专栏文章
我去,是 57 龙
P12551题解参与者 9已保存评论 8
文章操作
快速查看文章及其快照的属性,并进行相关操作。
- 当前评论
- 8 条
- 当前快照
- 1 份
- 快照标识符
- @minsf1qf
- 此快照首次捕获于
- 2025/12/02 07:35 3 个月前
- 此快照最后确认于
- 2025/12/02 07:35 3 个月前
标题来源:sasakure 的《Apollo》。小心 。
其实吧,抛开细节和码量(参考数据:我的代码有 , 个
if)不谈,这个题挺有趣的。我是一个 Sub 一个 Sub 写过来的。因为太难写了。
每个小部分只放核心代码,不然太长了。完整代码在最后。
讨论每个 Sub 的时候会排除做前面的 Sub 时已经判掉的情况。
Subtask1
这个 Subtask 还是非常简单的。显然把所有加在一起,判断总和是不是质数。由于数据规模稍大,以及后面要写爆搜对时间有一定要求,为了效率,我用了 Miller-Rabin。
代码
CPPif (k == 1){
for (int i = 1; i <= n; i++)
sum += a[i];
if (isp(sum)){
cout << "1\n" << n << " ";
for (int i = 1; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}else{
cout << "0\n" << n << " ";
for (int i = 1; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}
}
Subtask2
数据很小,直接状压爆搜。
代码
CPPvoid dfs(int S, int now, int dep){
// cerr << S << " " << mn[S] << " " << now << "\n";
if (S == (1 << n) - 1 && dep != k + 1)
return;
if (now >= mn[S])
return;
mn[S] = now;
if (dep >= k + 1)
return;
for (int T = 1; T < (1 << n); T++){
if (S & T)
continue;
long long sum = 0;
for (int i = 1; i <= n; i++)
if (T & (1 << i - 1))
sum += a[i];
// cerr << T << " " << sum << " " << isp(sum) << "\n";
// system("pause");
dfs(S | T, now + isp(sum), dep + 1);
}
}
void dfs2(int S, int now, int dep){
// cerr << S << " " << now << " " << dep << "\n";
// cerr << mn[S] << "\n";
// if (now > mn[S])
// return;
if (fnd)
return;
if (dep > k + 1)
return;
if (dep == k + 1 && S == (1 << n) - 1){
// cerr << now << " " << mn[S] << "\n";
if (now == mn[S]){
fnd = 1;
for (int i = 1; i <= k; i++){
cout << ans[i].size() << " ";
for (auto u : ans[i])
cout << u << " ";
cout << "\n";
ans[i].clear();
}
}
return;
}else if (dep == k + 1)
return;
for (int T = 1; T < (1 << n); T++){
if (S & T)
continue;
long long sum = 0;
for (int i = 1; i <= n; i++)
if (T & (1 << i - 1)){
sum += a[i];
ans[dep].emplace_back(a[i]);
}
dfs2(S | T, now + isp(sum), dep + 1);
ans[dep].clear();
}
}
Subtask3
上面的爆搜跑的很慢,可以改成记忆化,这样子优化会相当大,可以通过 ,。但是当 大的时候会挂掉。所以当 的时候搜 ,因为 的情况可能会很多,这样简化会比较好。 边界不多,跑不动就跑不动了。
代码
CPPvoid dfs(int S, int now, int dep){
// cerr << S << " " << mn[S] << " " << now << "\n";
if (S == (1 << n) - 1 && dep != k + 1)
return;
if (now >= mn[S])
return;
if (S == (1 << n) - 1){
for (int i = 1; i <= k; i++)
ans[i] = tmp[i];
}
mn[S] = now;
if (dep >= k + 1)
return;
for (int T = 1; T < (1 << n); T++){
if (S & T)
continue;
long long sum = 0;
for (int i = 1; i <= n; i++)
if (T & (1 << i - 1)){
sum += a[i];
tmp[dep].emplace_back(a[i]);
}
// cerr << T << " " << sum << " " << isp(sum) << "\n";
// system("pause");
dfs(S | T, now + isp(sum), dep + 1);
tmp[dep].clear();
}
}
Subtask4
是偶数且没有 ,显然奇素数可以两两配对,如果 ,这样配 组然后把剩下的直接分成一组就可以了。这种分法保证了每组和为偶数,奇异序列数量为 ;否则一定有 组是单个的,其余的两两分成一组。
代码
CPPif (!(n & 1)){
if (maimai > 2){
if (k <= n / 2){
cout << "0\n";
for (int i = 1; i <= k - 1; i++)
cout << "2 " << a[i * 2 - 1] << " " << a[i * 2] << "\n";
cout << n - 2 * (k - 1) << " ";
for (int i = (k - 1) * 2 + 1; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}else{
cout << 2 * k - n << "\n";
for (int i = 1; i <= 2 * k - n; i++)
cout << "1 " << a[i] << "\n";
for (int i = 2 * k - n + 1; i <= n; i += 2)
cout << "2 " << a[i] << " " << a[i + 1] << "\n";
}
}
}
Subtask5
难度从这里开始。
首先分析 。这种情况和偶数差不多,把单个的拎出来,把其他的两两配掉。
然后分析 的情况。考虑证明 时答案必定为 。
证明:考虑把每个质数按照 的余数分类。根据鸽巢原理,至少有一个余数出现了 次。所以一定能够分出一组 的倍数。找出哪个出现了至少 次即可。剩下的两两一组也一定是合数。
分这三种情况讨论就做完了。
代码
CPP if (maimai > 2){
if (k <= n / 2){
cout << "0\n";
memset(buk, 0, sizeof buk);
for (int i = 1; i <= n; i++)
buk[a[i] % 3]++;
for (int i = 1; i <= n; i++)
flg[i] = 0;
if (buk[0] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 0){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
cout << "\n";
}else if (buk[1] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 1){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}else{
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 2){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}
}else{
cout << 2 * k - n << "\n";
for (int i = 1; i <= 2 * k - n; i++)
cout << "1 " << a[i] << "\n";
for (int i = 2 * k - n + 1; i <= n; i += 2)
cout << "2 " << a[i] << " " << a[i + 1] << "\n";
}
}
Subtask6
现在可能有 了,但是 。
直接放可能会出问题,因为 和奇素数不能分在一起。处理方式其实很简单,有多的一个 就优先把 先拎出来,然后尽可能多配掉 和 还有 和奇数。因为 ,稍微算一下就可以发现非奇异序列一定可以在不考虑 加奇素数的情况下取到上界,这样就可以做了。
代码
CPPint cnt = 0;
for (int i = 1; i <= n; i++){
if (a[i] == 2)
++cnt;
else
break;
}
for (int i = 1; i <= n; i++)
flg[i] = 0;
cout << 2 * k - n << "\n";
if (cnt & 1)
cout << "1 2\n";
int qwq = (n - k);
for (int i = 1 + (cnt & 1); i <= 2 * qwq + (cnt & 1); i += 2)
cout << "2 " << a[i] << " " << a[i + 1] << "\n";
for (int i = 2 * qwq + (cnt & 1) + 1; i <= n; i++)
cout << "1 " << a[i] << "\n";
Subtask8
我先做的是这个 Subtask。
我们上面处理掉了很多情况,剩下有 并且 的情况。
首先,如果 是奇数个,可以把 个 分在一起,其他的就都可以两两分组,这样答案就是 。然后思考 是偶数个怎么做。
显然,当奇素数数量 的时候是好做的。根据前面 Subtask5 的方法处理掉奇素数就可以了。
那 呢?其实依旧可以套用上面的爆搜做,但是如果要分讨怎么办?直接分三种情况。
一、 个奇素数的情况
会发现答案依然可以为 。除去 个奇素数的三种情况,剩下的情况一定取满了每一个 的余数,把这三个放一起就可以了。
reverse 一下原数列会好判一点。二、 个奇素数的情况
这里开始就要考虑给奇数加上 了。给出两个结论:
结论
的所有素数 一定满足 或者 。
证明: ,,,,均不可能为素数。
结论
对于一个奇素数 ,当且仅当 时, 和 均为素数,否则 和 必有一个数为合数。
证明:根据结论 , 和 一定为合数。
由于 ,所以当存在奇素数不为 的时候,这样配掉至多 个数,剩下的肯定够配。当有奇素数 为合数的时候,因为 ,一定有至少 个 ,一定可以把 个 凑一组( 要和后面的 合并)。这样子分组既不会超限也不会不够。
然后就是奇素数全为 的情况。显然 是一个合数。剩下的全是 ,可以轻松配掉。
至此,这一部分得到了解决。
三、 个奇素数的情况
分类讨论这个奇素数加多少是合数。
如果 是合数,那么依旧奇素数和 配掉, 个 凑一组,剩下的划分。 合并两组即可。
如果 是合数,那么奇素数和两个 配掉,剩下的直接划分。
如果是一个 并且 卡满了,会发现一定有一个 落单,所以会有 个奇异序列。特判掉。没卡满的话依然可以分出来。
讨论完这些,这个 Subtask 就完成了。
代码
CPPint cnt = 0;
for (int i = 1; i <= n; i++){
if (a[i] == 2)
++cnt;
else
break;
}
if (cnt & 1){
cout << "0\n";
if (k == 2){
cout << "3 " << a[1] << " " << a[2] << " " << a[3] << "\n";
cout << n - 3 << " ";
for (int i = 4; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}else{
cout << "3 " << a[1] << " " << a[2] << " " << a[3] << "\n";
int pos = 4, js = 1;
while (1){
if (js == k - 1)
break;
cout << "2 " << a[pos] << " " << a[pos + 1] << "\n";
pos += 2;
++js;
}
cout << (n - pos + 1) << " ";
for (int i = pos; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}
}else{
if (n - cnt > 3){
cout << "0\n";
memset(buk, 0, sizeof buk);
for (int i = 1; i <= n; i++)
if (a[i] != 2)
buk[a[i] % 3]++;
for (int i = 1; i <= n; i++)
flg[i] = 0;
if (buk[0] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 0){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
cout << "\n";
}else if (buk[1] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 1){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}else if (buk[2] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 2 && a[i] != 2){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}else{
reverse(a + 1, a + 1 + n);
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 3;
int p1, p2, p3;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 0){
p1 = i;
flg[i] = 1;
cout << a[i] << " ";
break;
}
}
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 1){
p2 = i;
flg[i] = 1;
cout << a[i] << " ";
break;
}
}for (int i = 1; i <= n; i++){
if (a[i] % 3 == 2){
p3 = i;
flg[i] = 1;
cout << a[i] << " ";
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}
}else if (n - cnt == 1){
reverse(a + 1, a + 1 + n);
int pos, cnt = 1;
if (!isp(a[1] + 2)){
cout << "0\n2 " << a[1] << " " << a[2] << "\n";
pos = 3;
}else if (!isp(a[1] + 4)){
cout << "0\n3 " << a[1] << " " << a[2] << " " << a[3] << "\n";
pos = 4;
}else if (!isp(a[1] + 6)){
cout << (k == n / 2) << "\n4 " << a[1] << " " << a[2] << " " << a[3] << " " << a[4] << "\n";
pos = 5;
}
while (cnt < k - 1){
cout << "2 " << a[pos] << " " << a[pos + 1] << "\n";
pos += 2;
++cnt;
}
cout << n - pos + 1 << " ";
for (int i = pos; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}else if (n - cnt == 3){
reverse(a + 1, a + 1 + n);
// reverse(a + 1, a + 4);
int pos, cnt = 1;
if (!isp(a[1] + 2)){
cout << "0\n2 " << a[1] << " " << a[4] << "\n";
pos = 5;
}else if (!isp(a[1] + 4)){
cout << "0\n3 " << a[1] << " " << a[4] << " " << a[5] << "\n";
pos = 6;
}else if (!isp(a[1] + 6)){
cout << "0\n3 3 3 3\n";
pos = 4;
while (cnt < k - 1){
cout << "2 " << a[pos] << " " << a[pos + 1] << "\n";
pos += 2;
++cnt;
}
cout << n - pos + 1 << " ";
for (int i = pos; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
continue;
}
while (cnt < k - 1){
cout << "2 " << a[pos] << " " << a[pos + 1] << "\n";
pos += 2;
++cnt;
}
cout << n - pos + 3 << " ";
cout << a[2] << " " << a[3] << " ";
for (int i = pos; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}
}
Subtask7
其实和 为奇数会差不多,略难一些。
有偶数个是好做的。 和 分,奇素数和奇素数分。
有奇数个的时候要特判 ,这种情况直接找有没有一个奇素数加上 是合数,有就和 配掉,奇异序列个数为 ;没有就随便拉一个配,个数为 。
剩下的情况还是和上面一样讨论。唯一的区别在于只有一个奇素数 的时候由于 ,我们多了两个 ,可以把 配掉了。这种情况没有奇异序列了。
这里只给出偶数个 和 的代码:
代码
CPPif (!(cnt & 1)){
cout << "0\n";
for (int i = 1; i <= 2 * k - 2; i += 2)
cout << "2 " << a[i] << " " << a[i + 1] << "\n";
vector<int> tmp;
tmp.clear();
for (int i = 2 * k - 1; i <= n; i++)
tmp.emplace_back(i);
cout << tmp.size() << " ";
for (int i = 2 * k - 1; i <= n; i++)
cout << a[i] << " ";
cout <<"\n";
}else if (k == n / 2){
bool chk = 1;
for (int i = 1; i <= n; i++)
if ((a[i] & 1) && !isp(a[i] + 2)){
chk = 0;
swap(a[i], a[1]);
break;
}
cout << chk << "\n";
sort(a + 2, a + 1 + n);
for (int i = 1; i <= n; i += 2)
cout << "2 " << a[i] << " " << a[i + 1] << "\n";
}
完整代码
CPP#include<bits/stdc++.h>
using namespace std;
int t, n, k, a[100005], flg[100005], maimai, tt;
vector<int> ans[100005], tmp[105];
long long p[] = {0, 2, 3, 5, 7, 11, 13, 17, 19};
int mn[2005], fnd, buk[5];
typedef long long ll;
ll slowtm(ll x, ll k, ll m){
return (__int128)x * k % m;
}
ll qpow(ll x, ll k, ll m){
ll ans = 1;
while(k){
if (k & 1)
ans = slowtm(ans, x, m);
x = slowtm(x, x, m);
k >>= 1;
}
return ans;
}
bool Miller_Rabin(ll n, ll a){
ll vp = n - 1, r = 0, pan;
while (!(vp & 1))
r++, vp >>= 1;
pan = qpow(a, vp, n);
if (pan == 1)
return 1;
for (int i = 0; i < r; i++){
if (pan == n - 1)
return 1;
pan = slowtm(pan, pan, n);
}
return 0;
}
bool isp(ll n){
if (n < 2)
return 0;
for (int i = 1; i <= 8; i++){
if (n == p[i])
return 1;
if (n % p[i] == 0)
return 0;
if (!Miller_Rabin(n, p[i]))
return 0;
}
return 1;
}
void dfs(int S, int now, int dep){
if (S == (1 << n) - 1 && dep != k + 1)
return;
if (now >= mn[S])
return;
if (S == (1 << n) - 1){
for (int i = 1; i <= k; i++)
ans[i] = tmp[i];
}
mn[S] = now;
if (dep >= k + 1)
return;
for (int T = 1; T < (1 << n); T++){
if (S & T)
continue;
long long sum = 0;
for (int i = 1; i <= n; i++)
if (T & (1 << i - 1)){
sum += a[i];
tmp[dep].emplace_back(a[i]);
}
dfs(S | T, now + isp(sum), dep + 1);
tmp[dep].clear();
}
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);cout.tie(0);
cin >> t;
tt = t;
while (t--){
cin >> n >> k;
ll sum = 0;
maimai = INT_MAX;
for (int i = 1; i <= n; i++){
cin >> a[i];
maimai = min(maimai, a[i]);
}
if (k == 1){
for (int i = 1; i <= n; i++)
sum += a[i];
if (isp(sum)){
cout << "1\n" << n << " ";
for (int i = 1; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}else{
cout << "0\n" << n << " ";
for (int i = 1; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}
}else if (n <= 10 && tt <= 20 || n <= 5){
memset(mn, 0x3f, sizeof mn);
fnd = 0;
dfs(0, 0, 1);
cout << mn[(1 << n) - 1] << "\n";
for (int i = 1; i <= k; i++){
cout << ans[i].size() << " ";
for (auto u : ans[i])
cout << u << " ";
cout << "\n";
ans[i].clear();
}
}else if (!(n & 1)){
if (maimai > 2){
if (k <= n / 2){
cout << "0\n";
for (int i = 1; i <= k - 1; i++)
cout << "2 " << a[i * 2 - 1] << " " << a[i * 2] << "\n";
cout << n - 2 * (k - 1) << " ";
for (int i = (k - 1) * 2 + 1; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}else{
cout << 2 * k - n << "\n";
for (int i = 1; i <= 2 * k - n; i++)
cout << "1 " << a[i] << "\n";
for (int i = 2 * k - n + 1; i <= n; i += 2)
cout << "2 " << a[i] << " " << a[i + 1] << "\n";
}
}else{
if (k <= n / 2){
int cnt = 0;
for (int i = 1; i <= n; i++){
if (a[i] == 2)
++cnt;
else
break;
}
if (!(cnt & 1)){
cout << "0\n";
for (int i = 1; i <= 2 * k - 2; i += 2)
cout << "2 " << a[i] << " " << a[i + 1] << "\n";
vector<int> tmp;
tmp.clear();
for (int i = 2 * k - 1; i <= n; i++)
tmp.emplace_back(i);
cout << tmp.size() << " ";
for (int i = 2 * k - 1; i <= n; i++)
cout << a[i] << " ";
cout <<"\n";
}else if (k == n / 2){
bool chk = 1;
for (int i = 1; i <= n; i++)
if ((a[i] & 1) && !isp(a[i] + 2)){
chk = 0;
swap(a[i], a[1]);
break;
}
cout << chk << "\n";
sort(a + 2, a + 1 + n);
for (int i = 1; i <= n; i += 2)
cout << "2 " << a[i] << " " << a[i + 1] << "\n";
}else if (n - cnt > 3){
cout << "0\n";
memset(buk, 0, sizeof buk);
for (int i = 1; i <= n; i++)
if (a[i] != 2)
buk[a[i] % 3]++;
for (int i = 1; i <= n; i++)
flg[i] = 0;
if (buk[0] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 0){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
if (p == 1 && a[i] == 2 && a[i + 1] != 2){
continue;
}
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
cout << "\n";
}else if (buk[1] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 1){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
if (p == 1 && a[i] == 2 && a[i + 1] != 2){
continue;
}
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}else if (buk[2] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 2 && a[i] != 2){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
if (p == 1 && a[i] == 2 && a[i + 1] != 2){
continue;
}
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}else{
reverse(a + 1, a + 1 + n);
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 3;
int p1, p2, p3;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 0){
p1 = i;
flg[i] = 1;
cout << a[i] << " ";
break;
}
}
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 1){
p2 = i;
flg[i] = 1;
cout << a[i] << " ";
break;
}
}for (int i = 1; i <= n; i++){
if (a[i] % 3 == 2){
p3 = i;
flg[i] = 1;
cout << a[i] << " ";
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
if (p == 1 && a[i] == 2 && a[i + 1] != 2){
continue;
}
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}
}else if (n - cnt == 1){
reverse(a + 1, a + 1 + n);
int pos, cnt = 1;
if (!isp(a[1] + 2)){
cout << "0\n2 " << a[1] << " " << a[2] << "\n";
pos = 3;
}else if (!isp(a[1] + 4)){
cout << "0\n3 " << a[1] << " " << a[2] << " " << a[3] << "\n";
pos = 4;
}else if (!isp(a[1] + 6)){
cout << "0\n4 " << a[1] << " " << a[2] << " " << a[3] << " " << a[4] << "\n";
pos = 5;
}
while (cnt < k - 1){
cout << "2 " << a[pos] << " " << a[pos + 1] << "\n";
pos += 2;
++cnt;
}
cout << n - pos + 1 << " ";
for (int i = pos; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}else if (n - cnt == 3){
reverse(a + 1, a + 1 + n);
// reverse(a + 1, a + 4);
int pos, cnt = 1;
if (!isp(a[1] + 2)){
cout << "0\n2 " << a[1] << " " << a[4] << "\n";
pos = 5;
}else if (!isp(a[1] + 4)){
cout << "0\n3 " << a[1] << " " << a[4] << " " << a[5] << "\n";
pos = 6;
}else if (!isp(a[1] + 6)){
cout << "0\n3 3 3 3\n";
pos = 4;
while (cnt < k - 1){
cout << "2 " << a[pos] << " " << a[pos + 1] << "\n";
pos += 2;
++cnt;
}
cout << n - pos + 1 << " ";
for (int i = pos; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
continue;
}
while (cnt < k - 1){
cout << "2 " << a[pos] << " " << a[pos + 1] << "\n";
pos += 2;
++cnt;
}
cout << n - pos + 3 << " ";
cout << a[2] << " " << a[3] << " ";
for (int i = pos; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}
}else{
int cnt = 0;
for (int i = 1; i <= n; i++){
if (a[i] == 2)
++cnt;
else
break;
}
for (int i = 1; i <= n; i++)
flg[i] = 0;
cout << 2 * k - n << "\n";
if (cnt & 1)
cout << "1 2\n";
int qwq = (n - k);
for (int i = 1 + (cnt & 1); i <= 2 * qwq + (cnt & 1); i += 2)
cout << "2 " << a[i] << " " << a[i + 1] << "\n";
for (int i = 2 * qwq + (cnt & 1) + 1; i <= n; i++)
cout << "1 " << a[i] << "\n";
}
}
}else{
if (maimai > 2){
if (k <= n / 2){
cout << "0\n";
memset(buk, 0, sizeof buk);
for (int i = 1; i <= n; i++)
buk[a[i] % 3]++;
for (int i = 1; i <= n; i++)
flg[i] = 0;
if (buk[0] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 0){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
cout << "\n";
}else if (buk[1] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 1){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}else{
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 2){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}
}else{
cout << 2 * k - n << "\n";
for (int i = 1; i <= 2 * k - n; i++)
cout << "1 " << a[i] << "\n";
for (int i = 2 * k - n + 1; i <= n; i += 2)
cout << "2 " << a[i] << " " << a[i + 1] << "\n";
}
}else{
if (k <= n / 2){
int cnt = 0;
for (int i = 1; i <= n; i++){
if (a[i] == 2)
++cnt;
else
break;
}
if (cnt & 1){
cout << "0\n";
if (k == 2){
cout << "3 " << a[1] << " " << a[2] << " " << a[3] << "\n";
cout << n - 3 << " ";
for (int i = 4; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}else{
cout << "3 " << a[1] << " " << a[2] << " " << a[3] << "\n";
int pos = 4, js = 1;
while (1){
if (js == k - 1)
break;
cout << "2 " << a[pos] << " " << a[pos + 1] << "\n";
pos += 2;
++js;
}
cout << (n - pos + 1) << " ";
for (int i = pos; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}
}else{
if (n - cnt > 3){
cout << "0\n";
memset(buk, 0, sizeof buk);
for (int i = 1; i <= n; i++)
if (a[i] != 2)
buk[a[i] % 3]++;
for (int i = 1; i <= n; i++)
flg[i] = 0;
if (buk[0] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 0){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
cout << "\n";
}else if (buk[1] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 1){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}else if (buk[2] >= 3){
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 0;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 2 && a[i] != 2){
cout << a[i] << " ";
flg[i] = 1;
++cnt;
++tot;
if (cnt == 3)
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}else{
reverse(a + 1, a + 1 + n);
cout << "3 ";
int cnt = 0, p = 1, js = 1, tot = 3;
int p1, p2, p3;
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 0){
p1 = i;
flg[i] = 1;
cout << a[i] << " ";
break;
}
}
for (int i = 1; i <= n; i++){
if (a[i] % 3 == 1){
p2 = i;
flg[i] = 1;
cout << a[i] << " ";
break;
}
}for (int i = 1; i <= n; i++){
if (a[i] % 3 == 2){
p3 = i;
flg[i] = 1;
cout << a[i] << " ";
break;
}
}
cout << "\n";
if (js != k - 1){
for (int i = 1; i <= n; i++){
if (!flg[i]){
++tot;
if (p == 1)
cout << "2 " << a[i] << " ";
else
cout << a[i] << "\n";
p ^= 1;
flg[i] = 1;
if (!p)
js++;
else if (js == k - 1)
break;
}
}
}
cout << n - tot << " ";
for (int i = 1; i <= n; i++){
if (!flg[i])
cout << a[i] << " ";
}
}
}else if (n - cnt == 1){
reverse(a + 1, a + 1 + n);
int pos, cnt = 1;
if (!isp(a[1] + 2)){
cout << "0\n2 " << a[1] << " " << a[2] << "\n";
pos = 3;
}else if (!isp(a[1] + 4)){
cout << "0\n3 " << a[1] << " " << a[2] << " " << a[3] << "\n";
pos = 4;
}else if (!isp(a[1] + 6)){
cout << (k == n / 2) << "\n4 " << a[1] << " " << a[2] << " " << a[3] << " " << a[4] << "\n";
pos = 5;
}
while (cnt < k - 1){
cout << "2 " << a[pos] << " " << a[pos + 1] << "\n";
pos += 2;
++cnt;
}
cout << n - pos + 1 << " ";
for (int i = pos; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}else if (n - cnt == 3){
reverse(a + 1, a + 1 + n);
// reverse(a + 1, a + 4);
int pos, cnt = 1;
if (!isp(a[1] + 2)){
cout << "0\n2 " << a[1] << " " << a[4] << "\n";
pos = 5;
}else if (!isp(a[1] + 4)){
cout << "0\n3 " << a[1] << " " << a[4] << " " << a[5] << "\n";
pos = 6;
}else if (!isp(a[1] + 6)){
cout << "0\n3 3 3 3\n";
pos = 4;
while (cnt < k - 1){
cout << "2 " << a[pos] << " " << a[pos + 1] << "\n";
pos += 2;
++cnt;
}
cout << n - pos + 1 << " ";
for (int i = pos; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
continue;
}
while (cnt < k - 1){
cout << "2 " << a[pos] << " " << a[pos + 1] << "\n";
pos += 2;
++cnt;
}
cout << n - pos + 3 << " ";
cout << a[2] << " " << a[3] << " ";
for (int i = pos; i <= n; i++)
cout << a[i] << " ";
cout << "\n";
}
}
}else{
int cnt = 0;
for (int i = 1; i <= n; i++){
if (a[i] == 2)
++cnt;
else
break;
}
for (int i = 1; i <= n; i++)
flg[i] = 0;
cout << 2 * k - n << "\n";
if (cnt & 1)
cout << "1 2\n";
int qwq = (n - k);
for (int i = 1 + (cnt & 1); i <= 2 * qwq + (cnt & 1); i += 2)
cout << "2 " << a[i] << " " << a[i + 1] << "\n";
for (int i = 2 * qwq + (cnt & 1) + 1; i <= n; i++)
cout << "1 " << a[i] << "\n";
}
}
}
}
return 0;
}
结语 做完这道题的感想
萌新时期,总会觉得过掉一道黑题是十分遥远的,写掉一个码量巨大的题是永远做不到的。
但是,真正花时间下去,用最朴素的热爱钻研出一个题,经过一番鏖战做完之后,才发现,不过如此。
难吗?难。但是不累。因为心中的热爱在驱动。或许写的时候会无数次破防,无数次质疑自己,但是,在 Accepted 跳出来的那一瞬间,就会意识到,一切都是值得的。静下心来,就能够一次次取得突破。
“蚓无爪牙之利,筋骨之强,上食埃土,下饮黄泉,用心一也;蟹六跪而二螯,非蛇鳝之穴无所寄托者,用心躁也。”
2025 赛季已经开始,愿我们都能在这段时间内静下心来,在每一场比赛中取得令自己满意的成绩,不给 OI 之旅留下遗憾。
相关推荐
评论
共 8 条评论,欢迎与作者交流。
正在加载评论...