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 "grader.cpp"
#include <cstdlib>
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define fi first
#define se second
#define sz(a) (int)(a.size())
#define all(a) a.begin(),a.end()
#define lb lower_bound
#define ub upper_bound
#define owo ios_base::sync_with_stdio(0);cin.tie(0);
#define MOD (ll)(1e9+7)
#define INF (ll)(1e18)
#define debug(...) fprintf(stderr, __VA_ARGS__),fflush(stderr)
#define time__(d) for(long blockTime = 0; (blockTime == 0 ? (blockTime=clock()) != 0 : false);\
debug("%s time : %.4fs\n", d, (double)(clock() - blockTime) / CLOCKS_PER_SEC))
typedef long long int ll;
typedef long double ld;
typedef pair<ll,ll> PII;
typedef pair<int,int> pii;
typedef vector<vector<int>> vii;
typedef vector<vector<ll>> VII;
ll gcd(ll a,ll b){if(!b)return a;else return gcd(b,a%b);}
std::string solve_puzzle(std::string s, std::vector<int> c){
int n = sz(s);
int k = sz(c);
vector<int>w(n+2),b(n+2);
vector<vector<bool>>dpp(n+2,vector<bool>(k+3)),dps(n+2,vector<bool>(k+3));
for(int i=1;i<=n+1;i++){
if(s[i-1] == '_')w[i]++;
if(s[i-1] == 'X')b[i]++;
b[i]+=b[i-1];
w[i]+=w[i-1];
}
dpp[0][0] = 1;
for(int i=1;i<=n;i++){
if(!b[i])dpp[i][0] = 1;
for(int j=1;j<=k;j++){
int L = i-c[j-1];
bool a = 0,b = 1;
a = dpp[i-1][j];
if(L > 0)b = (s[L-1] != 'X');
b= b&((L==0 && j==1) || (L>=1 && dpp[L-1][j-1]));
if(L>=0)b= b&(w[i]-w[L] == 0);
if(s[i-1] == '_')dpp[i][j] = a;
else if(s[i-1] == 'X')dpp[i][j] = b;
else dpp[i][j] = (a||b);
}
}
dps[n+1][k+1] = 1;
for(int i=n;i>0;i--){
if(!(b[n]-b[i-1]))dps[i][k+1] = 1;
for(int j=1;j<=k;j++){
int L = i+c[j-1];
bool a = 0,b = 1;
a = dps[i+1][j];
if(L<=n)b = (s[L-1] != 'X');
b= b&((L==n+1 && j==k) || (L<=n && dps[L+1][j+1]));
if(L<=n+1)b=b&(w[L-1]-w[i-1] == 0);
if(s[i-1] == '_')dps[i][j] = a;
else if(s[i-1] == 'X')dps[i][j] = b;
else dps[i][j] = (a||b);
}
}/*
for(int i=0;i<=k;i++){
for(int j=1;j<=n;j++){
cout<<dpp[j][i]<<" ";
}
cout<<'\n';
}
cout<<'\n';
for(int i=1;i<=k+1;i++){
for(int j=1;j<=n;j++){
cout<<dps[j][i]<<" ";
}
cout<<'\n';
}
cout<<'\n';
*/
vector<bool>canw(n+2,0);
vector<ll>canb(n+2);
for(int i=1;i<=n;i++){
if(s[i-1] == 'X')continue;
for(int j=0;j<=k;j++){
if(dpp[i-1][j] && dps[i+1][j+1])canw[i] = 1;
}
}//check for white ,this works
//to check for black iterate starting point and +1 -1,tedious fuck you
for(int i=1;i<=n;i++){
if(s[i-1] == 'W')continue;
for(int j=1;j<=k;j++){
int R = i+c[j-1];
bool ok = 1;
if(R<=n)ok = s[R-1] != 'X';
ok= ok&((R==n+1 && j==k) || (R<=n && dps[R+1][j+1])); //check right side
ok= ok&((i == 1 && j == 1) || (i>1 && dpp[i-2][j-1] && s[i-2] != 'X')); //check left side
ok= ok&(R-1<=n && w[R-1] - w[i-1] == 0); //check for no white space
if(ok){
canb[i]++;
canb[R]--;
}
}
}
/*
for(int i=1;i<=n;i++)cout<<canw[i]<<" ";
cout<<'\n';
for(int i=1;i<=n;i++)cout<<canb[i]<<" ";
cout<<'\n';
* */
for(int i=1;i<=n;i++)canb[i]+=canb[i-1];
//for(int i=1;i<=n;i++)cout<<canb[i]<<" ";
//cout<<'\n';
string ans;
for(int i=1;i<=n;i++){
if(canw[i] && canb[i])ans+="?";
else if(canw[i])ans+="_";
else ans+="X";
}
return ans;
}
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