【BJOI 2018】 求和

xiaoxiao2021-02-28  19

【题目链接】

           点击打开链接

【算法】

           预处理i^k的前缀和,对于每次询问,树上倍增即可

           时间复杂度 : O(nk + mlog(n))

【代码】

          

#include<bits/stdc++.h> using namespace std; #define MAXK 55 #define MAXN 300010 #define MAXLOG 20 const long long P = 998244353; struct Edge { int to,nxt; } e[MAXN<<1]; int n,x,i,j,y,q,k,Lca,tot; int anc[MAXN][MAXLOG],dep[MAXN],head[MAXN],fa[MAXN]; long long p[MAXN][MAXK],s[MAXN][MAXK]; long long ans; template <typename T> inline void read(T &x) { int f = 1; x = 0; char c = getchar(); for (; !isdigit(c); c = getchar()) { if (c == '-') f = -f; } for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0'; x *= f; } template <typename T> inline void write(T x) { if (x < 0) { putchar('-'); x = -x; } if (x > 9) write(x/10); putchar(x+'0'); } template <typename T> inline void writeln(T x) { write(x); puts(""); } inline void add(int x,int y) { tot++; e[tot] = (Edge){y,head[x]}; head[x] = tot; } inline void dfs(int u) { int i,v; anc[u][0] = fa[u]; for (i = 1; i < MAXLOG; i++) { if (dep[u] < (1 << i)) break; anc[u][i] = anc[anc[u][i-1]][i-1]; } for (i = head[u]; i; i = e[i].nxt) { v = e[i].to; if (fa[u] != v) { fa[v] = u; dep[v] = dep[u] + 1; dfs(v); } } } inline int lca(int x,int y) { int i,t; if (dep[x] > dep[y]) swap(x,y); t = dep[y] - dep[x]; for (i = 0; i < MAXLOG; i++) { if (t & (1 << i)) y = anc[y][i]; } if (x == y) return x; for (i = MAXLOG - 1; i >= 0; i--) { if (anc[x][i] != anc[y][i]) { x = anc[x][i]; y = anc[y][i]; } } return fa[x]; } int main() { read(n); for (i = 1; i < n; i++) { read(x); read(y); add(x,y); add(y,x); } for (i = 1; i < n; i++) { p[i][0] = 1; for (j = 1; j < MAXK; j++) p[i][j] = p[i][j-1] * i % P; } for (i = 1; i < n; i++) { for (j = 1; j < MAXK; j++) { s[i][j] = (s[i-1][j] + p[i][j]) % P; } } dfs(1); read(q); while (q--) { read(x); read(y); read(k); Lca = lca(x,y); ans = (s[dep[x]][k] + s[dep[y]][k]) % P; ans = ((ans - (2 * s[dep[Lca]][k]) % P) + P) % P; ans = (ans + p[dep[Lca]][k] + P) % P; writeln(ans); } return 0; }

          

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