#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
const int N = 1e6 + 5;
ll A[N];
pair<ll, ll> DP[N][2];
void CountDP(int start, int end)
{
DP[start][0] = {A[start] - 1, 0};
for(int i = start + 1; i <= end; i++) {
if(DP[i-1][0].second == 0) {
if(DP[i-1][0].first < A[i] - 1)
DP[i][0] = {A[i] - 2 - DP[i-1][0].first, 0};
else if(DP[i-1][0].first == A[i] - 1)
DP[i][0] = {0, 1};
else
DP[i][0] = {A[i] - 1, 2};
} else if(DP[i-1][0].second == 1) {
if(DP[i-1][0].first <= A[i] - 1)
DP[i][0] = {A[i] - DP[i-1][0].first - 1, 1};
else
DP[i][0] = {A[i] - 1, 2};
} else
DP[i][0] = {A[i] - 1, 2};
}
DP[end][1] = {A[end] - 1, 0};
for(int i = end-1; i >= start; i--) {
if(DP[i+1][1].second == 0) {
if(DP[i+1][1].first < A[i] - 1)
DP[i][1] = {A[i] - 2 - DP[i+1][1].first, 0};
else if(DP[i+1][1].first == A[i] - 1)
DP[i][1] = {0, 1};
else
DP[i][1] = {A[i] - 1, 2};
} else if(DP[i+1][1].second == 1) {
if(DP[i+1][1].first <= A[i] - 1)
DP[i][1] = {A[i] - DP[i+1][1].first - 1, 1};
else
DP[i][1] = {A[i] - 1, 2};
} else
DP[i][1] = {A[i] - 1, 2};
}
}
bool Solve(int n)
{
int start = 0, end = n-1;
while(start < n && A[start] == 0)
start++;
while(end >= 0 && A[end] == 0)
end--;
for(int i = start; i <= end; i++) {
if(A[i] == 0)
return false;
}
if(start == n)
return true;
CountDP(start, end);
if(DP[end][0].first == 0 && DP[end][0].second != 2)
return true;
if(DP[start][1].first == 0 && DP[start][1].second != 2)
return true;
for(int i = start + 1; i <= end - 1; i++) {
if(DP[i][0].second == 0) {
if(DP[i+1][1].second == 0 && (DP[i][0].first == DP[i+1][1].first || DP[i][0].first - 1 == DP[i+1][1].first))
return true;
else if(DP[i+1][1].second == 1 && DP[i+1][1].first == DP[i][0].first)
return true;
}
if(DP[i][1].second == 0) {
if(DP[i-1][0].second == 0 && (DP[i][1].first == DP[i-1][0].first || DP[i][1].first - 1 == DP[i-1][0].first))
return true;
else if(DP[i-1][0].second == 1 && DP[i-1][0].first == DP[i][1].first)
return true;
}
}
return false;
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
int t, n;
cin >> t;
while(t --> 0) {
cin >> n;
for(int i = 0; i < n; i++)
cin >> A[i];
if(Solve(n))
cout << "TAK\n";
else
cout << "NIE\n";
}
}
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 | #include <bits/stdc++.h> using namespace std; typedef long long int ll; const int N = 1e6 + 5; ll A[N]; pair<ll, ll> DP[N][2]; void CountDP(int start, int end) { DP[start][0] = {A[start] - 1, 0}; for(int i = start + 1; i <= end; i++) { if(DP[i-1][0].second == 0) { if(DP[i-1][0].first < A[i] - 1) DP[i][0] = {A[i] - 2 - DP[i-1][0].first, 0}; else if(DP[i-1][0].first == A[i] - 1) DP[i][0] = {0, 1}; else DP[i][0] = {A[i] - 1, 2}; } else if(DP[i-1][0].second == 1) { if(DP[i-1][0].first <= A[i] - 1) DP[i][0] = {A[i] - DP[i-1][0].first - 1, 1}; else DP[i][0] = {A[i] - 1, 2}; } else DP[i][0] = {A[i] - 1, 2}; } DP[end][1] = {A[end] - 1, 0}; for(int i = end-1; i >= start; i--) { if(DP[i+1][1].second == 0) { if(DP[i+1][1].first < A[i] - 1) DP[i][1] = {A[i] - 2 - DP[i+1][1].first, 0}; else if(DP[i+1][1].first == A[i] - 1) DP[i][1] = {0, 1}; else DP[i][1] = {A[i] - 1, 2}; } else if(DP[i+1][1].second == 1) { if(DP[i+1][1].first <= A[i] - 1) DP[i][1] = {A[i] - DP[i+1][1].first - 1, 1}; else DP[i][1] = {A[i] - 1, 2}; } else DP[i][1] = {A[i] - 1, 2}; } } bool Solve(int n) { int start = 0, end = n-1; while(start < n && A[start] == 0) start++; while(end >= 0 && A[end] == 0) end--; for(int i = start; i <= end; i++) { if(A[i] == 0) return false; } if(start == n) return true; CountDP(start, end); if(DP[end][0].first == 0 && DP[end][0].second != 2) return true; if(DP[start][1].first == 0 && DP[start][1].second != 2) return true; for(int i = start + 1; i <= end - 1; i++) { if(DP[i][0].second == 0) { if(DP[i+1][1].second == 0 && (DP[i][0].first == DP[i+1][1].first || DP[i][0].first - 1 == DP[i+1][1].first)) return true; else if(DP[i+1][1].second == 1 && DP[i+1][1].first == DP[i][0].first) return true; } if(DP[i][1].second == 0) { if(DP[i-1][0].second == 0 && (DP[i][1].first == DP[i-1][0].first || DP[i][1].first - 1 == DP[i-1][0].first)) return true; else if(DP[i-1][0].second == 1 && DP[i-1][0].first == DP[i][1].first) return true; } } return false; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); int t, n; cin >> t; while(t --> 0) { cin >> n; for(int i = 0; i < n; i++) cin >> A[i]; if(Solve(n)) cout << "TAK\n"; else cout << "NIE\n"; } } |
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