This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
typedef int ll;
const ll INF = 1e9+7;
const ll MOD = 998244353;
typedef pair<ll,ll> ii;
#define iii pair<ll,ii>
#define f(i,a,b) for(ll i = a;i < b;i++)
#define pb push_back
#define vll vector<ll>
#define F first
#define S second
#define all(x) (x).begin(), (x).end()
///I hope I will get uprating and don't make mistakes
///I will never stop programming
///sqrt(-1) Love C++
///Please don't hack me
///@TheofanisOrfanou Theo830
///Think different approaches (bs,dp,greedy,graphs,shortest paths,mst)
///Stay Calm
///Look for special cases
///Beware of overflow and array bounds
///Think the problem backwards
///Training
#include "paint.h"
ll ans[200005] = {0};
ll n,k;
string S;
vector<int>C;
int dp[200001][101];
int Next[200005];
ll exo[200005] = {0};
int solve(ll idx,ll p){
if(idx == n){
return (p == k);
}
if(dp[idx][p] != -1){
return dp[idx][p];
}
bool ok = 0;
if(S[idx] == '_'){
ok = solve(idx + 1,p);
ans[idx] |= ok;
return dp[idx][p] = ok;
}
if(p != k){
if(idx + C[p] > n){
ok = 0;
}
else if(idx + C[p] == n){
if(Next[idx] >= n){
ok = solve(idx + C[p],p + 1);
if(ok){
exo[idx]++;
exo[idx + C[p]]--;
}
}
else{
ok = 0;
}
}
else{
if(Next[idx] >= idx + C[p] && S[idx + C[p]] != 'X'){
ok = solve(idx + C[p] + 1,p + 1);
if(ok){
exo[idx]++;
exo[idx + C[p]]--;
ans[idx + C[p]] = 1;
}
}
else{
ok = 0;
}
}
}
else{
if(S[idx] == 'X'){
return dp[idx][p] = 0;
}
}
if(S[idx] == '.'){
bool v = solve(idx + 1,p);
ans[idx] |= v;
ok |= v;
}
return dp[idx][p] = ok;
}
std::string solve_puzzle(std::string s, std::vector<int> c){
n = s.size();
k = c.size();
S = s;
C = c;
Next[n-1] = INF;
for(ll i = n-2;i >= 0;i--){
Next[i] = Next[i+1];
if(s[i+1] == '_'){
Next[i] = i+1;
}
}
memset(dp,-1,sizeof dp);
solve(0,0);
string res = "";
ll cur = 0;
f(i,0,n){
cur += exo[i];
if(cur){
ans[i] |= 2;
}
}
f(i,0,n){
assert(ans[i]);
if(ans[i] == 3){
res += "?";
}
else if(ans[i] == 2){
res += "X";
}
else{
res += "_";
}
}
return res;
}
/*
const int S_MAX_LEN = 200 * 1000;
char buf[S_MAX_LEN + 1];
int main() {
assert(1 == scanf("%s", buf));
std::string s = buf;
int c_len;
assert(1 == scanf("%d", &c_len));
std::vector<int> c(c_len);
for (int i = 0; i < c_len; i++) {
assert(1 == scanf("%d", &c[i]));
}
std::string ans = solve_puzzle(s, c);
printf("%s\n", ans.data());
return 0;
}
*/
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