#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef pair<int,int> ii;
template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;
const int MOD = 998244353;
ll read(){
ll i;
cin>>i;
return i;
}
vi readvi(int n,int off=0,int shift=0){
vi v(n+shift);
rep(i,shift)v[i]=0;
rep(i,n)v[i+shift]=read()+off;
return v;
}
void YesNo(bool condition, bool do_exit=true) {
if (condition)
cout << "TAK" << endl;
else
cout << "NIE" << endl;
if (do_exit)
exit(0);
}
int main(void ) {
ios::sync_with_stdio(false);
cin.tie(NULL);
int t;
cin >> t;
rep(_,t) {
int n;
cin >> n;
vi a = readvi(n);
a.insert(a.begin(), 0);
a.push_back(0);
n += 2;
int num_blocks = 0;
bool in_block = false;
for (int x : a) {
if (x) {
if (not in_block)
++num_blocks;
in_block = true;
}
else
in_block = false;
}
if (num_blocks > 1) {
cout << "NIE\n";
continue;
}
vc<vc<set<int>>> dp(n, vc<set<int>>(3));
int i = 0;
while (a[i] == 0)
++i;
dp[i][0].insert(a[i]);
dp[i][1].insert(a[i]-1);
dp[i][2].insert(a[i]-1);
++i;
while (a[i] > 0) {
for (int x : dp[i-1][0])
if (x > 0 and a[i] - x >= 0)
dp[i][0].insert(a[i] - x);
for (int x : dp[i-1][0])
if (x > 0 and a[i] - 1 - x >= 0)
dp[i][1].insert(a[i] - 1 - x);
for (int x : dp[i-1][1])
if (a[i] - 1 - x >= 0)
dp[i][1].insert(a[i] - 1 - x);
for (int x : dp[i-1][0])
if (x > 0 and a[i] - 1 - x >= 0)
dp[i][2].insert(a[i] - 1 - x);
for (int x : dp[i-1][1])
if (a[i] - 1 - x >= 0)
dp[i][2].insert(a[i] - 1 - x);
for (int x : dp[i-1][2])
if (x > 0 and a[i] - x >= 0)
dp[i][2].insert(a[i] - x);
++i;
}
YesNo(dp[i-1][2].find(0) != dp[i-1][2].end(), false);
}
return 0;
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 | #include <bits/stdc++.h> using namespace std; #define ll long long #define rng(i,a,b) for(int i=int(a);i<int(b);i++) #define rep(i,b) rng(i,0,b) typedef vector<int> vi; typedef vector<vi> vvi; typedef vector<vvi> vvvi; typedef vector<ll> vl; typedef vector<vl> vvl; typedef vector<vvl> vvvl; typedef pair<int,int> ii; template<class t> using vc=vector<t>; template<class t> using vvc=vc<vc<t>>; const int MOD = 998244353; ll read(){ ll i; cin>>i; return i; } vi readvi(int n,int off=0,int shift=0){ vi v(n+shift); rep(i,shift)v[i]=0; rep(i,n)v[i+shift]=read()+off; return v; } void YesNo(bool condition, bool do_exit=true) { if (condition) cout << "TAK" << endl; else cout << "NIE" << endl; if (do_exit) exit(0); } int main(void ) { ios::sync_with_stdio(false); cin.tie(NULL); int t; cin >> t; rep(_,t) { int n; cin >> n; vi a = readvi(n); a.insert(a.begin(), 0); a.push_back(0); n += 2; int num_blocks = 0; bool in_block = false; for (int x : a) { if (x) { if (not in_block) ++num_blocks; in_block = true; } else in_block = false; } if (num_blocks > 1) { cout << "NIE\n"; continue; } vc<vc<set<int>>> dp(n, vc<set<int>>(3)); int i = 0; while (a[i] == 0) ++i; dp[i][0].insert(a[i]); dp[i][1].insert(a[i]-1); dp[i][2].insert(a[i]-1); ++i; while (a[i] > 0) { for (int x : dp[i-1][0]) if (x > 0 and a[i] - x >= 0) dp[i][0].insert(a[i] - x); for (int x : dp[i-1][0]) if (x > 0 and a[i] - 1 - x >= 0) dp[i][1].insert(a[i] - 1 - x); for (int x : dp[i-1][1]) if (a[i] - 1 - x >= 0) dp[i][1].insert(a[i] - 1 - x); for (int x : dp[i-1][0]) if (x > 0 and a[i] - 1 - x >= 0) dp[i][2].insert(a[i] - 1 - x); for (int x : dp[i-1][1]) if (a[i] - 1 - x >= 0) dp[i][2].insert(a[i] - 1 - x); for (int x : dp[i-1][2]) if (x > 0 and a[i] - x >= 0) dp[i][2].insert(a[i] - x); ++i; } YesNo(dp[i-1][2].find(0) != dp[i-1][2].end(), false); } return 0; } |
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