Update README_EN.md

Author: samarthswami1016

solution/3400-3499/3470.Permutations IV/README_EN.md

@@ -108,25 +108,341 @@ tags:
 #### Python3
 
 ```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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