[CSU1809] Parenthesis（RMQ）

Posted 2020-08-06

题目链接：http://acm.csu.edu.cn/OnlineJudge/problem.php?id=1809

题意：给一个长为n的匹配好的括号串，q个询问，每次询问交换一对括号。问交换后是否依然匹配。

维护一个数组b和一个数，表示当前字符串下左右匹配过后左括号剩余的数量。更新的时候遇到左括号则++cnt，否则--cnt。交换l,r则在区间内查询[l,r-1]，看看最小值是否是<2。

  1 /*
  2 ━━━━━┒ギリギリ♂ eye！
  3 ┓┏┓┏┓┃キリキリ♂ mind！
  4 ┛┗┛┗┛┃＼○／
  5 ┓┏┓┏┓┃ /
  6 ┛┗┛┗┛┃ノ)
  7 ┓┏┓┏┓┃
  8 ┛┗┛┗┛┃
  9 ┓┏┓┏┓┃
 10 ┛┗┛┗┛┃
 11 ┓┏┓┏┓┃
 12 ┛┗┛┗┛┃
 13 ┓┏┓┏┓┃
 14 ┃┃┃┃┃┃
 15 ┻┻┻┻┻┻
 16 */
 17 #include <algorithm>
 18 #include <iostream>
 19 #include <iomanip>
 20 #include <cstring>
 21 #include <climits>
 22 #include <complex>
 23 #include <fstream>
 24 #include <cassert>
 25 #include <cstdio>
 26 #include <bitset>
 27 #include <vector>
 28 #include <deque>
 29 #include <queue>
 30 #include <stack>
 31 #include <ctime>
 32 #include <set>
 33 #include <map>
 34 #include <cmath>
 35 using namespace std;
 36 #define fr first
 37 #define sc second
 38 #define cl clear
 39 #define BUG puts("here!!!")
 40 #define W(a) while(a--)
 41 #define pb(a) push_back(a)
 42 #define Rint(a) scanf("%d", &a)
 43 #define Rll(a) scanf("%I64d", &a)
 44 #define Rs(a) scanf("%s", a)
 45 #define Cin(a) cin >> a
 46 #define FRead() freopen("in", "r", stdin)
 47 #define FWrite() freopen("out", "w", stdout)
 48 #define Rep(i, len) for(int i = 0; i < (len); i++)
 49 #define For(i, a, len) for(int i = (a); i < (len); i++)
 50 #define Cls(a) memset((a), 0, sizeof(a))
 51 #define Clr(a, x) memset((a), (x), sizeof(a))
 52 #define Full(a) memset((a), 0x7f7f7f, sizeof(a))
 53 #define lrt rt << 1
 54 #define rrt rt << 1 | 1
 55 #define pi 3.14159265359
 56 #define RT return
 57 #define lowbit(x) x & (-x)
 58 #define onecnt(x) __builtin_popcount(x)
 59 typedef long long LL;
 60 typedef long double LD;
 61 typedef unsigned long long ULL;
 62 typedef pair<int, int> pii;
 63 typedef pair<string, int> psi;
 64 typedef pair<LL, LL> pll;
 65 typedef map<string, int> msi;
 66 typedef vector<int> vi;
 67 typedef vector<LL> vl;
 68 typedef vector<vl> vvl;
 69 typedef vector<bool> vb;
 70  
 71 #define lson l,m,lrt
 72 #define rson m+1,r,rrt
 73 const int maxn = 200100;
 74 int n, q;
 75 char s[maxn];
 76 int b[maxn];
 77 int sum[maxn<<2];
 78  
 79 void pushUP(int rt) {
 80     sum[rt] = min(sum[rt<<1], sum[rt<<1|1]);
 81 }
 82  
 83 void build(int l, int r, int rt) {
 84     if(l == r) {
 85         sum[rt] = b[l];
 86         return;
 87     }
 88     int m = (l + r) >> 1;
 89     build(lson);
 90     build(rson);
 91     pushUP(rt);
 92 }
 93  
 94 int query(int L, int R, int l, int r, int rt) {
 95     if(L <= l && r <= R) return sum[rt];
 96     int m = (l + r) >> 1;
 97     int ret = 0x7f7f7f7f;
 98     if(L <= m) ret = min(ret, query(L, R, lson));
 99     if(R > m) ret = min(ret, query(L, R, rson));
100     return ret;
101 }
102  
103 signed main() {
104     // FRead();
105     int u, v;
106     while(~Rint(n)&&~Rint(q)) {
107         Cls(b); Rs(s+1);
108         int cnt = 0;
109         For(i, 1, n+1) {
110             if(s[i] == ‘(‘) b[i] = ++cnt;
111             else b[i] = --cnt;
112         }
113         build(1, n, 1);
114         W(q) {
115             Rint(u); Rint(v);
116             if(u > v) swap(u, v);
117             if((s[u]==‘)‘&&s[v]==‘(‘)||(s[u]==s[v])) {
118                 puts("Yes");
119                 continue;
120             }
121             int ret = query(u, v-1, 1, n, 1);
122             if(ret < 2) puts("No");
123             else puts("Yes");
124         }
125     }
126     RT 0;
127 }