洛谷 小白逛公园 线段树 最大子序列

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以前的普通做法是O(N^3)做法，同时也不会更新，这里用了线段树 + 单点更新。

题目链接

思路

用线段树维护一个子序列，同时进行更新。

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#include <set>
#include <map>
#include <ctime>
#include <queue>
#include <cmath>
#include <stack>
#include <bitset>
#include <vector>
#include <cstdio>
#include <sstream>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#define eps 1e-8
#define lc k * 2
#define rc k * 2 + 1
#define pi acos(-1.0)
#define ll long long
#define ull unsigned long long
using namespace std;
const int inf = 0x3f3f3f3f;
const int maxn = 500005;
struct Node
{
    int sum, max_sum, max_post, max_pre;
}tree[maxn * 4];
int a[maxn];
void pushup(int node)
{
    int ls = node << 1;
    int rs = node << 1|1;
    tree[node].sum = tree[ls].sum + tree[rs].sum;
    tree[node].max_post = max(tree[rs].max_post, tree[ls].max_post + tree[rs].sum);
    tree[node].max_pre = max(tree[ls].max_pre, tree[ls].sum + tree[rs].max_pre);
    tree[node].max_sum = max(tree[ls].max_sum, max(tree[rs].max_sum, tree[ls].max_post + tree[rs].max_pre));
}

void build(int node, int l, int r)
{
    if(l == r)
    {
        tree[node].max_post = tree[node].max_pre = a[l];
        tree[node].max_sum = tree[node].sum = a[l];
        return;
    }
    int mid = (l + r) >> 1;
    build(node << 1, l, mid);
    build(node << 1|1, mid + 1, r);
    pushup(node);
}

void update(int node, int l, int r, int pos, int k)
{
    if(l == r && l == pos)
    {
        tree[node].max_post = tree[node].max_pre =
        tree[node].max_sum = tree[node].sum = k;
        return;
    }
    int mid = (l + r) >> 1;
    if(pos <= mid)
        update(node << 1, l, mid, pos, k);
    else
        update(node << 1|1, mid + 1, r, pos, k);
    pushup(node);
}



Node query(int node, int l, int r, int ql, int qr)
{
    if(ql <= l && qr >= r)
    {
        return tree[node];
    }
    int mid = (l + r) >> 1;
    if(qr <= mid)
        return query(node << 1, l, mid, ql, qr);
    else if(ql > mid)
        return query(node <<1|1, mid + 1, r, ql, qr);
    else
    {
        Node ans, ls, rs;
        ls = query(node << 1, l, mid, ql, qr);
        rs = query(node <<1|1, mid + 1, r, ql, qr);
        ans.sum = ls.sum + rs.sum;
        ans.max_post = max(rs.max_post, ls.max_post + rs.sum);
        ans.max_pre = max(ls.max_pre, ls.sum + rs.max_pre);
        ans.max_sum = max(ls.max_sum, max(rs.max_sum, ls.max_post + rs.max_pre));
        return ans;
    }

}
int main()
{
    int n, m, k, p, s;
    scanf("%d %d",&n,&m);
    for(int i = 1; i <= n; ++i)
        scanf("%d",&a[i]);
    build(1, 1, n);
    for(int i = 1; i <= m; ++i)
    {
        scanf("%d%d%d",&k,&p,&s);
        if(k == 1)
        {
            if(p > s) swap(p,s);
            Node ans = query(1, 1, n, p, s);
            cout << ans.max_sum << '\n';
        }
        else
        {
            update(1,1,n, p, s);
        }
    }
}