线段树

静态区间查询

F. Maximum modulo equality

https://codeforces.com/contest/2050/problem/F

#include<bits/stdc++.h>
using namespace std;
using u32 = unsigned;
#define i128 __int128
using ll = long long;
//#define int ll
using u64 = unsigned long long;
const ll inf = 1e9;
const ll INF = 1e18;
template<class Info>
struct SegmentTree {
    int n;
    std::vector<Info> info;
    SegmentTree() : n(0) {}
    SegmentTree(int n_, Info v_ = Info()) {
        init(n_, v_);
    }
    template<class T>
    SegmentTree(std::vector<T> init_) {
        init(init_);
    }
    void init(int n_, Info v_ = Info()) {
        init(std::vector(n_, v_));
    }
    template<class T>
    void init(std::vector<T> init_) {
        n = init_.size();
        info.assign(4 << std::__lg(n), Info());
        std::function<void(int, int, int)> build = [&](int p, int l, int r) {
            if (r - l == 1) {
                info[p] = init_[l];
                return;
            }
            int m = (l + r) / 2;
            build(2 * p, l, m);
            build(2 * p + 1, m, r);
            pull(p);
        };
        build(1, 0, n);
    }
    void pull(int p) {
        info[p] = info[2 * p] + info[2 * p + 1];
    }
    void modify(int p, int l, int r, int x, const Info &v) {
        if (r - l == 1) {
            info[p] = v;
            return;
        }
        int m = (l + r) / 2;
        if (x < m) {
            modify(2 * p, l, m, x, v);
        } else {
            modify(2 * p + 1, m, r, x, v);
        }
        pull(p);
    }
    void modify(int p, const Info &v) {
        modify(1, 0, n, p, v);
    }
    Info rangeQuery(int p, int l, int r, int x, int y) {
        if (l >= y || r <= x) {
            return Info();
        }
        if (l >= x && r <= y) {
            return info[p];
        }
        int m = (l + r) / 2;
        return rangeQuery(2 * p, l, m, x, y) + rangeQuery(2 * p + 1, m, r, x, y);
    }
    Info rangeQuery(int l, int r) {
        return rangeQuery(1, 0, n, l, r);
    }
    template<class F>
    int findFirst(int p, int l, int r, int x, int y, F pred) {
        if (l >= y || r <= x || !pred(info[p])) {
            return -1;
        }
        if (r - l == 1) {
            return l;
        }
        int m = (l + r) / 2;
        int res = findFirst(2 * p, l, m, x, y, pred);
        if (res == -1) {
            res = findFirst(2 * p + 1, m, r, x, y, pred);
        }
        return res;
    }
    template<class F>
    int findFirst(int l, int r, F pred) {
        return findFirst(1, 0, n, l, r, pred);
    }
    template<class F>
    int findLast(int p, int l, int r, int x, int y, F pred) {
        if (l >= y || r <= x || !pred(info[p])) {
            return -1;
        }
        if (r - l == 1) {
            return l;
        }
        int m = (l + r) / 2;
        int res = findLast(2 * p + 1, m, r, x, y, pred);
        if (res == -1) {
            res = findLast(2 * p, l, m, x, y, pred);
        }
        return res;
    }
    template<class F>
    int findLast(int l, int r, F pred) {
        return findLast(1, 0, n, l, r, pred);
    }
};
struct Info {
    int g;
};
Info operator+(Info a, Info b) {
    return {gcd(a.g,b.g)};
}

void solve(){
    int n,q;
    cin>>n>>q;
    vector<int>a(n+1);
    for(int i=1;i<=n;i++)cin>>a[i];
    vector<Info>init(n);
    for(int i=0;i<n;i++)init[i].g=abs(a[i+1]-a[i]);
    SegmentTree<Info>seg(init);
    for(int i=1;i<=q;i++)
    {
        int l,r;
        cin>>l>>r;
        cout<<seg.rangeQuery(l,r).g<<" \n"[i==q];
    }
    
}

signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int tt;cin>>tt;
    while(tt--){
        solve();
    }


    return 0;    
}

P3865 【模板】ST 表 && RMQ 问题

https://www.luogu.com.cn/problem/P3865

线段树做法

#include<bits/stdc++.h>
using namespace std;
using u32 = unsigned;
#define i128 __int128;
using ll = long long;
//#define int ll
using u64 = unsigned long long;
const ll inf = 1e9;
const ll INF = 1e18;
template<class Info>
struct SegmentTree {
    int n;
    std::vector<Info> info;
    SegmentTree() : n(0) {}
    SegmentTree(int n_, Info v_ = Info()) {
        init(n_, v_);
    }
    template<class T>
    SegmentTree(std::vector<T> init_) {
        init(init_);
    }
    void init(int n_, Info v_ = Info()) {
        init(std::vector(n_, v_));
    }
    template<class T>
    void init(std::vector<T> init_) {
        n = init_.size();
        info.assign(4 << std::__lg(n), Info());
        std::function<void(int, int, int)> build = [&](int p, int l, int r) {
            if (r - l == 1) {
                info[p] = init_[l];
                return;
            }
            int m = (l + r) / 2;
            build(2 * p, l, m);
            build(2 * p + 1, m, r);
            pull(p);
        };
        build(1, 0, n);
    }
    void pull(int p) {
        info[p] = info[2 * p] + info[2 * p + 1];
    }
    void modify(int p, int l, int r, int x, const Info &v) {
        if (r - l == 1) {
            info[p] = v;
            return;
        }
        int m = (l + r) / 2;
        if (x < m) {
            modify(2 * p, l, m, x, v);
        } else {
            modify(2 * p + 1, m, r, x, v);
        }
        pull(p);
    }
    void modify(int p, const Info &v) {
        modify(1, 0, n, p, v);
    }
    Info rangeQuery(int p, int l, int r, int x, int y) {
        if (l >= y || r <= x) {
            return Info();
        }
        if (l >= x && r <= y) {
            return info[p];
        }
        int m = (l + r) / 2;
        return rangeQuery(2 * p, l, m, x, y) + rangeQuery(2 * p + 1, m, r, x, y);
    }
    Info rangeQuery(int l, int r) {
        return rangeQuery(1, 0, n, l, r);
    }
    template<class F>
    int findFirst(int p, int l, int r, int x, int y, F pred) {
        if (l >= y || r <= x || !pred(info[p])) {
            return -1;
        }
        if (r - l == 1) {
            return l;
        }
        int m = (l + r) / 2;
        int res = findFirst(2 * p, l, m, x, y, pred);
        if (res == -1) {
            res = findFirst(2 * p + 1, m, r, x, y, pred);
        }
        return res;
    }
    template<class F>
    int findFirst(int l, int r, F pred) {
        return findFirst(1, 0, n, l, r, pred);
    }
    template<class F>
    int findLast(int p, int l, int r, int x, int y, F pred) {
        if (l >= y || r <= x || !pred(info[p])) {
            return -1;
        }
        if (r - l == 1) {
            return l;
        }
        int m = (l + r) / 2;
        int res = findLast(2 * p + 1, m, r, x, y, pred);
        if (res == -1) {
            res = findLast(2 * p, l, m, x, y, pred);
        }
        return res;
    }
    template<class F>
    int findLast(int l, int r, F pred) {
        return findLast(1, 0, n, l, r, pred);
    }
};
struct Info {
    int g;
};
Info operator+(Info a, Info b) {
    return {max(a.g,b.g)};
}

signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n,m;
    cin>>n>>m;
    vector<Info>init(n);
    for(int i=0;i<n;i++)cin>>init[i].g;    
    SegmentTree<Info>seg(init);
    for(int i=1;i<=m;i++)
    {
        int l,r;
        cin>>l>>r;
        cout<<seg.rangeQuery(l-1,r).g<<'\n';
    }
    return 0;    
}

ST表

#include<bits/stdc++.h>
using namespace std;
using u32 = unsigned;
#define i128 __int128;
using ll = long long;
#define int ll
using u64 = unsigned long long;
const int inf = 2147483647;
const ll INF = 1e18;

signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n,m;
    cin>>n>>m;
    vector<vector<int>>dp(n+1,vector<int>(22));
    for(int i=1;i<=n;i++)cin>>dp[i][0];
    for(int len=1;len<=20;len++)
    {
        for(int i=1;(i+(1<<len)-1)<=n;i++)
        {
            dp[i][len]=max(dp[i][len-1],dp[i+(1<<(len-1))][len-1]);
        }
    }
    for(int i=1;i<=m;i++)
    {
        int l,r;
        cin>>l>>r;
        int k=log2(r-l+1);
        cout<<max(dp[l][k],dp[r-(1<<k)+1][k])<<'\n';
    }

    return 0;    
}

区间修改区间查询

P3372 【模板】线段树 1

https://www.luogu.com.cn/problem/P3372

线段树

```



#### 树状数组

```cpp
#include<bits/stdc++.h>
using namespace std;
using u32 = unsigned;
#define i128 __int128;
using ll = long long;
#define int ll
using u64 = unsigned long long;
const ll inf = 1e9;
const ll INF = 1e18;
template<typename T>
struct Fenwick{
    int n;
    vector<T> tr;
 
    Fenwick(int n) : n(n), tr(n + 1, 0){}
 
    int lowbit(int x){// 找到x最低有效位
        return x & -x;
    }
 
    void modify(int x, T c){// 点修
        for(int i = x; i <= n; i += lowbit(i)) tr[i] += c;
    }
 
    void modify(int l, int r, T c){// 区修
        modify(l, c);
        if (r + 1 <= n) modify(r + 1, -c);
    }
 
    T query(int x){// 前缀和
        T res = T();
        for(int i = x; i; i -= lowbit(i)) res += tr[i];
        return res;
    }
 
    T query(int l, int r){// 区间查询
        return query(r) - query(l - 1);
    }
 
    int find_first(T sum){// 查找第一个前缀和大于或等于 sum 的下标
        int ans = 0; T val = 0;
        for(int i = __lg(n); i >= 0; i--){
            if ((ans | (1 << i)) <= n && val + tr[ans | (1 << i)] < sum){
                ans |= 1 << i;
                val += tr[ans];
            }
        }
        return ans + 1;
    }
 
    int find_last(T sum){// 查找最后一个前缀和小于或等于 sum 的下标
        int ans = 0; T val = 0;
        for(int i = __lg(n); i >= 0; i--){
            if ((ans | (1 << i)) <= n && val + tr[ans | (1 << i)] <= sum){
                ans |= 1 << i;
                val += tr[ans];
            }
        }
        return ans;
    }
 
};
using BIT = Fenwick<int>;
signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n,m;
    cin>>n>>m;
    BIT d1(n),d2(n);
    vector<int>a(n+1);
    for(int i=1;i<=n;i++)cin>>a[i];    
    for(int i=1;i<=n;i++)
    {
        d1.modify(i,a[i]);
        d1.modify(i+1,-a[i]);
        d2.modify(i,i*a[i]);
        d2.modify(i+1,-(i+1)*a[i]);
    }
    for(int i=1;i<=m;i++)
    {
        int op,x,y;
        cin>>op>>x>>y;
        if(op==1)
        {
            int k;
            cin>>k;
            d1.modify(x,k);
            d1.modify(y+1,-k);
            d2.modify(x,k*x);
            d2.modify(y+1,-k*(y+1));
        }
        else
        {
            cout<<(y+1ll)*d1.query(y)-1ll*x*d1.query(x-1)-(d2.query(y)-d2.query(x-1))<<'\n';
        }
    }
    return 0;    
}