x[maxn];
LL y[maxn];
LL pre[maxn];

void getpre(LL *y, LL *pre) {
  LL j, k;
  memset(pre, -1, sizeof(-1));
  pre[0] = -1;
  j = 0; k = -1;
  while(j < nb) {
    if(k == -1 || y[j] == y[k]) {
      j++; k++;
      if(y[j] != y[k]) pre[j] = k;
      else pre[j] = pre[k];
    }
    else k = pre[k];
  }
}

LL kmp() {
  LL ans = 0;
  LL i = 0;
  LL j = 0;
  getpre(y, pre);
  while(i < na) {
    if(j == -1 || x[i] == y[j]) {
      i++; j++;
    }
    else j = pre[j];
    if(j == nb) ans++;
  }
  return ans;
}

signed main() {
  // freopen("in", "r", stdin);
  while(~scanf("%lld%lld",&n,&m)) {
    memset(x, 0, sizeof(x));
    memset(y, 0, sizeof(y));
    for(LL i = 0; i < n; i++) scanf("%lld%lld",&a[i].x,&a[i].y);
    for(LL i = 0; i < m; i++) scanf("%lld%lld",&b[i].x,&b[i].y);
    conv1.clear(); conv2.clear();
    for(LL i = 0; i < n; i++) point[i] = a[i];
    graham(n, conv1);
    for(LL i = 0; i < m; i++) point[i] = b[i];
    graham(m, conv2);
    if(conv1.size() != conv2.size()) printf("NO\n");
    else {
      na = conv1.size() * 6, nb = conv2.size() * 3;
      for(LL i = 0; i < conv1.size(); i++) {
        x[i*3] = dis(conv1[i],conv1[(i+1)%conv1.size()]);
        x[i*3+1] = cross(conv1[(i+1)%conv1.size()],conv1[i],conv1[(i+2)%conv1.size()]);
        x[i*3+2] = dis(conv1[(i+1)%conv1.size()],conv1[(i+2)%conv1.size()]);
        // cout << x[i*3]<<" "<<x[i*3+1]<<" "<<x[i*3+2]<<" ";
      }
      for(LL i = 0; i < conv1.size(); i++) {
        x[i*3+na/2] = x[i*3];
        x[i*3+1+na/2] = x[i*3+1];
        x[i*3+2+na/2] = x[i*3+2];
        // cout << x[i*3+na/2]<<" "<<x[i*3+1+na/2]<<" "<<x[i*3+2+na/2]<<" ";
      }
      // cout<<endl;
      for(LL i = 0; i < conv2.size(); i++) {
        y[i*3] = dis(conv2[i],conv2[(i+1)%conv2.size()]);
        y[i*3+1] = cross(conv2[(i+1)%conv2.size()],conv2[i],conv2[(i+2)%conv2.size()]);
        y[i*3+2] = dis(conv2[(i+1)%conv2.size()],conv2[(i+2)%conv2.size()]);
        // cout << y[i*3]<<" "<<y[i*3+1]<<" "<<y[i*3+2]<<" ";
      }
      // cout<<endl;
      LL ret = kmp();
      if(ret) printf("YES\n");
      else printf("NO\n");
    }
  }
  return 0;
}