2018 AICCSA Programming Contest

A Tree Game

B Rectangles

思路:如果存在大于0的交面积的话, 那么肯定能找到一条水平的直线 和 一条垂直的直线,

使得水平直线的左右两边点的个数相等且为n, 垂直直线的左右两边点的个数相等且为n

也就是说不能有点在这两条线上, 否则交面积为0

然后左上角的点和右下角的点配对, 左下角的点和右上角的点配对

代码:

  1. #pragma GCC optimize(2)
  2. #pragma GCC optimize(3)
  3. #pragma GCC optimize(4)
  4. #include<bits/stdc++.h>
  5. using namespace std;
  6. #define fi first
  7. #define se second
  8. #define pi acos(-1.0)
  9. #define LL long long
  10. //#define mp make_pair
  11. #define pb push_back
  12. #define ls rt<<1, l, m
  13. #define rs rt<<1|1, m+1, r
  14. #define ULL unsigned LL
  15. #define pll pair<LL, LL>
  16. #define pli pair<LL, int>
  17. #define pii pair<int, int>
  18. #define piii pair<pii, int>
  19. #define mem(a, b) memset(a, b, sizeof(a))
  20. #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  21. #define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);
  22. //head
  23.  
  24. const int N = 2e5 + , M = 1e5 + ;
  25. const int MOD = 1e9 + ;
  26. pii a[N];
  27. int fac[M];
  28. bool cmp(pii a, pii b) {
  29.     return a.se < b.se;
  30. }
  31. void init() {
  32.     fac[] = ;
  33.     for (int i = ; i < M; i++) fac[i] = (1LL * fac[i-] * i) % MOD;
  34. }
  35. int main() {
  36.     int T, n;
  37.     init();
  38.     scanf("%d", &T);
  39.     while(T--) {
  40.         scanf("%d", &n);
  41.         for (int i = ; i <= *n; i++) scanf("%d %d", &a[i].fi, &a[i].se);
  42.         bool f = false;
  43.         sort(a+, a++*n);
  44.         double x = , y = ;
  45.         if(a[n].fi != a[n+].fi) x = (a[n].fi + a[n+].fi) / 2.0;
  46.         else f = true;
  47.  
  48.         sort(a+, a++*n, cmp);
  49.         if(a[n].se != a[n+].se) y = (a[n].se + a[n+].se) / 2.0;
  50.         else f = true;
  51.         int cnt = ;
  52.         for (int i = ; i <= *n; i++) if(a[i].fi > x && a[i].se > y) cnt++;
  53.         if(f) printf("0\n");
  54.         else printf("%lld\n", (1LL * fac[cnt] * fac[n-cnt]) % MOD);
  55.     }
  56.     return ;
  57. }

C Function

思路:打表找规律, 发现ai的系数为C(n+1, i) - 1

代码:

  1. #pragma GCC optimize(2)
  2. #pragma GCC optimize(3)
  3. #pragma GCC optimize(4)
  4. #include<bits/stdc++.h>
  5. using namespace std;
  6. #define fi first
  7. #define se second
  8. #define pi acos(-1.0)
  9. #define LL long long
  10. //#define mp make_pair
  11. #define pb push_back
  12. #define ls rt<<1, l, m
  13. #define rs rt<<1|1, m+1, r
  14. #define ULL unsigned LL
  15. #define pll pair<LL, LL>
  16. #define pli pair<LL, int>
  17. #define pii pair<int, int>
  18. #define piii pair<pii, int>
  19. #define mem(a, b) memset(a, b, sizeof(a))
  20. #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  21. #define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);
  22. //head
  23.  
  24. const int N = 1e6 + ;
  25. const int MOD = 1e9 + ;
  26. int a[N];
  27. LL fac[N], inv[N];
  28. LL q_pow(LL n, LL k) {
  29.     LL ans = ;
  30.     while(k) {
  31.         if(k&) ans = (ans * n) % MOD;
  32.         n = (n * n) % MOD;
  33.         k >>= ;
  34.     }
  35.     return ans;
  36. }
  37. void init() {
  38.     fac[] = ;
  39.     for (int i = ; i < N; i++) fac[i] = fac[i-] * i % MOD;
  40.     inv[N-] = q_pow(fac[N-], MOD-);
  41.     for (int i = N-; i >= ; i--) inv[i] = inv[i+] * (i+) % MOD;
  42. }
  43. LL C(int n, int m) {
  44.     return fac[n] * inv[m] % MOD * inv[n-m] % MOD;
  45. }
  46. int main() {
  47.     int T;
  48.     init();
  49.     scanf("%d", &T);
  50.     while(T--) {
  51.         int n;
  52.         scanf("%d", &n);
  53.         for (int i = ; i <= n; i++) scanf("%d", &a[i]);
  54.         LL ans = ;
  55.         for (int i = ; i <= n; i++) {
  56.             (ans = ans + (C(n+, i) - ) * a[i] % MOD) %= MOD;
  57.         }
  58.         printf("%lld\n", (ans + MOD) % MOD);
  59.     }
  60.     return ;
  61. }

D Two Sequences

思路:将a数组放到集合里, 方便查找删除

代码:

  1. #pragma GCC optimize(2)
  2. #pragma GCC optimize(3)
  3. #pragma GCC optimize(4)
  4. #include<bits/stdc++.h>
  5. using namespace std;
  6. #define fi first
  7. #define se second
  8. #define pi acos(-1.0)
  9. #define LL long long
  10. //#define mp make_pair
  11. #define pb push_back
  12. #define ls rt<<1, l, m
  13. #define rs rt<<1|1, m+1, r
  14. #define ULL unsigned LL
  15. #define pll pair<LL, LL>
  16. #define pli pair<LL, int>
  17. #define pii pair<int, int>
  18. #define piii pair<pii, int>
  19. #define mem(a, b) memset(a, b, sizeof(a))
  20. #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  21. #define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);
  22. //head
  23.  
  24. const int N = 1e5 + ;
  25. int a[N], b[N];
  26. multiset<int> s;
  27. vector<int> vc;
  28. int main() {
  29.     int T, n, k;
  30.     scanf("%d", &T);
  31.     while(T--) {
  32.         scanf("%d %d", &n, &k);
  33.         s.clear();
  34.         vc.clear();
  35.         for (int i = ; i <= n; i++) scanf("%d", &a[i]), s.insert(a[i]);
  36.         for (int i = ; i <= n; i++) scanf("%d", &b[i]);
  37.         for (int i = ; i <= n; i++) {
  38.             multiset<int>:: iterator it = s.lower_bound(b[i]);
  39.             if(it == s.end() || *it != b[i]) {
  40.                 vc.pb(b[i]);
  41.             }
  42.             else s.erase(it);
  43.         }
  44.         if((int)vc.size() == ) puts("YES");
  45.         else if((int)vc.size() == ) {
  46.             if(*s.begin() - k <= vc[] && vc[] <= *s.begin() + k) puts("YES");
  47.             else puts("NO");
  48.         }
  49.         else puts("NO");
  50.     }
  51.     return ;
  52. }

E Connecting Components

F Mirror

G TeddyBearsDay

思路:对于每个点, 它连向父亲的边只有当它的子树中不能自销的多余部分才会用到

代码:

  1. #pragma GCC optimize(2)
  2. #pragma GCC optimize(3)
  3. #pragma GCC optimize(4)
  4. #include<bits/stdc++.h>
  5. using namespace std;
  6. #define fi first
  7. #define se second
  8. #define pi acos(-1.0)
  9. #define LL long long
  10. //#define mp make_pair
  11. #define pb push_back
  12. #define ls rt<<1, l, m
  13. #define rs rt<<1|1, m+1, r
  14. #define ULL unsigned LL
  15. #define pll pair<LL, LL>
  16. #define pli pair<LL, int>
  17. #define pii pair<int, int>
  18. #define piii pair<pii, int>
  19. #define mem(a, b) memset(a, b, sizeof(a))
  20. #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  21. #define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);
  22. //head
  23.  
  24. const int N = 1e4 + ;
  25. vector<pii> g[N];
  26. int send[N], rev[N];
  27. LL ans = ;
  28.  
  29. pii dfs(int u, int o, int w) {
  30.     pii tmp = {send[u], rev[u]};
  31.     for (pii p : g[u]) {
  32.         if(p.fi != o) {
  33.              pii pp = dfs(p.fi, u, p.se);
  34.              tmp.fi += pp.fi;
  35.              tmp.se += pp.se;
  36.         }
  37.     }
  38.     ans += 1LL * abs(tmp.fi - tmp.se) * w;
  39.     return tmp;
  40. }
  41. int main() {
  42.     int T, n, u, v, w, q;
  43.     scanf("%d", &T);
  44.     while(T--) {
  45.         scanf("%d", &n);
  46.         for (int i = ; i <= n; i++) g[i].clear(), send[i] = rev[i] = ;
  47.         for (int i = ; i < n; i++) {
  48.             scanf("%d %d %d", &u, &v, &w);
  49.             g[u].pb({v, w});
  50.             g[v].pb({u, w});
  51.         }
  52.         scanf("%d", &q);
  53.         while(q--) {
  54.             scanf("%d %d", &u, &v);
  55.             send[u]++;
  56.             rev[v]++;
  57.         }
  58.         ans = ;
  59.         dfs(, , );
  60.         printf("%lld\n", ans);
  61.     }
  62.     return ;
  63. }

H Win Strategy

思路:背包dp变形

代码:

  1. #pragma GCC optimize(2)
  2. #pragma GCC optimize(3)
  3. #pragma GCC optimize(4)
  4. #include<bits/stdc++.h>
  5. using namespace std;
  6. #define fi first
  7. #define se second
  8. #define pi acos(-1.0)
  9. #define LL long long
  10. //#define mp make_pair
  11. #define pb push_back
  12. #define ls rt<<1, l, m
  13. #define rs rt<<1|1, m+1, r
  14. #define ULL unsigned LL
  15. #define pll pair<LL, LL>
  16. #define pli pair<LL, int>
  17. #define pii pair<int, int>
  18. #define piii pair<pii, int>
  19. #define mem(a, b) memset(a, b, sizeof(a))
  20. #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  21. #define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);
  22. //head
  23.  
  24. const int N = 1e3 + ;
  25. pii a[N];
  26. int dp[N];
  27. int main() {
  28.     int T, n, L;
  29.     scanf("%d", &T);
  30.     while(T--) {
  31.         scanf("%d %d", &n, &L);
  32.         for (int i = ; i <= n; i++) scanf("%d %d", &a[i].fi, &a[i].se);
  33.         for (int i = ; i <= L; i++) dp[i] = ;
  34.         for (int i = ; i <= n; i++) {
  35.             for (int j = L; j >= a[i].se; j--) {
  36.                 if(j-a[i].se +  >= a[i].fi) dp[j] = max(dp[j], dp[j-a[i].se] + );
  37.             }
  38.         }
  39.         printf("%d\n", dp[L]);
  40.     }
  41.     return ;
  42. }

I Tours

思路:二分答案, check时对于每辆bus, 如果它上一天是空闲的, 才能填补今天的空缺, 然后今天原本的车就是昨天需要的车, 不够的拿昨天剩余的补

代码:

  1. #pragma GCC optimize(2)
  2. #pragma GCC optimize(3)
  3. #pragma GCC optimize(4)
  4. #include<bits/stdc++.h>
  5. using namespace std;
  6. #define fi first
  7. #define se second
  8. #define pi acos(-1.0)
  9. #define LL long long
  10. //#define mp make_pair
  11. #define pb push_back
  12. #define ls rt<<1, l, m
  13. #define rs rt<<1|1, m+1, r
  14. #define ULL unsigned LL
  15. #define pll pair<LL, LL>
  16. #define pli pair<LL, int>
  17. #define pii pair<int, int>
  18. #define piii pair<pii, int>
  19. #define mem(a, b) memset(a, b, sizeof(a))
  20. #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  21. #define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);
  22. //head
  23.  
  24. const int N = 1e5 + ;
  25. vector<int> a[N];
  26. int T, m, n, r, t, tmp[N];
  27. bool check(int x) {
  28.     int pre = ;
  29.     for (int i = ; i <= n; i++) {
  30.         if(i == ) {
  31.             int tot = ;
  32.             for (int j = ; j <= m; j++) {
  33.                 tmp[j] = (a[j][i] + r - ) / r;
  34.                 tot += tmp[j];
  35.             }
  36.             if(tot > x) return false;
  37.             pre = x - tot;
  38.         }
  39.         else {
  40.             int tot = ;
  41.             for (int j = ; j <= m; j++) {
  42.                 if(tmp[j] >= (a[j][i] + r - ) / r) tmp[j] = (a[j][i] + r - ) / r;
  43.                 else {
  44.                     if(pre >= (a[j][i] + r - ) / r - tmp[j]) pre -= (a[j][i] + r - ) / r - tmp[j];
  45.                     else return false;
  46.                     tmp[j] = (a[j][i] + r - ) / r;
  47.                 }
  48.                 tot += (a[j][i] + r - ) / r;
  49.             }
  50.             if(tot > x) return false;
  51.             pre = x - tot;
  52.         }
  53.     }
  54.     return true;
  55. }
  56. int main() {
  57.     scanf("%d", &T);
  58.     while(T--) {
  59.         scanf("%d %d %d", &m, &n, &r);
  60.         for (int i = ; i <= m; i++) {
  61.             a[i].clear();
  62.             a[i].pb();
  63.             for (int j = ; j <= n; j++) {
  64.                 scanf("%d", &t);
  65.                 a[i].pb(t);
  66.             }
  67.         }
  68.         int l = , r = 5e5, mid = l+r >> ;
  69.         while(l < r) {
  70.             if(check(mid)) r = mid;
  71.             else l = mid+;
  72.             mid = l+r >> ;
  73.         }
  74.         printf("%d\n", mid);
  75.     }
  76.     return ;
  77. }

J Restricted Vertex Cover

思路:2-sat

建边:

对于一条mark的边,

如果其中一点在点覆盖中, 那么另外一点肯定不在点覆盖中

如果其中一点不在点覆盖中, 那么另外一点肯定在点覆盖中

对于一条unmark的边,

如果其中一点在点覆盖中, 那么另外一点不确定

如果其中一点不在点覆盖中, 那么另外一点肯定在点覆盖中

代码:

  1. #include<bits/stdc++.h>
  2. using namespace std;
  3. const int N=;
  4. int ins[N],dfn[N],low[N],cnt,sta[N];
  5. int top,v,u;
  6. int Next[N],head[N],to[N];
  7. int tot;
  8. int scc[N];
  9. int scccnt;
  10. void make_list(int u,int v){
  11.     Next[++tot]=head[u],head[u]=tot,to[tot]=v;
  12. }
  13. void tarjan(int x){
  14.     ins[x]=dfn[x]=low[x]=++cnt,sta[top++]=x;
  15.     for(int p=head[x],v=to[p];p;p=Next[p],v=to[p])
  16.         if(!dfn[v])tarjan(v),low[x]=min(low[x],low[v]);
  17.         else if(ins[v])low[x]=min(low[x],dfn[v]);
  18.     if(low[x]==dfn[x]){
  19.         scc[x]=++scccnt,ins[x]=;
  20.         while((u=sta[--top])!=x)ins[u]=,scc[u]=scccnt;
  21.     }
  22. }
  23. int main(){
  24.     int T;
  25.     int n,m;
  26.     int u,v,w;
  27.     scanf("%d",&T);
  28.     for(int t=;t<=T;t++){
  29.         scanf("%d%d",&n,&m);
  30.         memset(head,,sizeof(int)*(n*+));
  31.         memset(dfn,,sizeof(int)*(n*+));
  32.         top=;
  33.         tot=;
  34.         memset(scc,,sizeof(int)*(n*+));
  35.         memset(low,,sizeof(int)*(n*+));
  36.         scccnt=;
  37.         memset(ins,,sizeof(int)*(n*+));
  38.         cnt=;
  39.         memset(sta,,sizeof(int)*(n*+));
  40.         for(int i=;i<=m;i++){
  41.             scanf("%d%d%d",&u,&v,&w);
  42.             if(w){
  43.                 make_list(u,v+n);
  44.                 make_list(v,u+n);
  45.                 make_list(u+n,v);
  46.                 make_list(v+n,u);
  47.             }
  48.             else{
  49.                 make_list(u+n,v);
  50.                 make_list(v+n,u);
  51.             }
  52.         }
  53.         for(int i=;i<=*n;i++){
  54.             if(!dfn[i])tarjan(i);
  55.         }
  56.         bool ok=;
  57.         for(int i=;i<=n;i++){
  58.             ok&=(scc[i]!=scc[i+n]);
  59.         }
  60.         if(ok)puts("YES");
  61.         else puts("NO");
  62.     }
  63.     return ;
  64. }

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