이 제출은 이전 버전의 oj.uz에서 채점하였습니다. 현재는 제출 당시와는 다른 서버에서 채점을 하기 때문에, 다시 제출하면 결과가 달라질 수도 있습니다.
#include "bits/stdc++.h"
using namespace std;
void abc() {cout << endl;}
template <typename T, typename ...U> void abc(T a, U ...b) {
cout << a << ' ', abc(b...);
}
template <typename T> void printv(T l, T r) {
while (l != r) cout << *l << " \n"[++l == r];
}
template <typename A, typename B> istream& operator >> (istream& o, pair<A, B> &a) {
return o >> a.first >> a.second;
}
template <typename A, typename B> ostream& operator << (ostream& o, pair<A, B> a) {
return o << '(' << a.first << ", " << a.second << ')';
}
template <typename T> ostream& operator << (ostream& o, vector<T> a) {
bool is = false;
for (T i : a) {o << (is ? ' ' : '{'), is = true, o << i;}
return o << '}';
}
#ifdef local
#define test(args...) abc("[" + string(#args) + "]", args)
#else
#define test(args...) void(0)
#endif
using ll = long long;
ll dp[1000005][2][2];
int a[1000005], b[1000005];
string ans = "";
void retrieve(int pos, int col, int aleft) {
if (pos == 1) {
if (col == 1) ans += "A";
else ans += "B";
return;
}
if (col == 0) {
ans += "A";
if (a[pos - 1] <= a[pos] && dp[pos - 1][0][0] <= (aleft - 1) && (aleft - 1) <= dp[pos - 1][0][1]) {
retrieve(pos - 1, 0, aleft - 1);
} else {
retrieve(pos - 1, 1, aleft);
}
} else {
ans += "B";
if (a[pos - 1] <= b[pos] && dp[pos - 1][0][0] <= (aleft) && (aleft) <= dp[pos - 1][0][1]) {
retrieve(pos - 1, 0, aleft - 1);
} else {
retrieve(pos - 1, 1, aleft);
}
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
// freopen("", "r", stdin);
// freopen("", "w", stdout);
int n; cin >> n;
for (int i = 1; i <= 2 * n; i++) cin >> a[i];
for (int i = 1; i <= 2 * n; i++) cin >> b[i];
for (int i = 1; i <= 2 * n; i++) {
dp[i][0][0] = dp[i][1][0] = 1e16;
dp[i][0][1] = dp[i][1][1] = -1;
}
dp[1][0][0] = 1;
dp[1][0][1] = 1;
dp[1][1][0] = 0;
dp[1][1][1] = 0;
for (int i = 2; i <= 2 * n; i++) {
if (a[i - 1] <= a[i]) {
dp[i][0][0] = min(dp[i][0][0], dp[i - 1][0][0] + 1);
dp[i][0][1] = max(dp[i][0][1], dp[i - 1][0][1] + 1);
}
if (b[i - 1] <= a[i]) {
dp[i][0][0] = min(dp[i][0][0], dp[i - 1][1][0] + 1);
dp[i][0][1] = max(dp[i][0][1], dp[i - 1][1][1] + 1);
}
if (a[i-1] <= b[i]) {
dp[i][1][0] = min(dp[i][1][0], dp[i-1][0][0]);
dp[i][1][1] = max(dp[i][1][1], dp[i-1][0][1]);
}
if (b[i-1] <= b[i]) {
dp[i][1][0] = min(dp[i][1][0], dp[i-1][1][0]);
dp[i][1][1] = max(dp[i][1][1], dp[i-1][1][1]);
}
}
if ((dp[2 * n][0][0] <= n && dp[2 * n][0][1] >= n)) {
retrieve(2 * n, 0, n);
reverse(ans.begin(), ans.end());
cout << ans;
} else if ((dp[2 * n][1][0] <= n && dp[2 * n][1][1] <= n)) {
retrieve(2 * n, 1, n);
reverse(ans.begin(), ans.end());
cout << ans;
} else {
cout << -1;
}
}
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