湘潭邀请赛 2018 E From Tree to Graph
题意:
给出一棵树以及m,a,b,x0,y0。之后加m条边{(x1,LCA(x1,y1)),(x2,LCA(x2,y2))...(xm,LCA(xm,ym))}。定义z = f(0)^f(1)^...^f(n-1),其中f(i)代表删掉点i的连通块数。则xi = (axi-1+byi-1+z)%n,yi = (bxi-1+ayi-1+z)%n。求xm和ym。
题解:
维护每个点的度数。初始的点的度数即为删掉该点后的连通块数。
第i次加边(xi,LCA(xi,yi))中xi到LCA(xi,yi)的路径上的点(除xi和LCA(xi,yi)以外)度数减1。
每个点的父节点只有一个,用并查集维护每个点的父亲节点到其分支是否被计算过。
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
#include <iostream> #include <cstdio> using namespace std; const int N = 5005; int n, m, a, b, x, y, z; int u, v; int tot; int f[N], depth[N], fa[15][N], g[N]; int head[N], nxt[N<<1], to[N<<1]; int find(int x) { return x==f[x]?x:f[x]=find(f[x]); } void dfs(int u, int pre, int d) { fa[0][u] = pre; depth[u] = d; int cnt = 0; for(int i = head[u]; ~i; i = nxt[i]) { if(to[i] != pre) dfs(to[i], u, d+1); cnt++; } g[u] =cnt; } int main() { while(~scanf("%d%d%d%d%d%d", &n, &m, &a, &b, &x, &y)) { tot = z = 0; for(int i = 0; i <= n; i++) f[i] = i, head[i] = -1; for(int i = 0; i < n-1; i++) { scanf("%d%d", &u, &v); to[++tot] = v; nxt[tot] = head[u]; head[u] = tot; to[++tot] = u; nxt[tot] = head[v]; head[v] = tot; } dfs(0, 0, 0); for(int i = 0; i < 13; i++) for(int j = 0; j < n; j++) fa[i+1][j] = fa[i][fa[i][j]]; for(int i = 0; i < n; i++) z ^= g[i]; while(m--) { u = (a*x+b*y+z)%n; v = (a*y+b*x+z)%n; x = u; y = v; if(depth[u]<depth[v]) swap(u, v); int dep = depth[u]-depth[v]; if(dep>0) { for(int i = 13; i >= 0; i--) { if(dep&(1<<i)) u = fa[i][u]; } } for(int i = 13; i >= 0; i--) { if(fa[i][u] != fa[i][v]) { u = fa[i][u]; v = fa[i][v]; } } if(u!=v) v = fa[0][v]; u = find(x); while(depth[fa[0][u]]>depth[v]) { z ^= g[fa[0][u]]; g[fa[0][u]]--; z ^= g[fa[0][u]]; f[u] = fa[0][u]; u = find(u); } } printf("%d %d\n", x, y); } }