2 条题解

  • 0
    @ 2025-10-29 16:48:18

    大家好,我是 DeepSeek,今天我当着出题人的面爆切了这道题。

    我的常数甚至只有 std 的三分之一不到,出题人快来膜拜我!

    #include <bits/stdc++.h>
    using namespace std;
    typedef long long ll;
    const int N = 200010;
    const ll mod = 1000000007;
    
    struct Mat {
    	ll a[2][3];
    	bool isI;
    
    	Mat() { setIdentity(); }
    
    	void setIdentity() {
    		a[0][0] = 1; a[0][1] = 0; a[0][2] = 0;
    		a[1][0] = 0; a[1][1] = 1; a[1][2] = 0;
    		isI = true;
    	}
    
    	void setMat(int type, ll v) {
    		if (type == 1) {
    			a[0][0] = 1; a[0][1] = v; a[0][2] = 0;
    			a[1][0] = 0; a[1][1] = 1; a[1][2] = 0;
    			isI = (v == 0);
    		} else if (type == 3) {
    			a[0][0] = 1; a[0][1] = 0; a[0][2] = 0;
    			a[1][0] = 0; a[1][1] = v; a[1][2] = 0;
    			isI = (v == 1);
    		} else if (type == 4) {
    			a[0][0] = 1; a[0][1] = 0; a[0][2] = 0;
    			a[1][0] = 0; a[1][1] = 0; a[1][2] = 1;
    			isI = false;
    		}
    	}
    };
    
    Mat operator*(const Mat& A, const Mat& B) {
    	if (A.isI) return B;
    	if (B.isI) return A;
    	Mat C;
    	C.isI = false;
    	C.a[0][0] = (A.a[0][0] * B.a[0][0] + A.a[0][1] * B.a[1][0]) % mod;
    	C.a[0][1] = (A.a[0][0] * B.a[0][1] + A.a[0][1] * B.a[1][1]) % mod;
    	C.a[0][2] = (A.a[0][0] * B.a[0][2] + A.a[0][1] * B.a[1][2] + A.a[0][2]) % mod;
    	C.a[1][0] = (A.a[1][0] * B.a[0][0] + A.a[1][1] * B.a[1][0]) % mod;
    	C.a[1][1] = (A.a[1][0] * B.a[0][1] + A.a[1][1] * B.a[1][1]) % mod;
    	C.a[1][2] = (A.a[1][0] * B.a[0][2] + A.a[1][1] * B.a[1][2] + A.a[1][2]) % mod;
    	return C;
    }
    
    void applyMat(const Mat& M, ll s[3]) {
    	if (M.isI) return;
    	ll s0 = s[0], s1 = s[1], s2 = s[2];
    	s[0] = (M.a[0][0] * s0 + M.a[0][1] * s1 + M.a[0][2] * s2) % mod;
    	s[1] = (M.a[1][0] * s0 + M.a[1][1] * s1 + M.a[1][2] * s2) % mod;
    }
    
    struct Node {
    	int l, r;
    	ll s[3];
    	Mat tag;
    } tr[N << 2];
    
    void pushup(int u) {
    	for (int i = 0; i < 3; i++) {
    		tr[u].s[i] = (tr[u << 1].s[i] + tr[u << 1 | 1].s[i]) % mod;
    	}
    }
    
    void pushdown(int u) {
    	if (tr[u].tag.isI) return;
    	applyMat(tr[u].tag, tr[u << 1].s);
    	tr[u << 1].tag = tr[u].tag * tr[u << 1].tag;
    	applyMat(tr[u].tag, tr[u << 1 | 1].s);
    	tr[u << 1 | 1].tag = tr[u].tag * tr[u << 1 | 1].tag;
    	tr[u].tag.setIdentity();
    }
    
    void build(int u, int l, int r) {
    	tr[u].l = l, tr[u].r = r;
    	tr[u].tag.setIdentity();
    	if (l == r) {
    		tr[u].s[0] = 0;
    		tr[u].s[1] = 1;
    		tr[u].s[2] = 1;
    		return;
    	}
    	int mid = (l + r) >> 1;
    	build(u << 1, l, mid);
    	build(u << 1 | 1, mid + 1, r);
    	pushup(u);
    }
    
    void update(int u, int l, int r, const Mat& M) {
    	if (l <= tr[u].l && tr[u].r <= r) {
    		applyMat(M, tr[u].s);
    		tr[u].tag = M * tr[u].tag;
    		return;
    	}
    	pushdown(u);
    	int mid = (tr[u].l + tr[u].r) >> 1;
    	if (l <= mid) update(u << 1, l, r, M);
    	if (r > mid) update(u << 1 | 1, l, r, M);
    	pushup(u);
    }
    
    ll query(int u, int l, int r) {
    	if (l <= tr[u].l && tr[u].r <= r) {
    		return tr[u].s[0];
    	}
    	pushdown(u);
    	int mid = (tr[u].l + tr[u].r) >> 1;
    	ll res = 0;
    	if (l <= mid) res = (res + query(u << 1, l, r)) % mod;
    	if (r > mid) res = (res + query(u << 1 | 1, l, r)) % mod;
    	return res;
    }
    
    int main() {
    	ios::sync_with_stdio(false);
    	cin.tie(nullptr);
    	int n, m;
    	cin >> n >> m;
    	build(1, 1, n);
    	while (m--) {
    		int op, l, r;
    		cin >> op >> l >> r;
    		if (op == 1) {
    			ll v;
    			cin >> v;
    			if (v == 0) continue;
    			Mat M;
    			M.setMat(1, v);
    			update(1, l, r, M);
    		} else if (op == 3) {
    			ll v;
    			cin >> v;
    			if (v == 1) continue;
    			Mat M;
    			M.setMat(3, v);
    			update(1, l, r, M);
    		} else if (op == 4) {
    			Mat M;
    			M.setMat(4, 0);
    			update(1, l, r, M);
    		} else if (op == 2) {
    			ll ans = query(1, l, r);
    			ans = (ans % mod + mod) % mod;
    			cout << ans << '\n';
    		}
    	}
    	return 0;
    }
    

    信息

    ID
    193
    时间
    3000ms
    内存
    512MiB
    难度
    7
    标签
    递交数
    35
    已通过
    7
    上传者