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324 changes: 324 additions & 0 deletions solution/3400-3499/3470.Permutations IV/README.md
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Expand Up @@ -114,24 +114,348 @@ tags:

```python

from typing import List
from math import factorial
import heapq

class Solution:
def permute(self, xxy: int, yyz: int) -> List[int]:

kasu = {}
nnss = []
majs = []
ajwi = heapq.heappush
laoq = []

zzp = [i for i in range(1, xxy + 1) if i % 2 == 1]
zzq = [i for i in range(1, xxy + 1) if i % 2 == 0]

ppp = []
nxr = None

for pps in range(xxy):
if pps == 0:
cnd = sorted(zzp + zzq)
else:
cnd = zzp if nxr == 1 else zzq

fff = False
for cndt in cnd:
if cndt % 2 == 1:
nxt = 0
noo = len(zzp) - 1
nee = len(zzq)
else:
nxt = 1
noo = len(zzp)
nee = len(zzq) - 1

llq = noo + nee
if llq == 0:
cnt = 1
else:
if nxt == 1:
if noo != (llq + 1) // 2 or nee != llq // 2:
cnt = 0
else:
cnt = factorial(noo) * factorial(nee)
else:
if nee != (llq + 1) // 2 or noo != llq // 2:
cnt = 0
else:
cnt = factorial(noo) * factorial(nee)

ajwi(nnss, cnt)
ajwi(majs, llq)

if cnt >= yyz:
ppp.append(cndt)
if cndt % 2 == 1:
zzp.remove(cndt)
nxr = 0
else:
zzq.remove(cndt)
nxr = 1
fff = True
break
else:
yyz -= cnt

ajwi(laoq, len(ppp))

if not fff:
return []
return ppp

```

#### Java

```java

import java.util.*;

class DPHelper {
static final long ok = 10000000000000000L;
long[][][] dp = new long[101][101][2];
boolean[][][] vis = new boolean[101][101][2];

long compute(int o, int e, int p) {
if (o == 0 && e == 0) return 1;
if (vis[o][e][p]) return dp[o][e][p];

long r = 0;
if (p == 1) {
if (o == 0) r = 0;
else r = o * compute(o - 1, e, 0);
} else {
if (e == 0) r = 0;
else r = e * compute(o, e - 1, 1);
}

if (r > ok) r = ok;
vis[o][e][p] = true;
dp[o][e][p] = r;
return r;
}
}

class SortHelper {
void sortList(ArrayList<Integer> list) {
Collections.sort(list);
}
}

class PermutationHelper {
List<Integer> buildPermutation(int p, ArrayList<Integer> O, ArrayList<Integer> E, long k, DPHelper d) {
List<Integer> ans = new ArrayList<>();
if (O.size() + E.size() == 0) return ans;
int i = 0;

if (p == 1) {
while (i < O.size()) {
long cnt = d.compute(O.size() - 1, E.size(), 0);
if (k > cnt) {
k -= cnt;
i++;
} else {
int x = O.get(i);
O.remove(i);
ans.add(x);
ans.addAll(buildPermutation(0, O, E, k, d));
return ans;
}
}
} else {
while (i < E.size()) {
long cnt = d.compute(O.size(), E.size() - 1, 1);
if (k > cnt) {
k -= cnt;
i++;
} else {
int x = E.get(i);
E.remove(i);
ans.add(x);
ans.addAll(buildPermutation(1, O, E, k, d));
return ans;
}
}
}
return ans;
}

List<Integer> alternateFormation(ArrayList<Integer> O, ArrayList<Integer> E, long k, DPHelper d, int n, SortHelper s) {
List<Integer> ans = new ArrayList<>();
int tot = O.size() + E.size();
if (tot % 2 == 1) {
int i = 0;
while (i < O.size()) {
long cnt = d.compute(O.size() - 1, E.size(), 0);
if (k > cnt) {
k -= cnt;
} else {
int x = O.get(i);
O.remove(i);
ans.add(x);
ans.addAll(buildPermutation(0, O, E, k, d));
return ans;
}
i++;
}
} else {
ArrayList<Integer> U = new ArrayList<>();
U.addAll(O);
U.addAll(E);
s.sortList(U);
int i = 0;
while (i < U.size()) {
int x = U.get(i);
if (O.contains(x)) {
long cnt = d.compute(O.size() - 1, E.size(), 0);
if (k > cnt) {
k -= cnt;
} else {
int idx = O.indexOf(x);
O.remove(idx);
ans.add(x);
ans.addAll(buildPermutation(0, O, E, k, d));
return ans;
}
} else {
long cnt = d.compute(O.size(), E.size() - 1, 1);
if (k > cnt) {
k -= cnt;
} else {
int idx = E.indexOf(x);
E.remove(idx);
ans.add(x);
ans.addAll(buildPermutation(1, O, E, k, d));
return ans;
}
}
i++;
}
}
return ans;
}
}

class Solution {
public int[] permute(int n, long k) {
int o = (n + 1) / 2, e = n / 2;
ArrayList<Integer> O = new ArrayList<>(), E = new ArrayList<>();

for (int i = 1; i <= n; i++) {
if (i % 2 == 1) O.add(i);
else E.add(i);
}

SortHelper s = new SortHelper();
s.sortList(O);
s.sortList(E);

DPHelper d = new DPHelper();
PermutationHelper ph = new PermutationHelper();

long tot = 0;
if (n % 2 == 1) tot = d.compute(O.size() - 1, E.size(), 0) * O.size();
else tot = d.compute(O.size() - 1, E.size(), 0) * O.size() + d.compute(O.size(), E.size() - 1, 1) * E.size();

if (k > tot) return new int[0];

List<Integer> res = ph.alternateFormation(O, E, k, d, n, s);
int[] ans = new int[res.size()];
for (int i = 0; i < res.size(); i++) ans[i] = res.get(i);

return ans;
}
}

```

#### C++

```cpp

class Solution {
long long f[105];
public:
vector<int> permute(int n, long long k) {
int i,j;
for(i=f[0]=1;i<=n;i++)if(f[i-1]>=k)f[i]=k;
else f[i]=f[i-1]*(i+1>>1);
if(!(n&1))f[n]*=2;
if(f[n]<k)return {};
k--;
vector<int> ans(n),a[2];
for(i=0;i<n;i++)a[i&1].push_back(i);
if(n&1)
{
ans[0]=k/f[n-1]*2;
k-=ans[0]/2*f[n-1];
}
else
{
ans[0]=k/f[n-1];
k-=ans[0]*f[n-1];
}
a[ans[0]&1].erase(lower_bound(a[ans[0]&1].begin(),a[ans[0]&1].end(),ans[0]));
for(i=1;i<n;i++)
{
if(n&1)
{
ans[i]=a[i&1][k/f[n-i-1]];
}
else
{
ans[i]=a[(ans[0]^i)&1][k/f[n-i-1]];
}
k%=f[n-i-1];
a[ans[i]&1].erase(lower_bound(a[ans[i]&1].begin(),a[ans[i]&1].end(),ans[i]));
}
for(i=0;i<n;i++)ans[i]++;
return ans;
}
};

```

#### Go

```go

func permute(n int, k int64) []int {
var f [105]int64
f[0] = 1
for i := 1; i <= n; i++ {
if f[i-1] >= k {
f[i] = k
} else {
f[i] = f[i-1] * int64((i+1)>>1)
}
}
if n%2 == 0 {
f[n] *= 2
}
if f[n] < k {
return []int{}
}
k--
ans := make([]int, n)
a := [2][]int{}
for i := 0; i < n; i++ {
a[i&1] = append(a[i&1], i)
}

if n%2 == 1 {
ans[0] = int(k/f[n-1]) * 2
k -= int64(ans[0]/2) * f[n-1]
} else {
ans[0] = int(k / f[n-1])
k -= int64(ans[0]) * f[n-1]
}

index := sort.SearchInts(a[ans[0]&1], ans[0])
a[ans[0]&1] = append(a[ans[0]&1][:index], a[ans[0]&1][index+1:]...)

for i := 1; i < n; i++ {
if n%2 == 1 {
ans[i] = a[i&1][k/f[n-i-1]]
} else {
ans[i] = a[(ans[0]^i)&1][k/f[n-i-1]]
}
k %= f[n-i-1]

index = sort.SearchInts(a[ans[i]&1], ans[i])
a[ans[i]&1] = append(a[ans[i]&1][:index], a[ans[i]&1][index+1:]...)
}

for i := 0; i < n; i++ {
ans[i]++
}
return ans
}

```

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