codeforces div2 603 E. Editor(线段树)

题目链接：https://codeforces.com/contest/1263/problem/E

题意：一个编译器，每次输入一些字符，R表示光标右移，L表示光标左移，然后有一些左括号（  和 右括号 ），每次会询问当前输入的数据的括号是否合法，如果不合法输出-1，如果合法输出最大合法的括号对数，合法的括号就是（）这种形式的。

思路：大致思路是用线段树维护区间一个区间前缀和，初始化前缀和为0。遇到单点更新，（让管辖区间+1，）就让管辖区间-1，，判断是否是合法括号需要判断区间最小值是否为0，且保证1到n区间的前缀和为0（画图思考一下），满足两种条件的同时才能说明此为合法括号序列，最终查询区间最大值就是最大匹配的括号对数（画图思考）。

代码：

 #include<iostream>
 #include<cmath>
 #include<algorithm>
 #include<cstdio>
 #include<vector>
 #include<queue>
 #include<cstring>
 #include<set>
 #define inf 0x3f3f3f3f
 using namespace std;
 typedef long long LL;
 const int maxn = 1e6+;
 struct node{
     int l,r;
     int Min,Max;
     int val;
     int lazy;
 }tree[maxn*+];
 void pushdown(int index){
     if(tree[index].lazy){
         tree[index<<].val += (tree[index<<].r-tree[index<<].l+)*tree[index].lazy;
         tree[index<<|].val +=(tree[index<<|].r-tree[index<<|].l+)*tree[index].lazy;
         tree[index<<].Max += tree[index].lazy;
         tree[index<<|].Max += tree[index].lazy;
         tree[index<<].Min += tree[index].lazy;
         tree[index<<|].Min += tree[index].lazy;
         tree[index<<].lazy += tree[index].lazy;
         tree[index<<|].lazy += tree[index].lazy;
         tree[index].lazy = ;
     }
 }
 void pushup(int index){
     tree[index].val = tree[index<<].val+tree[index<<|].val;
     tree[index].Max = max(tree[index<<].Max,tree[index<<|].Max);
     tree[index].Min = min(tree[index<<].Min,tree[index<<|].Min);
 }

 void build(int l,int r,int index){//建树
     tree[index].l = l,tree[index].r = r,tree[index].lazy = ;
     if(l == r){
         //scanf("%d",&tree[index].val);
         tree[index].val = ;
         tree[index].Max = tree[index].Min = tree[index].val;
         return;
     }
     int mid = (l+r)>>;//
     build(l,mid,index<<);
     build(mid+,r,index<<|);
     pushup(index);
 }
 void update(int l,int r,int index,int val){//区间修改
     if(l <= tree[index].l && r >= tree[index].r){
         tree[index].val += (tree[index].r-tree[index].l+)*val;
         tree[index].Max += val;
         tree[index].Min += val;
         tree[index].lazy += val;//延时标记
         return ;
     }
     pushdown(index);
     int mid = (tree[index].l+tree[index].r)>>;
     if(l <= mid){
         update(l,r,index<<,val);
     }
     if(r > mid){
         update(l,r,index<<|,val);
     }
     pushup(index);
 }

 LL query_range(int l,int r,int index){//区间查询
     if(l <= tree[index].l && r >= tree[index].r){
         return tree[index].val;
         //return tree[index].mn;
     }
     pushdown(index);
     int mid = (tree[index].l+tree[index].r)>>;
     LL res = ;
     LL Max = ;
     LL Min = inf;
     if(l <= mid){
         res += query_range(l,r,index<<);
     }
     if(r > mid){
         res += query_range(l,r,index<<|);
     }
     return res;
 }

 LL query_max(int l,int r,int index){//最大值查询
     if(l<= tree[index].l && r>= tree[index].r ){
         return tree[index].Max;
     }
     pushdown(index);
     int mid = (tree[index].l + tree[index].r )>>;
     LL ans = ;
     LL MAX = ,MIN = inf;
     if(l <= mid) MAX = max(query_max(l,r,index<<),MAX);
     if(r > mid) MAX = max(query_max(l,r,index<<|),MAX);
     return MAX;
 }
 LL query_min(int l,int r,int index){//最小值查询
     if(l<= tree[index].l && r>= tree[index].r ){
         return tree[index].Min;
     }
     pushdown(index);
     int mid = (tree[index].l + tree[index].r )>>;
     LL ans = ;
     LL MAX = ,MIN = inf;
     if(l <= mid) MIN = min(query_min(l,r,index<<),MIN);
     if(r > mid) MIN = min(query_min(l,r,index<<|),MIN);
     return MIN;
 }
 string s;
 LL ss[maxn];
 int main(){
     int n;
     scanf("%d",&n);
     n = n+;
     build(,n,);
     cin>>s;
     int pos = ;
     vector<int> ans;
     for(int i = ;i<s.length() ;i++){
         if(s[i] == '('){
             update(pos,n,,-ss[pos]);
             ss[pos] = ;
         }
         else if(s[i] == ')'){
             update(pos,n,,--ss[pos]);
             ss[pos] = -;
         }
         else if(s[i] == 'R'){
             pos++;
         }
         else if(s[i] == 'L'){
             if(pos>) pos--;
         }
         else{
             if(ss[pos] == ){
                 update(pos,n,,-);
             }
             else if(ss[pos] == -){
                 update(pos,n,,);
             }
             ss[pos] = ;
         }
         if(query_min(,n,) ==  && query_range(n,n,) == ){
             ans.push_back(query_max(,n,));
         }
         else{
             ans.push_back(-);
         }
     }
     for(int i = ;i<ans.size() ;i++){
         cout<<ans[i]<<" ";
     }
     //cout<<endl;
     return ;
 }