日常刷题2025-2-20

日常刷题2025-2-20

lz的序列问题

思路：常规线段树

比较常规的线段树。

代码

#include <bits/stdc++.h>
#define lson (rt << 1)
#define rson (rt << 1 | 1)

using i64 = long long;

const int mod = 1000000007;

int a[200005];
struct node {
    i64 v, rmx, lz;
}tr[200005 << 2];

i64 ksm(i64 a, i64 b) {
    i64 res = 1;
    while(b) {
        if (b & 1) {
            res = res * a % mod;
        }
        b >>= 1;
        a = a * a % mod;
    }

    return res;
}

node mer(node x, node y) {
    if (x.v == 0) return y;
    node res = {0, 0, 0};
    res.v = x.rmx * y.v % mod + x.v;
    res.v %= mod;
    res.rmx = x.rmx * y.rmx % mod;
    return res;
}

void push_down(int rt, int l, int r) {
    if (tr[rt].lz) {
        int mid = l + r >> 1;
        int x = tr[rt].lz;
        
        tr[lson].lz = x;
        tr[rson].lz = x;

        if (tr[rt].lz == 1) {
            tr[lson].v = mid - l + 1;
            tr[rson].v = r - mid;

            tr[lson].rmx = 1;
            tr[rson].rmx = 1;
        }
        else {
            tr[lson].v = (ksm(x, mid - l + 1) - 1) * x % mod * ksm(x - 1, mod - 2) % mod;
            tr[rson].v = (ksm(x, r - mid) - 1) * x % mod * ksm(x - 1, mod - 2) % mod;

            tr[lson].rmx = ksm(x, mid - l + 1);
            tr[rson].rmx = ksm(x, r - mid);
        }
        
        tr[rt].lz = 0;
    }
}

void build(int rt, int l, int r) {
    if (l == r) {
        tr[rt].v = a[l];
        tr[rt].rmx = a[l]; 
        return;
    }

    int mid = l + r >> 1;
    build(lson, l, mid);
    build(rson, mid + 1, r);
    tr[rt] = mer(tr[lson], tr[rson]);
}

void update(int rt, int l, int r, int L, int R, int x) {
    if (l >= L && r <= R) {
        tr[rt].lz = x;
        if (x == 1) {
            tr[rt].v = r - l + 1;
            tr[rt].rmx = 1;
        }
        else {
            tr[rt].v = (ksm(x, r - l + 1) - 1) * x % mod * ksm(x - 1, mod - 2) % mod;
            tr[rt].rmx = ksm(x, (r - l + 1));
        }
        return;
    }

    push_down(rt, l, r);

    int mid = l + r >> 1;
    if (mid >= L)
        update(lson, l, mid, L, R, x);
    if (mid < R) {
        update(rson, mid + 1, r, L, R, x);
    }
    tr[rt] = mer(tr[lson], tr[rson]);
}

node query(int rt, int l, int r, int L, int R) {
    if (l >= L && r <= R) {
        return tr[rt];
    }

    push_down(rt, l, r);
    node res = {0, 0, 0};

    int mid = l + r >> 1;
    if (mid >= L) {
        res = mer(res, query(lson, l, mid, L, R));
    }
    if (mid < R){
        res = mer(res, query(rson, mid + 1, r, L, R));
    }
    return res;
}

void solve() {
    int n, m;
    std::cin >> n >> m;

    for (int i = 1; i <= n; i++) {
        std::cin >> a[i];
    }

    build(1, 1, n);

    while (m--) {
        int op;
        std::cin >> op;
        if (op == 1) {
            int l, r, x;
            std::cin >> l >> r >> x;
            update(1, 1, n, l, r, x);
        }
        else {
            int l, r;
            std::cin >> l >> r;
            std::cout << query(1, 1, n, l, r).v << '\n';
        }
    }
}

signed main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
    std::cout.tie(0);

    int t = 1;
    // std::cin >> t;
    while (t--) {
        solve();
    }

    return 0;
}