#include <iostream> #include <iomanip> #include <string> #include <algorithm> using namespace std; //#define DEBUG #ifdef DEBUG #undef DEBUG #define DEBUG(x) x #else #define DEBUG(x) #endif #define REP(x,n) for(int x=0;x<(n);++x) #define VAR(x,n) __typeof(n) x = (n) #define FOREACH(x,c) for(VAR(x, (c).begin()); x != (c).end(); ++x) #define CONTAINS(x,elem) ((x).find(elem) != (x).end()) #define MAX_N 1000003 int input[MAX_N]; bool checkPreconditions(int* tab, int n) { REP(x,n) if (tab[x] == 0) { DEBUG(cerr<<"zero is present in the middle: " << x << " -> ";) return false; } int edges = 0; if (tab[0] > tab[1]) { if (tab[0]-tab[1]>1 || tab[2]>0) { DEBUG(cerr<<"leftmost " << 0 << " is too large (" << tab[1] << "<" << tab[0] << ") -> ";) return false; } else { ++edges; DEBUG(cerr << "found edge at " << 0 << endl;) } } if (tab[n-1] > tab[n-2]) { if (tab[n-1] - tab[n-2] > 1 || tab[n-3]>0) { DEBUG(cerr<<"rightmost " << n-1 << " is too large (" << tab[n-2] << "<" << tab[n-1] << ") -> ";) return false; } else { if (++edges == 2) { DEBUG(cerr << "found second edge at " << n-1 << " -> ";) return false; } else { DEBUG(cerr << "found edge at " << n-1 << endl;) } } } for(int x=1; x<n-1; ++x) { int diff = tab[x] - tab[x-1] - tab[x+1]; if (diff >= 2) { DEBUG(cerr<<"single point " << x << " is too large -> ";) return false; } else if (diff == 1) { if (++edges == 2) { DEBUG(cerr << "found second edge at " << x << " -> ";) return false; } DEBUG(cerr << "found edge at " << x << endl;) } } return true; } bool inline isLeftMost(int x) { return x == 0; } bool inline isRightMost(int x, int n) { return x == n-1; } bool findRightSolution(int* tab, int n) { //going right, starting point is tab[0] DEBUG( cerr<<"entering solveRight with " << n << " arguments, total shift is " << tab-input << endl; REP(x,n) cerr << tab[x] << " "; cerr << endl; ) if (n==1) { return tab[0]==1; } int remaining = tab[0]-1; REP(x,n-1) { int value = tab[x+1]; if (remaining == value) { if (x+1 == n-1) { return true; } else { DEBUG(cerr<<"remaining==value ("<<remaining<<") for element "<<x+1<<" -> ";) return false; } } else if (remaining > value-1 && (remaining > value || x+1 > n-1)) { DEBUG(cerr<<" found another starting point at "<<x+1<<" when going right --> ";) return false; } else { remaining = value - remaining - 1; } } if (remaining >= 1) { DEBUG(cerr<<" remaining "<<remaining<<" at the end --> ";) return false; } return true; } bool findLeftSolution(int* tab, int n) { // DUPADEBUG(cout << "DUPA_left_";) return true; //going right, starting point is tab[0] DEBUG( cerr<<"entering solveLeft with " << n << " arguments, total shift is " << tab-input << endl; REP(x,n) cerr << tab[x] << " "; cerr << endl; ) int remaining = tab[n-1]-1; for(int x=n-2; x>0; --x) { int value = tab[x]; if (remaining == value) { DEBUG(cerr << "value = remaining at " << x << " - result is " << (tab[x-1]==0) << " --> ";) return tab[x-1] == 0; } else if (remaining > value) { DEBUG(cerr<<" found another starting point at "<<x<<" when going left --> ";) return false; } else { remaining = value - remaining; } } return true; } bool findCenterPointSolution(int* tab, int mid, int n) { int remaining = tab[0]; REP(x,n-1) { if (x==mid) --remaining; int value = tab[x+1]; if (remaining - value > 1) { DEBUG(cerr<<"too much remaining at " << x << " (" << remaining-value << ") -> ";) return false; } else if (remaining - value == 1) { DEBUG(cerr<<"found another center point at " << x << endl;) return false; } else if (remaining == value && x+1 < n-1) { // x+1 / x+2 is a separation for line DEBUG(cerr<<"found separation at " << x+1 << "/" << x+2 << " but not legal in center point solution --> ";) return false; } else { remaining = tab[x+1] - remaining; } } if (remaining > 0) { DEBUG(cerr<<" remaining "<<remaining<<" at the end --> ";) return false; } return true; } bool findSolution(int* tab, int n) { int remaining = tab[0]; REP(x,n-1) { int value = tab[x+1]; if (remaining - value > 1) { DEBUG(cerr<<"too much remaining at " << x << " (" << remaining-value << ") -> ";) return false; } else if (remaining - value == 1) { // x is a starting point for both directions DEBUG(cerr<<"found center point at " << x << endl;) return findCenterPointSolution(tab, x, n); } else if (remaining == value && x+1 < n-1) { // x+1 / x+2 is a separation for line DEBUG(cerr<<"found separation at " << x+1 << "/" << x+2 << endl;) return findRightSolution(tab+x+2, n-(x+2)) && findLeftSolution(tab, x+2); } else { remaining = tab[x+1] - remaining; } } if (remaining > 1) { DEBUG(cerr<<" remaining "<<remaining<<" at the end --> ";) return false; } return true; } //tab[0..n) is the real range with non-zero numbers bool solve(int* tab, int n) { DEBUG( cerr<<"entering solve with " << n << " arguments, shift is " << tab-input << endl; REP(x,n) cerr << tab[x] << " "; cerr << endl; ) if (n == 1) { DEBUG(cerr << "only non-zero element is " << tab[0] << " -> ";) return tab[0] == 1; // for 1-element array result is true only when exactly 1 } return checkPreconditions(tab, n) && findSolution(tab, n); } bool solve() { int n; cin>>n; int firstNonZeroIndex=-1, lastNonZeroIndex=-1; REP(x, n) { cin>>input[x+1]; if (input[x+1] != 0) { lastNonZeroIndex = x+1; if (firstNonZeroIndex == -1) firstNonZeroIndex = x+1; } } input[++n] = 0; //safety margins: tab[0] = tab[n+1] = 0 if (!solve(input+firstNonZeroIndex, lastNonZeroIndex-firstNonZeroIndex+1)) { return false; } std::reverse(input+firstNonZeroIndex, input+lastNonZeroIndex+1); if (!solve(input+firstNonZeroIndex, lastNonZeroIndex-firstNonZeroIndex+1)) { return false; } // if (lastNonZeroIndex - firstNonZeroIndex > 2) { // if (input[lastNonZeroIndex] == 1 && input[lastNonZeroIndex-1] == 1) { // input[lastNonZeroIndex+1] = 1; // input[lastNonZeroIndex+2] = 0; // if (!solve(input+firstNonZeroIndex, lastNonZeroIndex-firstNonZeroIndex+2)) { // return false; // } // std::reverse(input+firstNonZeroIndex, input+lastNonZeroIndex+2); // if (!solve(input+firstNonZeroIndex, lastNonZeroIndex-firstNonZeroIndex+2)) { // return false; // } // std::reverse(input+firstNonZeroIndex, input+lastNonZeroIndex+2); // input[lastNonZeroIndex+1] = 0; // } // if (input[firstNonZeroIndex] == 1 && input[firstNonZeroIndex+1] == 1) { // input[lastNonZeroIndex+1] = 1; // input[lastNonZeroIndex+2] = 0; // std::reverse(input+firstNonZeroIndex, input+lastNonZeroIndex+1); // if (!solve(input+firstNonZeroIndex, lastNonZeroIndex-firstNonZeroIndex+2)) { // return false; // } // std::reverse(input+firstNonZeroIndex, input+lastNonZeroIndex+2); // if (!solve(input+firstNonZeroIndex, lastNonZeroIndex-firstNonZeroIndex+2)) { // return false; // } // } // } return true; } int main() { ios_base::sync_with_stdio(0); int t; cin>>t; REP(x, t) { cout << (solve() ? "TAK" : "NIE") << endl; } 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 | #include <iostream> #include <iomanip> #include <string> #include <algorithm> using namespace std; //#define DEBUG #ifdef DEBUG #undef DEBUG #define DEBUG(x) x #else #define DEBUG(x) #endif #define REP(x,n) for(int x=0;x<(n);++x) #define VAR(x,n) __typeof(n) x = (n) #define FOREACH(x,c) for(VAR(x, (c).begin()); x != (c).end(); ++x) #define CONTAINS(x,elem) ((x).find(elem) != (x).end()) #define MAX_N 1000003 int input[MAX_N]; bool checkPreconditions(int* tab, int n) { REP(x,n) if (tab[x] == 0) { DEBUG(cerr<<"zero is present in the middle: " << x << " -> ";) return false; } int edges = 0; if (tab[0] > tab[1]) { if (tab[0]-tab[1]>1 || tab[2]>0) { DEBUG(cerr<<"leftmost " << 0 << " is too large (" << tab[1] << "<" << tab[0] << ") -> ";) return false; } else { ++edges; DEBUG(cerr << "found edge at " << 0 << endl;) } } if (tab[n-1] > tab[n-2]) { if (tab[n-1] - tab[n-2] > 1 || tab[n-3]>0) { DEBUG(cerr<<"rightmost " << n-1 << " is too large (" << tab[n-2] << "<" << tab[n-1] << ") -> ";) return false; } else { if (++edges == 2) { DEBUG(cerr << "found second edge at " << n-1 << " -> ";) return false; } else { DEBUG(cerr << "found edge at " << n-1 << endl;) } } } for(int x=1; x<n-1; ++x) { int diff = tab[x] - tab[x-1] - tab[x+1]; if (diff >= 2) { DEBUG(cerr<<"single point " << x << " is too large -> ";) return false; } else if (diff == 1) { if (++edges == 2) { DEBUG(cerr << "found second edge at " << x << " -> ";) return false; } DEBUG(cerr << "found edge at " << x << endl;) } } return true; } bool inline isLeftMost(int x) { return x == 0; } bool inline isRightMost(int x, int n) { return x == n-1; } bool findRightSolution(int* tab, int n) { //going right, starting point is tab[0] DEBUG( cerr<<"entering solveRight with " << n << " arguments, total shift is " << tab-input << endl; REP(x,n) cerr << tab[x] << " "; cerr << endl; ) if (n==1) { return tab[0]==1; } int remaining = tab[0]-1; REP(x,n-1) { int value = tab[x+1]; if (remaining == value) { if (x+1 == n-1) { return true; } else { DEBUG(cerr<<"remaining==value ("<<remaining<<") for element "<<x+1<<" -> ";) return false; } } else if (remaining > value-1 && (remaining > value || x+1 > n-1)) { DEBUG(cerr<<" found another starting point at "<<x+1<<" when going right --> ";) return false; } else { remaining = value - remaining - 1; } } if (remaining >= 1) { DEBUG(cerr<<" remaining "<<remaining<<" at the end --> ";) return false; } return true; } bool findLeftSolution(int* tab, int n) { // DUPADEBUG(cout << "DUPA_left_";) return true; //going right, starting point is tab[0] DEBUG( cerr<<"entering solveLeft with " << n << " arguments, total shift is " << tab-input << endl; REP(x,n) cerr << tab[x] << " "; cerr << endl; ) int remaining = tab[n-1]-1; for(int x=n-2; x>0; --x) { int value = tab[x]; if (remaining == value) { DEBUG(cerr << "value = remaining at " << x << " - result is " << (tab[x-1]==0) << " --> ";) return tab[x-1] == 0; } else if (remaining > value) { DEBUG(cerr<<" found another starting point at "<<x<<" when going left --> ";) return false; } else { remaining = value - remaining; } } return true; } bool findCenterPointSolution(int* tab, int mid, int n) { int remaining = tab[0]; REP(x,n-1) { if (x==mid) --remaining; int value = tab[x+1]; if (remaining - value > 1) { DEBUG(cerr<<"too much remaining at " << x << " (" << remaining-value << ") -> ";) return false; } else if (remaining - value == 1) { DEBUG(cerr<<"found another center point at " << x << endl;) return false; } else if (remaining == value && x+1 < n-1) { // x+1 / x+2 is a separation for line DEBUG(cerr<<"found separation at " << x+1 << "/" << x+2 << " but not legal in center point solution --> ";) return false; } else { remaining = tab[x+1] - remaining; } } if (remaining > 0) { DEBUG(cerr<<" remaining "<<remaining<<" at the end --> ";) return false; } return true; } bool findSolution(int* tab, int n) { int remaining = tab[0]; REP(x,n-1) { int value = tab[x+1]; if (remaining - value > 1) { DEBUG(cerr<<"too much remaining at " << x << " (" << remaining-value << ") -> ";) return false; } else if (remaining - value == 1) { // x is a starting point for both directions DEBUG(cerr<<"found center point at " << x << endl;) return findCenterPointSolution(tab, x, n); } else if (remaining == value && x+1 < n-1) { // x+1 / x+2 is a separation for line DEBUG(cerr<<"found separation at " << x+1 << "/" << x+2 << endl;) return findRightSolution(tab+x+2, n-(x+2)) && findLeftSolution(tab, x+2); } else { remaining = tab[x+1] - remaining; } } if (remaining > 1) { DEBUG(cerr<<" remaining "<<remaining<<" at the end --> ";) return false; } return true; } //tab[0..n) is the real range with non-zero numbers bool solve(int* tab, int n) { DEBUG( cerr<<"entering solve with " << n << " arguments, shift is " << tab-input << endl; REP(x,n) cerr << tab[x] << " "; cerr << endl; ) if (n == 1) { DEBUG(cerr << "only non-zero element is " << tab[0] << " -> ";) return tab[0] == 1; // for 1-element array result is true only when exactly 1 } return checkPreconditions(tab, n) && findSolution(tab, n); } bool solve() { int n; cin>>n; int firstNonZeroIndex=-1, lastNonZeroIndex=-1; REP(x, n) { cin>>input[x+1]; if (input[x+1] != 0) { lastNonZeroIndex = x+1; if (firstNonZeroIndex == -1) firstNonZeroIndex = x+1; } } input[++n] = 0; //safety margins: tab[0] = tab[n+1] = 0 if (!solve(input+firstNonZeroIndex, lastNonZeroIndex-firstNonZeroIndex+1)) { return false; } std::reverse(input+firstNonZeroIndex, input+lastNonZeroIndex+1); if (!solve(input+firstNonZeroIndex, lastNonZeroIndex-firstNonZeroIndex+1)) { return false; } // if (lastNonZeroIndex - firstNonZeroIndex > 2) { // if (input[lastNonZeroIndex] == 1 && input[lastNonZeroIndex-1] == 1) { // input[lastNonZeroIndex+1] = 1; // input[lastNonZeroIndex+2] = 0; // if (!solve(input+firstNonZeroIndex, lastNonZeroIndex-firstNonZeroIndex+2)) { // return false; // } // std::reverse(input+firstNonZeroIndex, input+lastNonZeroIndex+2); // if (!solve(input+firstNonZeroIndex, lastNonZeroIndex-firstNonZeroIndex+2)) { // return false; // } // std::reverse(input+firstNonZeroIndex, input+lastNonZeroIndex+2); // input[lastNonZeroIndex+1] = 0; // } // if (input[firstNonZeroIndex] == 1 && input[firstNonZeroIndex+1] == 1) { // input[lastNonZeroIndex+1] = 1; // input[lastNonZeroIndex+2] = 0; // std::reverse(input+firstNonZeroIndex, input+lastNonZeroIndex+1); // if (!solve(input+firstNonZeroIndex, lastNonZeroIndex-firstNonZeroIndex+2)) { // return false; // } // std::reverse(input+firstNonZeroIndex, input+lastNonZeroIndex+2); // if (!solve(input+firstNonZeroIndex, lastNonZeroIndex-firstNonZeroIndex+2)) { // return false; // } // } // } return true; } int main() { ios_base::sync_with_stdio(0); int t; cin>>t; REP(x, t) { cout << (solve() ? "TAK" : "NIE") << endl; } return 0; } |