2019 ICPC 南昌 (C E G L)
https://vjudge.net/contest/440183#overview
当天过了两道,一个签到的简单模拟(L),还有一个最大生成树(E).
C - And and Pair
给出长度为1e5的01串,要求满足:
的(i,j)有多少对.
数学题,运用排列组合,推导过程里出现了二项式定理.
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
#include <algorithm> #include <cstdio> #include <cstring> #include <iostream> #include <string> using namespace std; #define M 1000000007 string s; long long ksm(long long b, long long p){ long long ans = 1 % M; while(p){ if(p & 1) ans = (long long)ans * b % M; b = (long long)b * b % M; p >>= 1; } return ans; } void solve(){ cin >> s; reverse(s.begin(), s.end()); long long ct1 = 0, ct0 = 0, ans = 0; for(auto i = s.begin(); i != s.end(); i++){ auto c = *i; if(c == '1') { ans = (ans + ksm(3, ct1) * ksm(2, ct0)) % M; ct1++; }else ct0++; } printf("%lld\n", ans + 1); } int main(){ int t; scanf("%d", &t); while(t--) solve(); return 0; }
E - Bob's Problem
最小(大)生成树,这种题目再怎么变好像都不是很难.
可以看出来加黑边没有任何坏处,所以直接全部加上,在此后得到的图上使用Kruskal,首先检验一下在k条白边内能否得到生成树,如果不能则输出-1,否则把树生成出来,然后从大到小把剩下的(如果有)边的值加上去.
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
#include <algorithm> #include <cstdio> #include <cstring> #include <iostream> #include <queue> using namespace std; struct E{ int from, to, wei, col; bool operator<(const E&other) const {return wei > other.wei;} }; vector<E> e; queue<int> q; int n, m, k, fa[50010]; int get(int x) {return fa[x] == x ? x : fa[x] = get(fa[x]);} void merge(int x, int y) {fa[get(x)] = fa[get(y)];} void solve(){ e.clear(); while(!q.empty()) q.pop(); scanf("%d%d%d", &n, &m, &k); for(int i = 1; i <= n; i++) fa[i] = i; long long ans = 0; while(m--){ int u, v, w, c; scanf("%d%d%d%d", &u, &v, &w, &c); if(c == 0) { ans += w; merge(u, v); }else e.push_back({u, v, w, c}); } sort(e.begin(), e.end()); for(auto i = e.begin();k && i != e.end(); i++){ auto cur = *i; if(get(cur.from) == get(cur.to)) q.push(cur.wei); else { merge(cur.from, cur.to); ans += cur.wei; k--; } } while(k-- && !q.empty()){ ans += q.front(); q.pop(); } int ct = 0; for(int i = 1; i <= n; i++) if(fa[i] == i) ct++; if(ct == 1) printf("%lld\n", ans); else puts("-1"); } int main(){ int t; scanf("%d", &t); while(t--) solve(); return 0; }
G - Eating Plan
将一个1~n的排列中的每个数转化为其对应的阶乘,得到一个序列.要求从中选择连续的一段,使得该段上的值的和对998857459取模后不小于给定的k(序列不变,对k进行m次询问).
n,m均为1e5.
可以想一想,如果不考虑序列内都是排列的阶乘这一性质,即序列中的数是无规律的,这一问题可能没有合理的时间复杂度的求解方法.
答案是,这个模数有猫腻.
如果用下面的方法分解一下998857459的因数:
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
#include <algorithm> #include <cstdio> #include <cstring> #include <iostream> #include <set> using namespace std; int t = 998857459; set<int> s; int main(){ for(int i = 2; i < 10000000; i++) while(t % i == 0) t /= i, s.insert(i); for(auto i : s) cout << i << endl; return 0; }
会得到
461 773 2803
这意味着对于一个x>=2803,x!=1*2*3*...*461*...*773*...*2803*...*x,其对998857459取模后为0.
因此不管n有多大,最多有2803个值不是0,对于为0的数是很好处理的.
这种题目算是用来开眼界吧.
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
#include <algorithm> #include <cstdio> #include <cstring> #include <iostream> #include <queue> using namespace std; struct E{ int from, to, wei, col; bool operator<(const E&other) const {return wei > other.wei;} }; vector<E> e; queue<int> q; int n, m, k, fa[50010]; int get(int x) {return fa[x] == x ? x : fa[x] = get(fa[x]);} void merge(int x, int y) {fa[get(x)] = fa[get(y)];} void solve(){ e.clear(); while(!q.empty()) q.pop(); scanf("%d%d%d", &n, &m, &k); for(int i = 1; i <= n; i++) fa[i] = i; long long ans = 0; while(m--){ int u, v, w, c; scanf("%d%d%d%d", &u, &v, &w, &c); if(c == 0) { ans += w; merge(u, v); }else e.push_back({u, v, w, c}); } sort(e.begin(), e.end()); for(auto i = e.begin();k && i != e.end(); i++){ auto cur = *i; if(get(cur.from) == get(cur.to)) q.push(cur.wei); else { merge(cur.from, cur.to); ans += cur.wei; k--; } } while(k-- && !q.empty()){ ans += q.front(); q.pop(); } int ct = 0; for(int i = 1; i <= n; i++) if(fa[i] == i) ct++; if(ct == 1) printf("%lld\n", ans); else puts("-1"); } int main(){ int t; scanf("%d", &t); while(t--) solve(); return 0; }
L - Who is the Champion
签到,排个序就好.
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
#include <algorithm> #include <cstdio> #include <cstring> #include <iostream> using namespace std; int n, G[110][110]; struct T{ int num, dif, sco; bool operator<(const T& other) const {if(sco != other.sco) return sco > other.sco; return dif > other.dif;} }t[110]; int main(){ scanf("%d", &n); for(int i = 1; i <= n; i++) for(int j = 1; j <= n; j++){ scanf("%d", &G[i][j]); t[i].dif += G[i][j]; t[j].dif -= G[i][j]; t[i].num = i; } for(int i = 1; i <= n; i++) for(int j = 1; j <= n; j++){ if(G[i][j] > G[j][i]) t[i].sco += 3; else if(G[i][j] == G[j][i]) t[i].sco += 1; } sort(t + 1, t + 1 + n); if(t[1].sco == t[2].sco && t[1].dif == t[2].dif) puts("play-offs"); else printf("%d\n", t[1].num); return 0; }