2016 the 12th session of Hunan Province University student computer Program Design Competition---parenthesis (segment tree to find interval maximum)

Link to original topic

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

Descriptionbobo has a balanced parenthesis sequence p=p1 p2...pn of length N and q questions. The i-th question is whether P remains balanced after Pai and PBI swapped. Note that questions is individual so that they has no affect on others. Parenthesis Sequence S is balanced if and only if:1.S is empty;2.or there exists balanced parenthesis sequence A, b such that s=ab;3.or there exists balanced parenthesis sequence s ' such that s= (S ').Inputthe input contains at the most sets. For each set:the the first line contains the integers n,q (2≤n≤105,1≤q≤105). The second line contains n characters P1 p2...pn. The i-th of the last Q lines contains 2 integers ai,bi (1≤ai,bi≤n,ai≠bi).

Outputfor each question, output " Yes"If P remains balanced, or" No"otherwise. Sample Input

4 2 (()) 1 32 32 1 () 1 2

Sample Output

Noyesno

Source

The 12th session of Hunan Province College students computer Program design Contest

Test instructions: gave a balanced bracket sequence s (balance is the brace match OK) now Q, each time input two number A, B Q will s[a] s[b] After the swap whether the balance, the balance is output "Yes" otherwise output "No";

Idea: Define array num[], Num[i] represents the difference between the number of left brackets in s[1] to s[i] minus the number of closing brackets, and the analysis shows that because S is the balance bracket sequence, then num[i]>=0 a<b, then S[a] s[b, only num[a]~num[ B-1], and when Num[k]<0 (A<=K<B) is not balanced after the exchange, only s[a]= ' (' s[b]= ') can be switched on to num[k]<0.   So when s[a]= ' (' s[b]= '), the minimum value of the interval a~b-1 is calculated by the segment tree, when the minimum value is less than 2 o'clock, that is, what is the imbalance after the exchange? S[a]= ' (' s[b]= ') ' Exchange num[a]~num[b-1] minus 2;

The code is as follows:

#include <iostream>#include<algorithm>#include<cstdio>#include<cstring>#include<cmath>#defineEPS 1e-8#defineMAXN 105#defineINF 0x3f3f3f3f3f3f3f3f#defineIn Freopen ("In.txt", "R", stdin);using namespacestd;Chars[100005];intnum[100005];intb;structnode{//int l,r;    intv;} node[100005*4]; voidBuildintLintRinti) {    if(l==r) {node[i].v=Num[l]; return; }    intMid= (l+r) >>1; Build (L,mid,i<<1); Build (Mid+1,r,i<<1|1); NODE[I].V=min (node[i<<1].v,node[i<<1|1].v);} voidQueryintLintRint&tmp,inti) {    if(l>=a&&r<=b) {tmp=node[i].v;return; } intMid= (l+r) >>1; if(mid>=b) query (l,mid,tmp,i<<1); Else  if(mid<a) query (mid+1,r,tmp,i<<1|1); Else {          intTMP2; Query (L,mid,tmp,i<<1); Query (Mid+1,r,tmp2,i<<1|1); TMP=min (TMP,TMP2); }} intMain () {intn,q;  while(SCANF ("%d%d", &n,&q)! =EOF) {scanf ("%s", s+1); num[0]=0;  for(intI=1; i<=n;i++) {Num[i]=num[i-1]; if(s[i]=='(') num[i]++; Elsenum[i]--; } Build (1N1);  while(q--) {scanf ("%d%d",&a,&b); if(a>b) Swap (A, a); if(s[a]==s[b]| | s[a]==')'&&s[b]=='(') puts ("Yes"); Else{b--; inttmp=99999999; Query (1, N,tmp,1); if(tmp<2) puts ("No"); ElsePuts"Yes"); }        }    }    return 0;}/**8 8 (()) (()) 2 7*/

2016 the 12th session of Hunan Province University student computer Program Design Competition---parenthesis (segment tree to find interval maximum)