Codeforces 607D Power Tree 线段树 (看题解)

Power Tree 

没想到一个点到 1 的贡献和到 u 的贡献存在比例关系， 只要乘以 deg[ u ] * m[ u ]， m[ u ] 表示 u 到 1， 所成的系数。

然后我们用dfs序建出线段树后， 维护每个点乘的系数， 区间值的和就可以了。

#include<bits/stdc++.h>
#define LL long long
#define LD long double
#define ull unsigned long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ALL(x) (x).begin(), (x).end()
#define fio ios::sync_with_stdio(false); cin.tie(0);

using namespace std;

const int N = 2e5 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-8;
const double PI = acos(-1);

template<class T, class S> inline void add(T& a, S b) {a += b; if(a >= mod) a -= mod;}
template<class T, class S> inline void sub(T& a, S b) {a -= b; if(a < 0) a += mod;}
template<class T, class S> inline bool chkmax(T& a, S b) {return a < b ? a = b, true : false;}
template<class T, class S> inline bool chkmin(T& a, S b) {return a > b ? a = b, true : false;}

int n, v1, q, qus[N][4];
int in[N], ot[N], idx;
int v[N], deg[N];

vector<int> G[N];

#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1
struct segmentTree {
    int sum[N << 2], mul[N << 2], k[N << 2];
    inline void pull(int rt) {
        sum[rt] = sum[rt << 1] + sum[rt << 1 | 1];
        if(sum[rt] >= mod) sum[rt] -= mod;
    }
    inline void push(int rt) {
        if(mul[rt] != 1) {
            sum[rt << 1] = 1LL * sum[rt << 1] * mul[rt] % mod;
            sum[rt << 1 | 1] = 1LL * sum[rt << 1 | 1] * mul[rt] % mod;

            k[rt << 1] = 1LL * k[rt << 1] * mul[rt] % mod;
            k[rt << 1 | 1] = 1LL * k[rt << 1 | 1] * mul[rt] % mod;

            mul[rt << 1] = 1LL * mul[rt << 1] * mul[rt] % mod;
            mul[rt << 1 | 1] = 1LL * mul[rt << 1 | 1] * mul[rt] % mod;

            mul[rt] = 1;
        }
    }
    void build(int l, int r, int rt) {
        mul[rt] = 1;
        if(l == r) {
            if(l == 1) sum[rt] = v1, k[rt] = 1;
            else sum[rt] = 0, k[rt] = 0;
            return;
        }
        int mid = l + r >> 1;
        build(lson); build(rson);
        pull(rt);
    }
    void updateS(int L, int R, int val, int l, int r, int rt) {
        if(R < l || r < L || R < L) return;
        if(L <= l && r <= R) {
            sum[rt] = 1LL * sum[rt] * val % mod;
            k[rt] = 1LL * k[rt] * val % mod;
            mul[rt] = 1LL * mul[rt] * val % mod;
            return;
        }
        push(rt);
        int mid = l + r >> 1;
        updateS(L, R, val, lson);
        updateS(L, R, val, rson);
        pull(rt);
    }
    void updateP(int p, int val, int l, int r, int rt) {
        if(l == r) {
            sum[rt] = 1LL * val * v[p] % mod;
            k[rt] = val;
            mul[rt] = 1;
            return;
        }
        push(rt);
        int mid = l + r >> 1;
        if(p <= mid) updateP(p, val, lson);
        else updateP(p, val, rson);
        pull(rt);
    }
    int querySum(int L, int R, int l, int r, int rt) {
        if(R < l || r < L || R < L) return 0;
        if(L <= l && r <= R) return sum[rt];
        push(rt);
        int mid = l + r >> 1;
        return (querySum(L, R, lson) + querySum(L, R, rson)) % mod;
    }
    int queryK(int p, int l, int r,  int rt) {
        if(l == r) return k[rt];
        push(rt);
        int mid = l + r >> 1;
        if(p <= mid) return queryK(p, lson);
        else return queryK(p, rson);
    }
} Tree;

void dfs(int u) {
    in[u] = ++idx;
    for(auto& v : G[u]) dfs(v);
    ot[u] = idx;
}

int power(int a, int b) {
    int ans = 1;
    while(b) {
        if(b & 1) ans = 1LL * ans * a % mod;
        a = 1LL * a * a % mod; b >>= 1;
    }
    return ans;
}

int main() {
    n = 1;
    scanf("%d%d", &v1, &q);
    v[1] = v1;
    for(int i = 1; i <= q; i++) {
        scanf("%d", &qus[i][0]);
        if(qus[i][0] == 1) {
            scanf("%d%d", &qus[i][1], &qus[i][3]);
            qus[i][2] = ++n;
            G[qus[i][1]].push_back(qus[i][2]);
        } else {
            scanf("%d", &qus[i][1]);
        }
    }

    dfs(1);
    for(int i = 1; i <= n; i++) deg[i] = 1;
    Tree.build(1, n, 1);
    for(int i = 1; i <= q; i++) {
        if(qus[i][0] == 1) {
            int fa = qus[i][1], u = qus[i][2];
            v[in[u]] = qus[i][3];
            Tree.updateS(in[fa], ot[fa], 1LL * (deg[fa] + 1) * power(deg[fa], mod - 2) % mod, 1, n, 1);
            deg[fa]++;
            Tree.updateP(in[u], Tree.queryK(in[fa], 1, n, 1), 1, n, 1);
        } else {
            int u = qus[i][1];
            int ans = Tree.querySum(in[u], ot[u], 1, n, 1);
            ans = 1LL * ans * deg[u] % mod;
            ans = 1LL * ans * power(Tree.queryK(in[u], 1, n, 1), mod - 2) % mod;
            printf("%d
", ans);
        }
    }
    return 0;
}

/*
*/