NC51097. Parity game
描述
输入描述
The first line of input contains one number, which is the length of the sequence of zeroes and ones. This length is less or equal to 1000000000. In the second line, there is one positive integer which is the number of questions asked and answers to them. The number of questions and answers is less or equal to 5000. The remaining lines specify questions and answers. Each line contains one question and the answer to this question: two integers (the position of the first and last digit in the chosen subsequence) and one word which is either `even' or `odd' (the answer, i.e. the parity of the number of ones in the chosen subsequence, where `even' means an even number of ones and `odd' means an odd number).
输出描述
There is only one line in output containing one integer X. Number X says that there exists a sequence of zeroes and ones satisfying first X parity conditions, but there exists none satisfying X+1 conditions. If there exists a sequence of zeroes and ones satisfying all the given conditions, then number X should be the number of all the questions asked.
示例1
输入:
10 5 1 2 even 3 4 odd 5 6 even 1 6 even 7 10 odd
输出:
3
C++(g++ 7.5.0) 解法, 执行用时: 17ms, 内存消耗: 7072K, 提交时间: 2023-07-25 18:56:04
#include<iostream> #include<cstdio> #include<cstring> #include<algorithm> #include<map> using namespace std; #define N 200010 struct node{ int fa,re; }; int n,q,m,num,a[N],b[N]; string s[N]; map<int,node>p; int root(int x){ if(x==p[x].fa)return x; int tmp=p[x].fa; p[x].fa=root(tmp); p[x].re=(p[x].re+p[tmp].re)%2; return p[x].fa; } void solve(){ cin>>n>>q; for(int i=1;i<=q;i++){ cin>>a[i]>>b[i]>>s[i]; a[i]--; p[a[i]].re=0,p[a[i]].fa=a[i]; p[b[i]].re=0,p[b[i]].fa=b[i]; } for(int i=1;i<=q;i++){ int x,y,z; x=a[i]; y=b[i]; z=s[i][0]=='o'?1:0; int rx=root(x),ry=root(y); if(rx!=ry){ p[rx].fa=ry; p[rx].re=(p[x].re+p[y].re+z)%2; }else{ if(p[x].re!=(p[y].re+z)%2){ cout<<i-1; return ; } } } cout<<q; } signed main(){ ios::sync_with_stdio(0); cin.tie(0); solve(); return 0; }
C++14(g++5.4) 解法, 执行用时: 12ms, 内存消耗: 996K, 提交时间: 2020-03-08 20:21:02
#include<iostream> #include<cstring> #include<map> #include<cstdio> using namespace std; map<int,int>fa; map<int,int>cnt; int findfather(int v) { if(fa[v]==0||fa[v]==v)return fa[v]=v; int pp=findfather(fa[v]); cnt[v]=cnt[v]+cnt[fa[v]]; cnt[v]&=1; fa[v]=pp; return pp; } int main() { int x,n; cin>>x>>n; for(int i=1;i<=n;i++) { int p,q; char r[15]={0}; scanf("%d%d%s",&p,&q,r); q++; int flg=1; if(r[0]=='e')flg=0; int p1=findfather(p),q1=findfather(q); if(p1==q1) { if(cnt[p]!=((cnt[q]+flg)&1))printf("%d\n",i-1); else continue; return 0; }else { cnt[q1]=(cnt[q]!=flg); fa[q1]=p; } } printf("%d\n",n); return 0; }
Python3 解法, 执行用时: 104ms, 内存消耗: 5508K, 提交时间: 2023-05-22 15:30:48
n = int(input()) n += 1 t = int(input()) root = {} def find(x): if x!=root[x]: root[x] = find(root[x]) return root[x] def union(a, b): root[find(a)] = find(b) ans = t for i in range(t): a, b, c = input().split() a, b = int(a), int(b) if b not in root: root[b] = b root[b+n] = b+n if a-1 not in root: root[a-1] = a-1 root[a-1+n] = a-1+n if c=='even': if find(a-1)==find(b+n) or find(a-1+n)==find(b): ans = i break else: union(a-1, b) union(a-1+n, b+n) else: if find(a-1)==find(b) or find(a-1+n)==find(b+n): ans = i break else: union(a-1, b+n) union(a-1+n, b) print(ans)
C++ 解法, 执行用时: 9ms, 内存消耗: 524K, 提交时间: 2022-01-07 11:54:01
#include<bits/stdc++.h> using namespace std; int fa[20001],m,n,a[20001],t; char st[20001]; struct node{int l,r,ty;}que[10001]; int ft(int x){return x==fa[x]?x:fa[x]=ft(fa[x]);} int main(){ cin>>m>>n; for(int i=1;i<=n;i++)cin>>que[i].l>>que[i].r>>st,que[i].ty=(st[0]=='o'?1:0),a[++t]=que[i].l-1,a[++t]=que[i].r; sort(a+1,a+t+1); m=unique(a+1,a+t+1)-a-1; for(int i=1;i<=2*m;i++)fa[i]=i; for(int i=1;i<=n;i++){ int x=lower_bound(a+1,a+m+1,que[i].l-1)-a,y=lower_bound(a+1,a+m+1,que[i].r)-a,xx=x+m,yy=y+m; if(que[i].ty==1){if(ft(x)==ft(y))cout<<i-1,exit(0);fa[ft(x)]=ft(yy);fa[ft(xx)]=ft(y);} else{if(ft(x)==ft(yy))cout<<i-1,exit(0);fa[ft(x)]=ft(y);fa[ft(xx)]=ft(yy);} } cout<<n; return 0; }