大意: 給定$n$個凸多邊形, $q$個詢問, 求$[l,r]$內閔可夫斯基區間和的頂點數.

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要用到一個結論, 閔可夫斯基和凸包上的點等于向量種類數.

#include <iostream> #include <algorithm> #include <cstdio> #include <queue> #include <map> #define REP(i,a,n) for(int i=a;i<=n;++i) #define pb push_back using namespace std; typedef pair<int,int> pii; const int N = 1e6+10; int n, q, cnt, x[N], y[N], c[N]; int L[N], R[N], ans[N]; struct _ {int l,r;} b[N]; vector<int> g[N]; pii a[N]; map<pii,int> pre;int gcd(int a,int b) {return b?gcd(b,a%b):a;} pii reduce(int x, int y) {int g = gcd(abs(x),abs(y));if (g) x/=g,y/=g;return pii(x,y); } void add(int x, int v) {for (; x<=cnt; x+=x&-x) c[x]+=v; } int query(int x) {int r = 0;for (; x; x^=x&-x) r+=c[x];return r; }int main() {scanf("%d", &n);REP(i,1,n) {int k;scanf("%d", &k);REP(j,0,k-1) scanf("%d%d",x+j,y+j);L[i] = cnt+1;REP(j,0,k-1) a[++cnt] = reduce(x[j]-x[(j+1)%k],y[j]-y[(j+1)%k]);R[i] = cnt;}scanf("%d", &q);REP(i,1,q) {int l, r;scanf("%d%d", &l, &r);b[i].l = L[l];b[i].r = R[r];g[b[i].r].pb(i);}int now = 1;REP(i,1,cnt) {if (pre[a[i]]) add(pre[a[i]],-1);pre[a[i]] = i;add(i,1);for (int j:g[i]) ans[j] = query(b[j].r)-query(b[j].l-1);}REP(i,1,q) printf("%d\n", ans[i]); }

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轉載于:https://www.cnblogs.com/uid001/p/11205919.html

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