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Create solution.java #4142

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157 changes: 157 additions & 0 deletions solution/3400-3499/3470.Permutations IV/solution.java
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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;
}
}
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