// Witold Milewski
// PA 2025
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define FOR(i, a, b) for(int i=a; i<=b; ++i)
#define FORB(i, b, a) for(int i=b; i>=a; --i)
#define ll long long
#define sz(A) (int)(A.size())
#define eb emplace_back
#define pb push_back
#define pi pair<int, int>
#define f first
#define s second
#define rs resize
#define V vector
int n;
bool odp(V<int> A, int p, int k) {
FOR(i, 1, n) if(A[i]==0) return 0;
if(n==1) {
if(A[1]==1) return 1;
else return 0;
}
V<int> deg = A;
deg[p]--;
FOR(i, 1, p-1) {
deg[i]--;
deg[i+1]--;
}
FOR(i, p, k-1) {
deg[i+1]--;
}
FOR(i, k, n-1) {
deg[i]--;
deg[i+1]--;
}
FOR(i, 1, n) if(deg[i]<0) return 0;
FOR(i, 1, n-1) {
int x = deg[i];
deg[i]-=x;
deg[i+1]-=x;
if(deg[i+1]<0) return 0;
}
if(deg[n]!=0) return 0;
return 1;
}
bool solve(V<int> A) {
FOR(i, 1, n) if(A[i]==0) return 0;
if(n==1) {
if(A[1]==1) return 1;
else return 0;
}
V<int> pref(n+2, -1);
pref[0]=0;
V<int> suf(n+2, -1);
suf[n+1]=0;
V<int> deg = A;
V<int> deg1 = A;
V<int> deg2 = A;
deg[1]-=1;
deg[n]-=1;
FOR(i, 2, n-1) deg[i]-=2;
deg1[1]-=1;
deg1[n]-=1;
FOR(i, 2, n-1) deg1[i]-=2;
deg2[1]-=1;
deg2[n]-=1;
FOR(i, 2, n-1) deg2[i]-=2;
bool ok=1;
int p=-1;
int k=-1;
FOR(i, 1, n-1) {
int x = deg1[i];
deg1[i]-=x;
deg1[i+1]-=x;
if(deg1[i+1]>=0) {
if(p==-1) pref[i]=x;
continue;
}
if(deg1[i+1]<-1) {
ok=0;
break;
}
p=i;
break;
}
FORB(i, n, 2) {
int x = deg2[i];
deg2[i]-=x;
deg2[i-1]-=x;
if(deg2[i-1]>=0) {
if(k==-1) suf[i]=x;
continue;
}
if(deg2[i-1]<-1) {
ok=0;
break;
}
k=i;
break;
}
FOR(i, 1, n) {
if(pref[i-1]==-1 || suf[i+1]==-1) continue;
if(pref[i-1]+suf[i+1]+1==deg[i]) return 1;
}
if(p==-1 || k==-1) ok=0;
if(ok && p<k-1) {
if(odp(A, p, k)) return 1;
}
if(odp(A, 1, 2)) return 1;
return 0;
}
void rozw() {
cin >> n;
V<int> A = {0};
bool bylowiekszeniz0 = 0;
int x;
FOR(i, 1, n) {
cin >> x;
if(x!=0 || (x==0 && bylowiekszeniz0)) A.eb(x);
if(x>0) bylowiekszeniz0=1;
}
while(!A.empty() && A.back()==0) A.pop_back();
n = sz(A)-1;
bool odp1 = 0;
if(solve(A)) odp1=1;
if(odp1) {
cout << "TAK\n";
} else {
cout << "NIE\n";
}
}
signed main() {
cin.tie(0) -> ios_base::sync_with_stdio(0);
int q; cin >> q;
while(q--) {
rozw();
}
}
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 | // Witold Milewski // PA 2025 #include <bits/stdc++.h> using namespace std; #define int long long #define FOR(i, a, b) for(int i=a; i<=b; ++i) #define FORB(i, b, a) for(int i=b; i>=a; --i) #define ll long long #define sz(A) (int)(A.size()) #define eb emplace_back #define pb push_back #define pi pair<int, int> #define f first #define s second #define rs resize #define V vector int n; bool odp(V<int> A, int p, int k) { FOR(i, 1, n) if(A[i]==0) return 0; if(n==1) { if(A[1]==1) return 1; else return 0; } V<int> deg = A; deg[p]--; FOR(i, 1, p-1) { deg[i]--; deg[i+1]--; } FOR(i, p, k-1) { deg[i+1]--; } FOR(i, k, n-1) { deg[i]--; deg[i+1]--; } FOR(i, 1, n) if(deg[i]<0) return 0; FOR(i, 1, n-1) { int x = deg[i]; deg[i]-=x; deg[i+1]-=x; if(deg[i+1]<0) return 0; } if(deg[n]!=0) return 0; return 1; } bool solve(V<int> A) { FOR(i, 1, n) if(A[i]==0) return 0; if(n==1) { if(A[1]==1) return 1; else return 0; } V<int> pref(n+2, -1); pref[0]=0; V<int> suf(n+2, -1); suf[n+1]=0; V<int> deg = A; V<int> deg1 = A; V<int> deg2 = A; deg[1]-=1; deg[n]-=1; FOR(i, 2, n-1) deg[i]-=2; deg1[1]-=1; deg1[n]-=1; FOR(i, 2, n-1) deg1[i]-=2; deg2[1]-=1; deg2[n]-=1; FOR(i, 2, n-1) deg2[i]-=2; bool ok=1; int p=-1; int k=-1; FOR(i, 1, n-1) { int x = deg1[i]; deg1[i]-=x; deg1[i+1]-=x; if(deg1[i+1]>=0) { if(p==-1) pref[i]=x; continue; } if(deg1[i+1]<-1) { ok=0; break; } p=i; break; } FORB(i, n, 2) { int x = deg2[i]; deg2[i]-=x; deg2[i-1]-=x; if(deg2[i-1]>=0) { if(k==-1) suf[i]=x; continue; } if(deg2[i-1]<-1) { ok=0; break; } k=i; break; } FOR(i, 1, n) { if(pref[i-1]==-1 || suf[i+1]==-1) continue; if(pref[i-1]+suf[i+1]+1==deg[i]) return 1; } if(p==-1 || k==-1) ok=0; if(ok && p<k-1) { if(odp(A, p, k)) return 1; } if(odp(A, 1, 2)) return 1; return 0; } void rozw() { cin >> n; V<int> A = {0}; bool bylowiekszeniz0 = 0; int x; FOR(i, 1, n) { cin >> x; if(x!=0 || (x==0 && bylowiekszeniz0)) A.eb(x); if(x>0) bylowiekszeniz0=1; } while(!A.empty() && A.back()==0) A.pop_back(); n = sz(A)-1; bool odp1 = 0; if(solve(A)) odp1=1; if(odp1) { cout << "TAK\n"; } else { cout << "NIE\n"; } } signed main() { cin.tie(0) -> ios_base::sync_with_stdio(0); int q; cin >> q; while(q--) { rozw(); } } |
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