Spoj 1557 Can you answer these queries II 线段树 随意区间最大子段和 不反复数字
2024-08-30 07:05:42
题目链接:点击打开链接
每一个点都是最大值,把一整个序列和都压缩在一个点里。
1、普通的区间求和就是维护2个值,区间和Sum和延迟标志Lazy
2、Old 是该区间里出现过最大的Sum, Oldlazy 是对于给下一层的子区间的标志,添加多少是能给子区间添加的值最大的(用来维护Old)
显然对于Old 。要么维持原样,要么更新为稍新的值:即 Sum(id) + Oldlazy
而对于Oldlazy, 要么维持原样,要么变成最新的延迟标记:即 Lazy(id) + Oldlazy
上2行的Oldlazy都是指对这个tree[id]有效的,即他们父节点的Oldlazy - > Oldlazy( id / 2 )
#include <vector>
#include <iostream>
#include <algorithm>
#include <string.h>
#include <stdio.h>
using namespace std;
#define N 100005
#define Lson(x) (x<<1)
#define Rson(x) (x<<1|1)
#define L(x) tree[x].l
#define R(x) tree[x].r
#define Old(x) tree[x].old
#define Sum(x) tree[x].sum
#define Lazy(x) tree[x].lazy
#define Olazy(x) tree[x].oldlazy
inline int Mid(int l, int r){return (l+r)>>1;}
struct Subtree{
int l, r;
int old, oldlazy, sum, lazy;
}tree[N<<2];
void push_down(int id){
if(L(id) == R(id)) return ;
if(Lazy(id) || Olazy(id)){
Olazy(Lson(id)) = max(Olazy(Lson(id)), Lazy(Lson(id)) + Olazy(id));
Old(Lson(id)) = max(Old(Lson(id)), Sum(Lson(id)) + Olazy(id));
Lazy(Lson(id)) += Lazy(id); Sum(Lson(id)) += Lazy(id); Olazy(Rson(id)) = max(Olazy(Rson(id)), Lazy(Rson(id)) + Olazy(id));
Old(Rson(id)) = max(Old(Rson(id)), Sum(Rson(id)) + Olazy(id));
Lazy(Rson(id)) += Lazy(id); Sum(Rson(id)) += Lazy(id);
Lazy(id) = Olazy(id) = 0;
}
}
void push_up(int id){
if(L(id) == R(id)) return ;
Old(id) = max(Old(Lson(id)), Old(Rson(id)));
Sum(id) = max(Sum(Lson(id)), Sum(Rson(id)));
}
void build(int l, int r, int id){
L(id) = l; R(id) = r;
Sum(id) = Old(id) = Lazy(id) = Olazy(id) = 0;
if(l == r) return ;
int mid = Mid(l, r);
build(l, mid, Lson(id)); build(mid+1, r, Rson(id));
}
void updata(int l, int r, int val, int id){
push_down(id);
if(l == L(id) && R(id) == r) {
Sum(id) += val;
Lazy(id) += val;
Olazy(id) = max(Olazy(id), Lazy(id));
Old(id) = max(Old(id), Sum(id));
return ;
}
int mid = Mid(L(id), R(id));
if(mid < l)
updata(l, r, val, Rson(id));
else if(r <= mid)
updata(l, r, val, Lson(id));
else {
updata(l, mid, val, Lson(id));
updata(mid+1, r, val, Rson(id));
}
push_up(id);
}
int Query(int l, int r, int id){
push_down(id);
if(l == L(id) && R(id) == r) return Old(id);
int ans , mid = Mid(L(id), R(id));
if(mid < l)
ans = Query(l, r, Rson(id));
else if(r <= mid)
ans = Query(l, r, Lson(id));
else
ans = max(Query(l, mid, Lson(id)), Query(mid+1, r, Rson(id)));
push_up(id);
return ans;
}
int a[N], n, las[N<<1];
struct node{
int l, r, num, ans;
}query[N];
bool cmp1(node a, node b){return a.r < b.r;}
bool cmp2(node a, node b){return a.num < b.num;}
void solve(){
int i, q;
for(i = 1; i <= n; i++)scanf("%d",&a[i]);
build(1, n, 1);
scanf("%d",&q);
for(i = 1; i <= q; i++)scanf("%d %d",&query[i].l, &query[i].r), query[i].num = i;
sort(query+1, query+q+1, cmp1);
int top = 1;
memset(las, 0, sizeof las);
for(i = 1; i <= n && top <= q; i++){
updata(las[a[i]+N]+1, i, a[i], 1);
las[a[i]+N] = i;
while(query[top].r == i && top <= q){
query[top].ans = Query(query[top].l, query[top].r, 1);
top++;
}
}
sort(query+1, query+q+1, cmp2);
for(i = 1; i <= q; i++)printf("%d\n", query[i].ans);
}
int main(){
while(~scanf("%d",&n))
solve();
return 0;
}
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