题目链接:D. Happy Tree Party
树链剖分是从下面两篇博客学的。
思想从这里看的(不能再清晰了):http://blog.anudeep2011.com/heavy-light-decomposition/
代码从这列看的(区间操作的非LCA思想太赞了):http://blog.sina.com.cn/s/blog_6974c8b20100zc61.html
然后是这道题目,正好学习了HLD,拿来练手了。
题意:给你一棵树,和边权值(<=1e18)。
操作1,从a走到b,经过一条边就用一正数c整除以边权值,输出最后的c。
操作2,把第a条边(输入顺序)的值改为b(b小于原来的值)。
c范围最大1e18,longlong可以存,然后a到b的路径可以先求出一路上的乘积,最后用c除就可以了。
然后问题就是乘积可能有点大,又不想写高精度乘除,结果随便用long double试了试边界值(1e9 * 1e9, (1e9-1) * 1e9, (1+1e9) * 1e9),在本地跑判断是否大于1e18,结果没发现精度问题,于是就写了=.=,用一个flag标志当前节点的乘积是不是大于1e18了,说起来long double到底是什么精度啊。。
#include<bits/stdc++.h> #define ll long long int; using namespace std; const int N = 200055; bool islarge(ll a, ll b){ long double t1 = a, t2 = b; if(t1 * t2 > 1e18) return true; return false; } struct eg{ int v, nex; ll w; eg(){} eg(int _v, ll _w, int _nex){ v = _v, w = _w, nex = _nex; } }edg[N<<2]; ll sav[N][3]; int fir[N], ecnt = 0; void add(int a, int b, ll c){ edg[ecnt] = eg(b, c, fir[a]), fir[a] = ecnt++; edg[ecnt] = eg(a, c, fir[b]), fir[b] = ecnt++; } int fa[N], siz[N], son[N], dep[N]; void dfs(int rt){ siz[rt] = 1, son[rt] = 0; for(int k = fir[rt]; k != -1; k = edg[k].nex){ if(edg[k].v != fa[rt]){ fa[edg[k].v] = rt; dep[edg[k].v] = dep[rt] + 1; dfs(edg[k].v); siz[rt] += siz[edg[k].v]; if(siz[edg[k].v] > siz[son[rt]]) son[rt] = edg[k].v; } } } int w[N] = {0}, top[N] = {0}, wcnt = 0; void dfs2(int rt, int tp){ w[rt] = ++wcnt, top[rt] = tp; if(son[rt]) dfs2(son[rt], tp); for(int k = fir[rt]; k != -1; k = edg[k].nex){ if(edg[k].v != son[rt] && edg[k].v != fa[rt]){ dfs2(edg[k].v, edg[k].v); } } } ll tree[N << 2]; bool mflag[N << 2] = {0}; void update(int rt, int l, int r, int pos, ll val){ if(l == r){ tree[rt] = val; return; } int mid = (l+r) >> 1; if(pos <= mid) update(rt<<1, l, mid, pos, val); else update(rt<<1|1, mid+1, r, pos, val); if(mflag[rt<<1] | mflag[rt<<1|1]) mflag[rt] = 1; else{ if(islarge(tree[rt<<1], tree[rt<<1|1])) mflag[rt] = 1; else tree[rt] = tree[rt<<1] * tree[rt<<1|1], mflag[rt] = 0; } } ll query(int rt, int l, int r, int ql, int qr){ if(ql <= l && qr >= r) { return mflag[rt]? -1 : tree[rt]; } int mid = (l+r) >> 1; ll tmp1 = 1, tmp2 = 1; if(ql <= mid) tmp1 = query(rt<<1, l, mid, ql, qr); if(qr > mid) tmp2 = query(rt<<1|1, mid+1, r, ql, qr); if(tmp1 < 0 || tmp2 < 0) return -1; if(islarge(tmp1, tmp2)) return -1; return tmp1*tmp2; } ll getmul(int va, int vb){ int f1 = top[va], f2 = top[vb]; ll res = 1, tmp; while(f1 != f2){ if(dep[f1] < dep[f2]){ swap(f1, f2); swap(va, vb); } tmp = query(1, 1, wcnt, w[f1], w[va]); if(tmp < 0) return -1; if(islarge(tmp, res)) return -1; res *= tmp; va = fa[f1], f1 = top[va]; } if(va == vb) return res; if(dep[va] > dep[vb]) swap(va, vb); tmp = query(1, 1, wcnt, w[son[va]], w[vb]); if(tmp < 0 ) return -1; if(islarge(tmp, res)) return -1; return res * tmp; } int main(){ int n, q, a, b, d; ll c; scanf("%d %d", &n, &q); memset(fir, -1, sizeof(fir)); wcnt = ecnt = fa[1] = dep[1] = 0; for(int i = 0; i < N; ++i) tree[i] = 1; for(int i = 1; i < n; ++i){ scanf("%d %d %lld", &a, &b, &c); sav[i][0] = a, sav[i][1] = b, sav[i][2] = c; add(a, b, c); } dfs(1); dfs2(1, 1); for(int i = 1; i < n; ++i){ if(dep[sav[i][0]] > dep[sav[i][1]]) swap(sav[i][0], sav[i][1]); update(1, 1, wcnt, w[sav[i][1]], sav[i][2]); } while(q--){ scanf("%d", &d); if(d == 1){ scanf("%d %d %lld", &a, &b, &c); ll t = getmul(a, b); if(t < 0) puts("0"); else printf("%lld\n", c/t); } else{ scanf("%d %lld", &a, &c); sav[a][2] = c; update(1, 1, wcnt, w[sav[a][1]], c); } } }