Luogu4427 [BJOI2018]求和 （树上差分）

预处理，树上差分。注意深度减一

#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <cmath>
#define R(a,b,c) for(register int a = (b); (a) <= (c); ++(a))
#define nR(a,b,c) for(register int a = (b); (a) >= (c); --(a))
#define Fill(a,b) memset(a, b, sizeof(a))
#define Max(a,b) ((a) > (b) ? (a) : (b))
#define Min(a,b) ((a) < (b) ? (a) : (b))
#define Swap(a,b) ((a) ^= (b) ^= (a) ^= (b))

//#define ON_DEBUGG

#ifdef ON_DEBUGG

#define D_e_Line printf("\n----------\n") 
#define D_e(x) cout << (#x) << " : " << x << endl
#define Pause() system("pause")
#define FileOpen() freopen("in.txt", "r", stdin)

#else

#define D_e_Line ;
#define D_e(x) ;
#define Pause() ;
#define FileOpen() ;

#endif
using namespace std;
struct ios{
    template<typename ATP>inline ios& operator >> (ATP &x){
        x = 0; int f = 1; char ch;
        for(ch = getchar(); ch < '0' || ch > '9'; ch = getchar()) if(ch == '-') f = -1;
        while(ch >= '0' && ch <= '9') x = x * 10 + (ch ^ '0'), ch = getchar();
        x *= f;
        return *this;
    }
}io;

const int N = 300007;
const int mod = 998244353;

#define int long long
struct Edge{
    int nxt, pre;
}e[N << 1];
int head[N], cntEdge;
inline void add(int u, int v){
    e[++cntEdge] = (Edge){ head[u], v}, head[u] = cntEdge;
}

int maxDep;
int fa[N], son[N], dep[N], siz[N];
inline void DFS_First(int u, int father){
    dep[u] = dep[father] + 1, fa[u] = father, siz[u] = 1;
    maxDep = Max(maxDep, dep[u]); //re define maxDep
    for(register int i = head[u]; i; i = e[i].nxt){
        int v = e[i].pre;
        if(v == father) continue;
        DFS_First(v, u);
        siz[u] += siz[v];
        if(!son[u] || siz[v] > siz[son[u]]){
            son[u] = v;
        }
    }
}
int top[N], rnk[N], dfn[N], dfnIndex;
inline void DFS_Second(int u, int ancester){
    top[u] = ancester, dfn[u] = ++dfnIndex, rnk[dfnIndex] = u;
    if(!son[u]) return;
    DFS_Second(son[u], ancester);
    for(register int i = head[u]; i; i = e[i].nxt){
        int v = e[i].pre;
        if(v != son[u] && v != fa[u])
            DFS_Second(v, v);
    }
}
int val[51][N], p[N][51];
inline int Query(int x, int y, int K){
    int sum = 0;
    while(top[x] != top[y]){
        if(dep[top[x]] < dep[top[y]]) Swap(x, y);
        sum = (sum + val[K][dfn[x]] - val[K][dfn[top[x]] - 1] + mod) % mod;
        x = fa[top[x]];
    }
    //D_e(sum);
    if(dep[x] < dep[y]) Swap(x, y);
    return (sum + val[K][dfn[x]] - val[K][dfn[y] - 1] + mod) % mod;
}

#undef int 
int main(){
#define int long long 
FileOpen();
    int n;
    io >> n;
    R(i,2,n){
        int u, v;
        io >> u >> v;
        add(u, v);
        add(v, u);
    }
    
    DFS_First(1, 0);
    DFS_Second(1, 1);

    --maxDep;
    R(i,1,n) --dep[i]; // !!!!!!
    R(i,1,maxDep){
        p[i][1] = i;
        R(k,2,50){
            p[i][k] = p[i][k - 1] * i % mod;
            //D_e(p[i][k]);
        }
    }
    R(k,1,50){
        R(i,1,n){
            val[k][i] = (val[k][i - 1] + p[dep[rnk[i]]][k]) % mod;//, D_e(val[k][i]);
        }
    }
    
    int Ques;
    io >> Ques;
    while(Ques--){
        int x, y, K;
        io >> x >> y >> K;
        printf("%lld\n", Query(x, y, K));
    }
    
    return 0;
}

来源：https://www.cnblogs.com/bingoyes/p/11374866.html