2021.10.23 组队选拔赛
比赛链接
A.Find Subsequence
B.operation
区间DP
- ((a & b) + (a | b)) >> 1 = (a + b)/2
点击查看代码
#include <iostream>
#include <cstdio>
#include <cmath>
using namespace std;
const int maxn = 1e3 + 10;
int dp[200][200][10];
int n;
int main(){
scanf("%d", &n);
for(int i = 1; i <= n; i ++){
int a;
scanf("%d", &a);
dp[i][i][a] = 1;
}
for(int len = 2; len <= n; len ++){
for(int i = 1; i < n; i ++){
int j = i + len - 1;
if(j > n)break;
for(int k = i; k < j; k ++){
for(int p1 = 0; p1 <= 7; p1 ++){
for(int p2 = 0; p2 <= 7; p2 ++){
if(dp[i][k][p1] && dp[k + 1][j][p2]){
dp[i][j][p1 + p2 >> 1] = 1;
}
}
}
}
}
}
for(int i = 0; i <= 7; i ++){
if(dp[1][n][i])printf("%d ", i);
}
return 0;
}
C.FQ之旅
D.SumMin
最短路floyd算法。
点击查看代码
#include <iostream>
#include <cstdio>
#include <cmath>
#include <vector>
using namespace std;
const int maxn = 5e2 + 10;
using ll = long long;
ll dp[maxn][maxn];
int n, ret[maxn];
int main() {
scanf("%d", &n);
for(int i = 1; i <= n; i ++) {
for(int j = 1; j <= n; j ++) {
scanf("%lld", &dp[i][j]);
}
}
for(int i = n; i >= 1; i --)scanf("%d", &ret[i]);
vector<ll> v;
for(int k = 1; k <= n; k ++) {
for(int i = 1; i <= n; i ++) {
for(int j = 1; j <= n; j ++) {
int u = ret[i], v = ret[j];
dp[u][v] = min(dp[u][v], dp[u][ret[k]] + dp[ret[k]][v]);
}
}
ll ans = 0;
for(int i = 1; i <= k; i ++) {
for(int j = 1; j <= k; j ++) {
if(i == j)continue;
ans += dp[ret[i]][ret[j]];
}
}
v.push_back(ans);
}
for(int i = v.size() - 1; i >= 0; i --)printf("%lld ", v[i]);
return 0;
}
E.Number Game
\(bfs\)
点击查看代码
#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>
#include <deque>
#include <cmath>
#include <ctime>
#include <map>
#include <set>
#include <unordered_map>
#define fi first
#define se second
#define pb push_back
// #define endl "\n"
#define debug(x) cout << #x << ":" << x << endl;
#define bug cout << "********" << endl;
#define all(x) x.begin(), x.end()
#define lowbit(x) x & -x
#define fin(x) freopen(x, "r", stdin)
#define fout(x) freopen(x, "w", stdout)
#define ull unsigned long long
#define ll long long
const double eps = 1e-5;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const double pi = acos(-1.0);
const int mod = 1e9 + 7;
const int maxn = 2e6 + 10;
using namespace std;
int n, k;
bool ban[20], vis[maxn];
vector<int> v;
int rd[maxn], pre[maxn];
int main(){
memset(pre, -1, sizeof pre);
scanf("%d%d", &k, &n);
for(int i = 1; i <= n; i ++){
int a; scanf("%d", &a);
ban[a] = true;
}
for(int i = 0; i <= 9; i ++){
if(!ban[i])v.pb(i);
}
queue<int> q;
int len = v.size();
for(int i = 0; i < len; i ++){
if(!v[i])continue;
int a = v[i] % k;
if(vis[a])continue;
vis[a] = 1, rd[a] = v[i];
q.push(a);
}
while(q.size()){
int p = q.front(); q.pop();
if(!p){
vector<int> ans;
for(int i = p; ~i; i = pre[i]){
ans.pb(rd[i]);
}
reverse(all(ans));
for(int i : ans)printf("%d", i);
return 0;
}
for(int i = 0; i < len; i ++){
int a = (p * 10 + v[i]) % k;
if(vis[a])continue;
vis[a] = 1;
rd[a] = v[i], pre[a] = p;
q.push(a);
}
}
puts("-1");
return 0;
}
F.Number Game2
容斥原理
点击查看代码
#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>
#include <deque>
#include <cmath>
#include <ctime>
#include <map>
#include <set>
#include <unordered_map>
#define fi first
#define se second
#define pb push_back
// #define endl "\n"
#define debug(x) cout << #x << ":" << x << endl;
#define bug cout << "********" << endl;
#define all(x) x.begin(), x.end()
#define lowbit(x) x & -x
#define fin(x) freopen(x, "r", stdin)
#define fout(x) freopen(x, "w", stdout)
#define ull unsigned long long
#define ll long long
const double eps = 1e-5;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const double pi = acos(-1.0);
const int mod = 1e9 + 7;
const int maxn = 1e6 + 10;
using namespace std;
int n;
ll s[maxn];
ll fac[maxn], inv[maxn], c[maxn];
ll qpow(ll a, ll b = mod - 2){
ll ret = 1;
while(b){
if(b & 1)ret = ret * a % mod;
b >>= 1;
a = a * a % mod;
}
return ret;
}
void init(int sum, int n){
fac[0] = inv[0] = 1;
for(int i = 1; i <= n; i ++){
fac[i] = fac[i - 1] * i % mod;
inv[i] = inv[i - 1] * qpow(2) % mod;
}
c[0] = 1;
for(int i = 1; i <= sum; i ++){
c[i] = c[i - 1] * (sum - i + 1) % mod * qpow(i) % mod;
}
}
int main(){
scanf("%d", &n);
for(int i = 1; i <= n; i ++)scanf("%lld", &s[i]);
sort(s + 1, s + n + 1);
int sum = 0;
for(int i = 1; i <= n; i ++){
if(s[i] == s[i + 1])sum ++;
}
init(sum, n);
ll ans = fac[n] * qpow(qpow(2, sum)) % mod, ret = 0;
for(int i = 1; i <= sum; i ++){
ll a = c[i] * (fac[n - i] * inv[sum - i] % mod) % mod;
if(i & 1)ret = (ret + a) % mod;
else ret = (ret - a) % mod;
}
ans = (ans - ret + mod) % mod;
printf("%lld\n", ans);
return 0;
}
G.小郑的疑惑
\(O(nlogn)\)的因子分解筛法
点击查看代码
#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>
#include <deque>
#include <cmath>
#include <ctime>
#include <map>
#include <set>
#include <unordered_map>
#define fi first
#define se second
#define pb push_back
// #define endl "\n"
#define debug(x) cout << #x << ":" << x << endl;
#define bug cout << "********" << endl;
#define all(x) x.begin(), x.end()
#define lowbit(x) x & -x
#define fin(x) freopen(x, "r", stdin)
#define fout(x) freopen(x, "w", stdout)
#define ull unsigned long long
#define ll long long
const double eps = 1e-5;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const double pi = acos(-1.0);
const int mod = 1e9 + 7;
const int maxn = 2e6 + 10;
using namespace std;
int n, m;
int s[maxn];
ll sum[maxn], ans[maxn];
ll vis[maxn], cnt[maxn];
int main(){
scanf("%d%d", &n, &m);
for(int i = 1; i <= n; i ++){
scanf("%d", &s[i]);
vis[s[i]] ++;
}
for(int i = 1; i <= m; i ++) {
for(int j = i; j <= m; j += i) {
int a = j / i;
if(a < i)continue;
if(a == i)cnt[j] += vis[a] * (vis[a] - 1) / 2;
else cnt[j] += vis[a] * vis[i];
}
}
for(int i = 1; i <= m; i ++){
for(int j = i; j <= m; j += i){
ans[j] += cnt[i];
}
}
for(int i = 1; i <= m; i ++)printf("%lld ", ans[i]);
return 0;
}
H.签到题
字典树
点击查看代码
#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>
#include <deque>
#include <cmath>
#include <ctime>
#include <map>
#include <set>
#include <unordered_map>
#define fi first
#define se second
#define pb push_back
// #define endl "\n"
#define debug(x) cout << #x << ":" << x << endl;
#define bug cout << "********" << endl;
#define all(x) x.begin(), x.end()
#define lowbit(x) x & -x
#define fin(x) freopen(x, "r", stdin)
#define fout(x) freopen(x, "w", stdout)
#define ull unsigned long long
#define ll long long
const double eps = 1e-5;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const double pi = acos(-1.0);
const int mod = 1e9 + 7;
const int maxn = 2e6 + 10;
using namespace std;
int t[maxn][2], tot = 1;
int sum = INT32_MAX;
void insert(int d){
int rt = 1;
for(int i = 31; i >= 0; i --){
int a = (d >> i) & 1;
if(!t[rt][a])t[rt][a] = ++ tot;
rt = t[rt][a];
}
}
void dfs(int rt, int ret, int xorr){
if(!t[rt][0] && !t[rt][1]){
if(xorr < sum)sum = xorr;
return ;
}
if(t[rt][0] && t[rt][1]){
dfs(t[rt][0], ret * 2 + 1, xorr * 2 + 1);
dfs(t[rt][1], ret * 2, xorr * 2 + 1);
}
else if(t[rt][1]){
dfs(t[rt][1], ret * 2 + 1, xorr * 2);
}
else if(t[rt][0]){
dfs(t[rt][0], ret * 2, xorr * 2);
}
}
int main(){
int n; scanf("%d", &n);
for(int i = 1; i <= n; i ++){
int a;
scanf("%d", &a);
insert(a);
}
dfs(1, 0, 0);
printf("%d\n", sum);
return 0;
}
I.一道题
单调栈 + 思维
点击查看代码
#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>
#include <deque>
#include <cmath>
#include <ctime>
#include <map>
#include <set>
#include <stack>
#include <unordered_map>
#include <bitset>
#define fi first
#define se second
#define pb push_back
// #define endl "\n"
#define debug(x) cout << #x << ":" << x << endl;
#define bug cout << "********" << endl;
#define all(x) x.begin(), x.end()
#define lowbit(x) x & -x
#define fin(x) freopen(x, "r", stdin)
#define fout(x) freopen(x, "w", stdout)
#define ull unsigned long long
#define ll long long
const double eps = 1e-5;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const double pi = acos(-1.0);
const int mod = 1e9 + 7;
const int maxn = 2e5 + 10;
using namespace std;
#define lson rt << 1
#define rson rt << 1 | 1
unordered_map<int, int> mp;
int n, s[maxn];
int l[maxn], r[maxn];
int wl[maxn], wr[maxn], p[40];
void initlr(){
stack<int> st;
for(int i = 1; i <= n; i ++){
while(st.size() && s[i] >= s[st.top()])st.pop();
l[i] = st.size() ? st.top() + 1 : 1;
st.push(i);
}
while(st.size())st.pop();
for(int i = n; i >= 1; i --){
while(st.size() && s[i] >= s[st.top()])st.pop();
r[i] = st.size() ? st.top() - 1 : n;
st.push(i);
}
}
void initwlr(){
memset(wl, -1, sizeof wl), memset(wr, inf, sizeof wr);
for(int i = 1; i <= n; i ++){
for(int j = 0; j <= 31; j ++){
int a = (s[i] >> j) & 1;
if(!a && p[j])wl[i] = max(wl[i], p[j]);
}
for(int j = 0; j <= 31; j ++){
int a = (s[i] >> j) & 1;
if(a)p[j] = i;
}
}
memset(p, 0, sizeof p);
for(int i = n; i >= 1; i --){
for(int j = 0; j <= 31; j ++){
int a = (s[i] >> j) & 1;
if(!a && p[j])wr[i] = min(wr[i], p[j]);
}
for(int j = 0; j <= 31; j ++){
int a = (s[i] >> j) & 1;
if(a)p[j] = i;
}
}
}
int main(){
scanf("%d", &n);
for(int i = 1; i <= n; i ++)scanf("%d", &s[i]);
initlr(), initwlr();
ll sum = 0;
for(int i = 1; i <= n; i ++){
int pos1, pos11, pos22, pos2;
pos1 = max(mp[s[i]], l[i]), pos2 = r[i];
mp[s[i]] = i + 1;
pos11 = wl[i], pos22 = wr[i];
if(i == pos1 && pos2 == i)continue;
if(pos1 <= pos11 && pos22 <= pos2){
sum += 1ll * (i - pos1 + 1) * (pos2 - i + 1) - 1ll * (i - pos11) * (pos22 - i);
}
else if(pos1 <= pos11){
sum += 1ll * (pos2 - i + 1) * (pos11 - pos1 + 1);
}
else if(pos22 <= pos2){
sum += 1ll * (i - pos1 + 1) * (pos2 - pos22 + 1);
}
}
printf("%lld\n", sum);
return 0;
}
J.City Union
线性基+并查集
点击查看代码
#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>
#include <deque>
#include <cmath>
#include <ctime>
#include <map>
#include <set>
#include <unordered_map>
#define fi first
#define se second
#define pb push_back
// #define endl "\n"
#define debug(x) cout << #x << ":" << x << endl;
#define bug cout << "********" << endl;
#define all(x) x.begin(), x.end()
#define lowbit(x) x & -x
#define fin(x) freopen(x, "r", stdin)
#define fout(x) freopen(x, "w", stdout)
#define ull unsigned long long
#define ll long long
const double eps = 1e-5;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const double pi = acos(-1.0);
const int mod = 1e9 + 7;
const int maxn = 2e5 + 10;
using namespace std;
int x[maxn][40];
int fa[maxn], s[maxn];
int vis[maxn], n, m;
int fid(int a){
return a == fa[a] ? a : fa[a] = fid(fa[a]);
}
bool check(int a, int p){
for(int i = 31; i >= 0; i --){
if((a >> i) & 1){
a ^= x[p][i];
}
}
if(!a)return true;
else return false;
}
void union1(int a, int b){
for(int i = 0; i <= 31; i ++){
if(!x[b][i])continue;
int ret = x[b][i];
for(int j = 31; j >= 0; j --){
if((ret >> j) & 1){
if(x[a][j])ret ^= x[a][j];
else{x[a][j] = ret; break;}
}
}
}
}
int main(){
scanf("%d%d", &n, &m);
for(int i = 1; i <= n; i ++){
scanf("%d", &s[i]);
for(int j = 31; j >= 0; j --){
if((s[i] >> j) & 1){
x[i][j] = s[i];
break;
}
}
}
for(int i = 1; i <= n; i ++)fa[i] = i;
int a, b, c;
for(int i = 1; i <= m; i ++){
scanf("%d%d%d", &a, &b, &c);
int p, xx = fid(a), yy = fid(b);
if(xx != yy){
fa[xx] = yy;
union1(yy, xx);
}
if(check(c, yy))puts("Yes");
else puts("No");
}
return 0;
}
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