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/*
--- Charakterystyka klasy AVL ---
Implementacja drzewa AVL, bez rekurencji
z nastepujacymi operacjami:
- insertUnique() O(log n)
Do porownywania element�w uzywany jest operator "<" i "=="
*/
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<string>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include <time.h>
#define FOR(x, b, e) for(long x = b; x <= (e); x++)
#define VAR(v, n) __typeof(n) v = (n)
#define ALL(c) (c).begin(), (c).end()
#define FOREACH(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i)
#define DEBUG if (debug)
#define MIN(a,b) ((a>b)?b:a)
#define MAX(a,b) ((a>b)?a:b)
#define LL long long
using namespace std;
bool OK;
class Error {
public:
string description;
Error(string p_description) { description=p_description; };
};
LL delta_zakres, delta_value;
LL INF=1000000000;
LL SMALLER_INF=100000000;
class Zakres
{
public:
LL pocz, kon;
LL value;
LL getPocz() { return pocz+delta_zakres; };
LL getKon() { return kon+delta_zakres; };
LL getValue() { return value+delta_value; };
Zakres() { pocz=0; kon=0; value=0; };
Zakres(const Zakres& another) { pocz=another.pocz; kon=another.kon; value=another.value; };
Zakres(LL p_pocz, LL p_kon, LL p_value) { pocz=p_pocz; kon=p_kon; value=p_value; };
inline bool operator < (const Zakres& another) { return (pocz<another.pocz); };
inline bool operator >= (const Zakres& another) { return (pocz>=another.pocz); };
inline bool operator <= (const Zakres& another) { return (pocz<=another.pocz); };
inline bool operator == (const Zakres& another) { return (pocz==another.pocz); };
void showInfo()
{
cout << pocz+delta_zakres << ".." << kon+delta_zakres << ": " << value+delta_value << "\n";
}
};
template <class AvlElem>
class AvlTreeNode
// Class representing a node in an AVL Tree
{
public:
AvlElem value;
LL count, count2;
long o;
short w;
AvlTreeNode *left;
AvlTreeNode *right;
//constructor
AvlTreeNode(AvlElem pValue)
{
value=pValue; this->count=1; o=0;
w=0; left=NULL; right=NULL;
};
pair<LL,LL> calculate(LL k, LL ileTrzeba, long obliczenie)
{
//cout << "calculating in node " << value << " (" << count << ") k=" << k << " ileTrzeba=" << ileTrzeba << "\n";
if (value>=k)
{
if (left==NULL) return pair<LL,LL>(0,0);
else return left->calculate(k, ileTrzeba, obliczenie);
}
else
{
// moje value jest < k, zatem jest potencjalnym kandydatem
if (o==obliczenie)
{
// juz tu bylem w ramach tego obliczenia, uzywam count2
}
else
{
// pierwszy raz w tym wezle w ramach tego obliczenia:
count2=count; o=obliczenie;
}
pair<LL,LL> w(0,0);
if (right!=NULL) w=right->calculate(k,ileTrzeba, obliczenie);
if (w.second>=ileTrzeba) return w; // juz jest OK
ileTrzeba-=w.second;
LL allHere=count2*value;
if (allHere>=ileTrzeba)
{
// wystarczy to, co jest tutaj
LL i=ileTrzeba/value;
w.first+=i; ileTrzeba-=i*value; w.second+=i*value; count2-=i;
if (ileTrzeba>0) { w.first++; w.second+=value; count2--; }
//cout << " zwracam " << w.first << " " << w.second << "\n";
return w;
}
else
{
// biore wszystko i ide dalej
w.first+=count2; w.second+=allHere; ileTrzeba-=allHere;
if (left!=NULL)
{
pair<LL,LL> wL = left->calculate(k, ileTrzeba, obliczenie);
w.first+=wL.first; w.second+=wL.second;
}
//cout << " zwracam " << w.first << " " << w.second << "\n";
return w;
}
}
}
void display(long level)
// Displays self.
{
for (long i=0; i<level; i++) cout << " ";
cout << value << " (" << w << ") count=" << count << "\n";
if ((left==NULL)&&(right==NULL)) return;
if (left==NULL) { for (long i=0; i<level+1; i++) cout << " "; cout << "left NULL\n"; }
else left->display(level+1);
if (right==NULL) { for (long i=0; i<level+1; i++) cout << " "; cout << "right NULL\n"; }
else right->display(level+1);
};
void displayValues()
// Displays self.
{
if (left!=NULL) left->displayValues();
value.showInfo();
if (right!=NULL) right->displayValues();
};
void checkBST(long a, long b)
{
if ((value<a)||(value>b)) {
cout << "Error BST in node " << value << "\n";
cout.flush();
throw new Error("");
};
if (left!=NULL) left->checkBST(a, value-1);
if (right!=NULL) right->checkBST(value+1, b);
};
long checkAVL()
// returns height of the tree
{
long leftHeight=0;
long rightHeight=0;
if (left!=NULL) leftHeight=left->checkAVL();
if (right!=NULL) rightHeight=right->checkAVL();
long height=1 + MAX(leftHeight, rightHeight);
long delta = rightHeight-leftHeight;
if ((delta<-1)||(delta>+1)) throw Error("07");
if (delta!=w) {
cout << "Node: " << value << " right: " << rightHeight << " left: " << leftHeight << " w=" << w << "\n";
throw Error("08");
};
return height;
};
long treeSize()
{
if (this->count<=0) OK=false;
long s=this->count;
if (left!=NULL) s+=left->treeSize();
if (right!=NULL) s+=right->treeSize();
return s;
}
AvlTreeNode<AvlElem>* rotateSingleToTheRight()
{
AvlTreeNode<AvlElem> *p=this;
AvlTreeNode<AvlElem> *q=p->left;
p->left=q->right;
q->right=p;
p->w=0; q->w=0;
return q;
};
AvlTreeNode<AvlElem>* rotateSingleToTheLeft()
{
AvlTreeNode<AvlElem> *p=this;
AvlTreeNode<AvlElem> *q=p->right;
p->right=q->left;
q->left=p;
p->w=0; q->w=0;
return q;
};
AvlTreeNode<AvlElem>* rotateGammaSingleToTheRight()
{
AvlTreeNode<AvlElem> *p=this;
AvlTreeNode<AvlElem> *q=p->left;
p->left=q->right;
q->right=p;
p->w=-1; q->w=1;
return q;
};
AvlTreeNode<AvlElem>* rotateGammaSingleToTheLeft()
{
AvlTreeNode<AvlElem> *p=this;
AvlTreeNode<AvlElem> *q=p->right;
p->right=q->left;
q->left=p;
p->w=1; q->w=-1;
return q;
};
AvlTreeNode<AvlElem>* rotateDoubleToTheRight()
{
AvlTreeNode<AvlElem> *p=this;
AvlTreeNode<AvlElem> *q=p->left;
AvlTreeNode<AvlElem> *r=q->right;
p->left=r->right;
q->right=r->left;
r->right=p; r->left=q;
if (r->w==0) { p->w=0; q->w=0; }
else if (r->w==-1) { p->w=1; q->w=0; }
else if (r->w==+1) { p->w=0; q->w=-1; }
else throw new Error("12");
r->w=0;
return r;
};
AvlTreeNode<AvlElem>* rotateDoubleToTheLeft()
{
AvlTreeNode<AvlElem> *p=this;
AvlTreeNode<AvlElem> *q=p->right;
AvlTreeNode<AvlElem> *r=q->left;
p->right=r->left;
q->left=r->right;
r->left=p; r->right=q;
if (r->w==0) { p->w=0; q->w=0; }
else if (r->w==-1) { p->w=0; q->w=1; }
else if (r->w==+1) { p->w=-1; q->w=0; }
else throw new Error("11");
r->w=0;
return r;
};
};
template <class AvlElem>
class AvlTree
// class representing AVL Tree
{
AvlTreeNode<AvlElem> *root;
stack<AvlTreeNode<AvlElem>* > trace;
public:
AvlTree() { root=NULL; };
bool isEmpty()
{
return (root==NULL);
}
void displayValues()
{
if (root==NULL) cout << "Empty tree\n";
else root->displayValues();
}
void insertValue(AvlElem pValue)
//Inserts pValue into the tree.
//Returns true if the value was already in the tree
{
bool found = findValue(pValue);
if (found)
{
trace.top()->count++;
return;
}
AvlTreeNode<AvlElem> *newNode = new AvlTreeNode<AvlElem>(pValue);
if (root==NULL) root=newNode;
else {
if (trace.empty()) throw new Error("13");
AvlTreeNode<AvlElem> *parent = trace.top();
if (pValue < parent->value) { parent->left=newNode; fixAfterInsert(newNode); }
else { parent->right=newNode; fixAfterInsert(newNode); }
};
};
bool deleteValue(AvlElem pValue)
// Removes given value from the tree.
// Returns true if the value was in the tree.
{
// cout << "Deleting " << pValue << "\n";
bool found = findValue(pValue);
if (!found) return false;
AvlTreeNode<AvlElem> *node=trace.top();
//cout << "Found: " << node->value << " count=" << node->count << "\n";
trace.top()->count--;
//cout << "And now: " << node->value << " count=" << node->count << "\n";
if ((trace.top()->count)==0) reallyDeleteNode();
return true;
};
pair<LL,LL> calculate(LL k, LL ileTrzeba, long obliczenie)
{
if (root==NULL) return pair<LL,LL>(0,0);
return root->calculate(k, ileTrzeba, obliczenie);
}
AvlElem deleteSmallestValue()
// Removes smallest node and returns its value.
// If tree is empty, raises an Error
{
if (root==NULL) throw new Error("Tree is empty!");
ensureTraceEmpty();
AvlTreeNode<AvlElem> *current=root; trace.push(current);
while (current->left!=NULL) {
current=current->left; trace.push(current);
};
AvlElem value = current->value;
current->count--;
if (current->count==0) reallyDeleteNode();
return value;
};
AvlElem deleteGreatestValue()
// Removes smallest node and returns its value.
// If tree is empty, raises an Error
{
if (root==NULL) throw new Error("Tree is empty!");
ensureTraceEmpty();
AvlTreeNode<AvlElem> *current=root; trace.push(current);
while (current->right!=NULL) {
current=current->right; trace.push(current);
};
AvlElem value = current->value;
current->count--;
if (current->count==0) reallyDeleteNode();
return value;
};
bool doesContain(AvlElem pValue)
//Returns true if the value is in the tree.
{
AvlTreeNode<AvlElem> *current=root;
while (current!=NULL) {
if (current->value==pValue) return true;
if (pValue<current->value) current=current->left; else current=current->right;
};
return false;
};
AvlTreeNode<AvlElem>* smallestNode()
// Returns smallest node in the tree
{
if (root==NULL) return NULL;
AvlTreeNode<AvlElem> *current=root;
while (current->left!=NULL) current=current->left;
return current;
};
AvlTreeNode<AvlElem>* greatestNode()
// Returns greatest node in the tree
{
if (root==NULL) return NULL;
AvlTreeNode<AvlElem> *current=root;
while (current->right!=NULL) current=current->right;
return current;
};
AvlTreeNode<AvlElem>* smallestGreaterThanNode(AvlElem &pValue)
// Returns node, which is smallest between greater than pValue
{
AvlTreeNode<AvlElem> *current=root;
AvlTreeNode<AvlElem> *candidate=NULL;
while (current!=NULL) {
if (current->value>pValue) {
candidate=current;
current=current->left;
} else current=current->right;
};
return candidate;
};
AvlTreeNode<AvlElem>* smallestGreaterOrEqualThanNode(AvlElem &pValue)
// Returns node, which is smallest between greater or equal than pValue
{
AvlTreeNode<AvlElem> *current=root;
AvlTreeNode<AvlElem> *candidate=NULL;
while (current!=NULL) {
if (current->value>=pValue) {
candidate=current;
current=current->left;
} else current=current->right;
};
return candidate;
};
AvlTreeNode<AvlElem>* greatestSmallerThanNode(AvlElem &pValue)
// Returns node, which is greatest between smaller than pValue
{
AvlTreeNode<AvlElem> *current=root;
AvlTreeNode<AvlElem> *candidate=NULL;
while (current!=NULL) {
if (current->value<pValue) {
candidate=current;
current=current->right;
} else current=current->left;
};
return candidate;
};
AvlTreeNode<AvlElem>* greatestSmallerOrEqualThanNode(AvlElem &pValue)
// Returns node, which is greatest between smaller or equal than pValue
{
AvlTreeNode<AvlElem> *current=root;
AvlTreeNode<AvlElem> *candidate=NULL;
while (current!=NULL) {
if (current->value<=pValue) {
candidate=current;
current=current->right;
} else current=current->left;
};
return candidate;
};
void display()
{
if (root==NULL) cout << "Empty tree\n";
else root->display(0);
};
void check()
{
if (root==NULL) return; // tree is correct
root->checkBST(-1000000000, 1000000000);
root->checkAVL();
};
long treeSize()
{
if (root==NULL) return 0;
return root->treeSize();
}
private:
void ensureTraceEmpty()
// Ensures that stack "trace" is empty.
{
while (!trace.empty()) trace.pop();
};
bool findValue(AvlElem &pValue)
//Finds given pValue in the tree.
//Returns true if the value is found.
{
ensureTraceEmpty();
AvlTreeNode<AvlElem> *current=root;
while (current!=NULL) {
trace.push(current);
if (current->value==pValue) return true;
if (pValue<current->value) current=current->left; else current=current->right;
};
return false;
};
void fixAfterInsert(AvlTreeNode<AvlElem> *child)
// Fixes AVL property after insertion.
// delta=-1 means: left tree is higher
// delta=+1 means: right tree is higher.
{
AvlTreeNode<AvlElem> *current = trace.top(); trace.pop();
long delta;
while (current!=NULL) {
if (current->left==child) delta=-1; else delta=+1;
current->w += delta;
if (current->w==0) return; // the tree does not change height
if (current->w==delta) {
// the tree changes height, but rotation is not required
child=current;
if (trace.empty()) return;
current=trace.top(); trace.pop();
}
else {
AvlTreeNode<AvlElem> *parent;
if (trace.empty()) parent=NULL; else parent = trace.top();
AvlTreeNode<AvlElem> *newTop;
if (current->w==-2) {
if (current->left->w==-1) newTop=current->rotateSingleToTheRight();
else if (current->left->w==+1) newTop=current->rotateDoubleToTheRight();
else throw new Error("Error 002");
}
else if (current->w==+2) {
if (current->right->w==+1) newTop=current->rotateSingleToTheLeft();
else if (current->right->w==-1) newTop=current->rotateDoubleToTheLeft();
else throw new Error("Error 002");
}
else throw new Error("Error 001");
if (parent==NULL) root=newTop;
else {
if (current==parent->left) parent->left=newTop; else parent->right=newTop;
};
return; // no further action is required.
};
};
};
void reallyDeleteNode()
// Removes a node from the tree - node found by findValue().
{
if (trace.empty()) throw new Error("15");
AvlTreeNode<AvlElem> *toDelete=trace.top();
if ((toDelete->left!=NULL)&&(toDelete->right!=NULL)) {
// go to the greatest value in left subtree:
AvlTreeNode<AvlElem> *current=toDelete->left;
trace.push(current);
while (current->right!=NULL) { current=current->right; trace.push(current); };
toDelete->value=current->value;
toDelete->count=current->count;
toDelete->count2=current->count2;
toDelete->o=current->o;
toDelete=current;
};
// now really remove "toDelete" from the tree
// we know it has at most one child
AvlTreeNode<AvlElem> *child=toDelete->left;
if (child==NULL) child=toDelete->right;
trace.pop(); // pop "toDelete" from the trace;
AvlTreeNode<AvlElem> *parent;
long delta;
if (trace.empty()) {
// "toDelete" is a root
root=child;
delete toDelete;
return;
} else {
parent=trace.top();
if (toDelete==parent->left) {
parent->left=child; delta=+1;
} else {
parent->right=child; delta=-1;
};
delete toDelete;
};
fixAfterDeletion(delta);
};
void fixAfterDeletion(long delta)
// Fixes AVL property after deletion
{
AvlTreeNode<AvlElem> *current=trace.top(); trace.pop();
while (current!=NULL) {
current->w += delta;
if (current->w==delta) return;
if (current->w==0) {
// just pass it higher;
if (trace.empty()) return;
AvlTreeNode<AvlElem> *child=current;
current=trace.top(); trace.pop();
if (current->left==child) delta=+1; else delta=-1;
} else {
// we will have to rotate:
bool stop=false;
AvlTreeNode<AvlElem> *parent=NULL;
AvlTreeNode<AvlElem> *newTop;
if (!trace.empty()) parent=trace.top();
if (current->w==-2) {
// rotations to the right
if (current->left->w==-1) newTop=current->rotateSingleToTheRight();
else if (current->left->w==+1) newTop=current->rotateDoubleToTheRight();
else if (current->left->w==0) {
newTop=current->rotateGammaSingleToTheRight();
stop=true;
} else throw new Error("Error 002");
} else if (current->w==+2) {
// rotations to the left
if (current->right->w==+1) newTop=current->rotateSingleToTheLeft();
else if (current->right->w==-1) newTop=current->rotateDoubleToTheLeft();
else if (current->right->w==0) {
newTop=current->rotateGammaSingleToTheLeft();
stop=true;
} else throw new Error("Error 002");
} else throw new Error("14");
if (parent==NULL) root=newTop;
else {
if (current==parent->left) {
parent->left=newTop; delta=+1;
} else { parent->right=newTop; delta=-1; };
};
if (stop) return;
current=parent; if (!trace.empty()) trace.pop();
};
};
};
};
AvlTree<Zakres> t;
void showInfo(AvlTreeNode<Zakres> *node)
{
cout << "Info: ";
if (node==NULL) cout << "Empty\n"; else cout << node->value.pocz << ".." << node->value.kon << ": " << node->value.value << "\n";
}
void ulepsz(LL f, LL valu)
{
Zakres zf(f,0,0);
AvlTreeNode<Zakres> *node = t.greatestSmallerOrEqualThanNode(zf);
//showInfo(node);
LL po,ko; po=f;
if (node==NULL) {
node = t.smallestNode();
ko=node->value.pocz-1;
} else {
if (node->value.value<=valu) return; // nic interesujacego
ko=node->value.kon;
if (node->value.pocz!=f) {
// kawalek zostaje:
node->value.kon=f-1;
} else {
// ten node jest caly do usuniecia:
t.deleteValue(zf);
}
}
bool koniec=false;
while (!koniec && ko<SMALLER_INF)
{
// szukaj wezla do usuniecia:
zf.pocz=ko+1;
node = t.greatestSmallerOrEqualThanNode(zf);
if (node->value.value>=valu)
{
// do usuniecia
ko=node->value.kon;
t.deleteValue(zf);
}
else koniec=true; // dalej nie usuwamy
}
zf.pocz=po; zf.kon=ko; zf.value=valu; t.insertValue(zf);
}
int main()
{
// magic formula, which makes streams work faster:
ios_base::sync_with_stdio(0);
INF=INF*INF; SMALLER_INF=SMALLER_INF*SMALLER_INF;
delta_zakres=0; delta_value=0;
LL pop_delta_zakres; LL pop_delta_value;
long n; cin >> n;
Zakres z;
LL kp=0; LL p;
long pos=1;
cin >> p;
while (p==0)
{
pos++;
if (pos>n)
{
// same 0:
cout << "0\n"; return 0;
}
cin >> p;
}
z.pocz=-p; z.kon=INF; z.value=0; t.insertValue(z);
//cout << "--- After first step at: " << pos << "\n";
//t.displayValues();
AvlTreeNode<Zakres> *node = NULL;
FOR(i,pos+1,n)
{
kp++;
cin >> p;
if (p==0) { continue; };
z.pocz=0-delta_zakres;
node = t.greatestSmallerOrEqualThanNode(z);
pop_delta_zakres=delta_zakres; pop_delta_value=delta_value;
LL k3=0; if (node!=NULL) k3=node->value.value;
delta_zakres-=p; delta_value+=kp; kp=0;
//cout << "--- Step " << i << " before bettering:\n"; t.displayValues();
if (node!=NULL) {
//cout << " ulepszanie: " << -p << " " << k3+pop_delta_value << "\n";
ulepsz(-p-delta_zakres, k3+pop_delta_value-delta_value);
}
//cout << "--- Step " << i << " after bettering:\n"; t.displayValues();
//cout << "\n";
}
z.pocz=0-delta_zakres;
node = t.greatestSmallerOrEqualThanNode(z);
if (node==NULL) cout << "-1\n";
else cout << node->value.value+delta_value << "\n";
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 | /* --- Charakterystyka klasy AVL --- Implementacja drzewa AVL, bez rekurencji z nastepujacymi operacjami: - insertUnique() O(log n) Do porownywania element�w uzywany jest operator "<" i "==" */ #include<cstdio> #include<cstdlib> #include<iostream> #include<string> #include<map> #include<set> #include<queue> #include<stack> #include <time.h> #define FOR(x, b, e) for(long x = b; x <= (e); x++) #define VAR(v, n) __typeof(n) v = (n) #define ALL(c) (c).begin(), (c).end() #define FOREACH(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i) #define DEBUG if (debug) #define MIN(a,b) ((a>b)?b:a) #define MAX(a,b) ((a>b)?a:b) #define LL long long using namespace std; bool OK; class Error { public: string description; Error(string p_description) { description=p_description; }; }; LL delta_zakres, delta_value; LL INF=1000000000; LL SMALLER_INF=100000000; class Zakres { public: LL pocz, kon; LL value; LL getPocz() { return pocz+delta_zakres; }; LL getKon() { return kon+delta_zakres; }; LL getValue() { return value+delta_value; }; Zakres() { pocz=0; kon=0; value=0; }; Zakres(const Zakres& another) { pocz=another.pocz; kon=another.kon; value=another.value; }; Zakres(LL p_pocz, LL p_kon, LL p_value) { pocz=p_pocz; kon=p_kon; value=p_value; }; inline bool operator < (const Zakres& another) { return (pocz<another.pocz); }; inline bool operator >= (const Zakres& another) { return (pocz>=another.pocz); }; inline bool operator <= (const Zakres& another) { return (pocz<=another.pocz); }; inline bool operator == (const Zakres& another) { return (pocz==another.pocz); }; void showInfo() { cout << pocz+delta_zakres << ".." << kon+delta_zakres << ": " << value+delta_value << "\n"; } }; template <class AvlElem> class AvlTreeNode // Class representing a node in an AVL Tree { public: AvlElem value; LL count, count2; long o; short w; AvlTreeNode *left; AvlTreeNode *right; //constructor AvlTreeNode(AvlElem pValue) { value=pValue; this->count=1; o=0; w=0; left=NULL; right=NULL; }; pair<LL,LL> calculate(LL k, LL ileTrzeba, long obliczenie) { //cout << "calculating in node " << value << " (" << count << ") k=" << k << " ileTrzeba=" << ileTrzeba << "\n"; if (value>=k) { if (left==NULL) return pair<LL,LL>(0,0); else return left->calculate(k, ileTrzeba, obliczenie); } else { // moje value jest < k, zatem jest potencjalnym kandydatem if (o==obliczenie) { // juz tu bylem w ramach tego obliczenia, uzywam count2 } else { // pierwszy raz w tym wezle w ramach tego obliczenia: count2=count; o=obliczenie; } pair<LL,LL> w(0,0); if (right!=NULL) w=right->calculate(k,ileTrzeba, obliczenie); if (w.second>=ileTrzeba) return w; // juz jest OK ileTrzeba-=w.second; LL allHere=count2*value; if (allHere>=ileTrzeba) { // wystarczy to, co jest tutaj LL i=ileTrzeba/value; w.first+=i; ileTrzeba-=i*value; w.second+=i*value; count2-=i; if (ileTrzeba>0) { w.first++; w.second+=value; count2--; } //cout << " zwracam " << w.first << " " << w.second << "\n"; return w; } else { // biore wszystko i ide dalej w.first+=count2; w.second+=allHere; ileTrzeba-=allHere; if (left!=NULL) { pair<LL,LL> wL = left->calculate(k, ileTrzeba, obliczenie); w.first+=wL.first; w.second+=wL.second; } //cout << " zwracam " << w.first << " " << w.second << "\n"; return w; } } } void display(long level) // Displays self. { for (long i=0; i<level; i++) cout << " "; cout << value << " (" << w << ") count=" << count << "\n"; if ((left==NULL)&&(right==NULL)) return; if (left==NULL) { for (long i=0; i<level+1; i++) cout << " "; cout << "left NULL\n"; } else left->display(level+1); if (right==NULL) { for (long i=0; i<level+1; i++) cout << " "; cout << "right NULL\n"; } else right->display(level+1); }; void displayValues() // Displays self. { if (left!=NULL) left->displayValues(); value.showInfo(); if (right!=NULL) right->displayValues(); }; void checkBST(long a, long b) { if ((value<a)||(value>b)) { cout << "Error BST in node " << value << "\n"; cout.flush(); throw new Error(""); }; if (left!=NULL) left->checkBST(a, value-1); if (right!=NULL) right->checkBST(value+1, b); }; long checkAVL() // returns height of the tree { long leftHeight=0; long rightHeight=0; if (left!=NULL) leftHeight=left->checkAVL(); if (right!=NULL) rightHeight=right->checkAVL(); long height=1 + MAX(leftHeight, rightHeight); long delta = rightHeight-leftHeight; if ((delta<-1)||(delta>+1)) throw Error("07"); if (delta!=w) { cout << "Node: " << value << " right: " << rightHeight << " left: " << leftHeight << " w=" << w << "\n"; throw Error("08"); }; return height; }; long treeSize() { if (this->count<=0) OK=false; long s=this->count; if (left!=NULL) s+=left->treeSize(); if (right!=NULL) s+=right->treeSize(); return s; } AvlTreeNode<AvlElem>* rotateSingleToTheRight() { AvlTreeNode<AvlElem> *p=this; AvlTreeNode<AvlElem> *q=p->left; p->left=q->right; q->right=p; p->w=0; q->w=0; return q; }; AvlTreeNode<AvlElem>* rotateSingleToTheLeft() { AvlTreeNode<AvlElem> *p=this; AvlTreeNode<AvlElem> *q=p->right; p->right=q->left; q->left=p; p->w=0; q->w=0; return q; }; AvlTreeNode<AvlElem>* rotateGammaSingleToTheRight() { AvlTreeNode<AvlElem> *p=this; AvlTreeNode<AvlElem> *q=p->left; p->left=q->right; q->right=p; p->w=-1; q->w=1; return q; }; AvlTreeNode<AvlElem>* rotateGammaSingleToTheLeft() { AvlTreeNode<AvlElem> *p=this; AvlTreeNode<AvlElem> *q=p->right; p->right=q->left; q->left=p; p->w=1; q->w=-1; return q; }; AvlTreeNode<AvlElem>* rotateDoubleToTheRight() { AvlTreeNode<AvlElem> *p=this; AvlTreeNode<AvlElem> *q=p->left; AvlTreeNode<AvlElem> *r=q->right; p->left=r->right; q->right=r->left; r->right=p; r->left=q; if (r->w==0) { p->w=0; q->w=0; } else if (r->w==-1) { p->w=1; q->w=0; } else if (r->w==+1) { p->w=0; q->w=-1; } else throw new Error("12"); r->w=0; return r; }; AvlTreeNode<AvlElem>* rotateDoubleToTheLeft() { AvlTreeNode<AvlElem> *p=this; AvlTreeNode<AvlElem> *q=p->right; AvlTreeNode<AvlElem> *r=q->left; p->right=r->left; q->left=r->right; r->left=p; r->right=q; if (r->w==0) { p->w=0; q->w=0; } else if (r->w==-1) { p->w=0; q->w=1; } else if (r->w==+1) { p->w=-1; q->w=0; } else throw new Error("11"); r->w=0; return r; }; }; template <class AvlElem> class AvlTree // class representing AVL Tree { AvlTreeNode<AvlElem> *root; stack<AvlTreeNode<AvlElem>* > trace; public: AvlTree() { root=NULL; }; bool isEmpty() { return (root==NULL); } void displayValues() { if (root==NULL) cout << "Empty tree\n"; else root->displayValues(); } void insertValue(AvlElem pValue) //Inserts pValue into the tree. //Returns true if the value was already in the tree { bool found = findValue(pValue); if (found) { trace.top()->count++; return; } AvlTreeNode<AvlElem> *newNode = new AvlTreeNode<AvlElem>(pValue); if (root==NULL) root=newNode; else { if (trace.empty()) throw new Error("13"); AvlTreeNode<AvlElem> *parent = trace.top(); if (pValue < parent->value) { parent->left=newNode; fixAfterInsert(newNode); } else { parent->right=newNode; fixAfterInsert(newNode); } }; }; bool deleteValue(AvlElem pValue) // Removes given value from the tree. // Returns true if the value was in the tree. { // cout << "Deleting " << pValue << "\n"; bool found = findValue(pValue); if (!found) return false; AvlTreeNode<AvlElem> *node=trace.top(); //cout << "Found: " << node->value << " count=" << node->count << "\n"; trace.top()->count--; //cout << "And now: " << node->value << " count=" << node->count << "\n"; if ((trace.top()->count)==0) reallyDeleteNode(); return true; }; pair<LL,LL> calculate(LL k, LL ileTrzeba, long obliczenie) { if (root==NULL) return pair<LL,LL>(0,0); return root->calculate(k, ileTrzeba, obliczenie); } AvlElem deleteSmallestValue() // Removes smallest node and returns its value. // If tree is empty, raises an Error { if (root==NULL) throw new Error("Tree is empty!"); ensureTraceEmpty(); AvlTreeNode<AvlElem> *current=root; trace.push(current); while (current->left!=NULL) { current=current->left; trace.push(current); }; AvlElem value = current->value; current->count--; if (current->count==0) reallyDeleteNode(); return value; }; AvlElem deleteGreatestValue() // Removes smallest node and returns its value. // If tree is empty, raises an Error { if (root==NULL) throw new Error("Tree is empty!"); ensureTraceEmpty(); AvlTreeNode<AvlElem> *current=root; trace.push(current); while (current->right!=NULL) { current=current->right; trace.push(current); }; AvlElem value = current->value; current->count--; if (current->count==0) reallyDeleteNode(); return value; }; bool doesContain(AvlElem pValue) //Returns true if the value is in the tree. { AvlTreeNode<AvlElem> *current=root; while (current!=NULL) { if (current->value==pValue) return true; if (pValue<current->value) current=current->left; else current=current->right; }; return false; }; AvlTreeNode<AvlElem>* smallestNode() // Returns smallest node in the tree { if (root==NULL) return NULL; AvlTreeNode<AvlElem> *current=root; while (current->left!=NULL) current=current->left; return current; }; AvlTreeNode<AvlElem>* greatestNode() // Returns greatest node in the tree { if (root==NULL) return NULL; AvlTreeNode<AvlElem> *current=root; while (current->right!=NULL) current=current->right; return current; }; AvlTreeNode<AvlElem>* smallestGreaterThanNode(AvlElem &pValue) // Returns node, which is smallest between greater than pValue { AvlTreeNode<AvlElem> *current=root; AvlTreeNode<AvlElem> *candidate=NULL; while (current!=NULL) { if (current->value>pValue) { candidate=current; current=current->left; } else current=current->right; }; return candidate; }; AvlTreeNode<AvlElem>* smallestGreaterOrEqualThanNode(AvlElem &pValue) // Returns node, which is smallest between greater or equal than pValue { AvlTreeNode<AvlElem> *current=root; AvlTreeNode<AvlElem> *candidate=NULL; while (current!=NULL) { if (current->value>=pValue) { candidate=current; current=current->left; } else current=current->right; }; return candidate; }; AvlTreeNode<AvlElem>* greatestSmallerThanNode(AvlElem &pValue) // Returns node, which is greatest between smaller than pValue { AvlTreeNode<AvlElem> *current=root; AvlTreeNode<AvlElem> *candidate=NULL; while (current!=NULL) { if (current->value<pValue) { candidate=current; current=current->right; } else current=current->left; }; return candidate; }; AvlTreeNode<AvlElem>* greatestSmallerOrEqualThanNode(AvlElem &pValue) // Returns node, which is greatest between smaller or equal than pValue { AvlTreeNode<AvlElem> *current=root; AvlTreeNode<AvlElem> *candidate=NULL; while (current!=NULL) { if (current->value<=pValue) { candidate=current; current=current->right; } else current=current->left; }; return candidate; }; void display() { if (root==NULL) cout << "Empty tree\n"; else root->display(0); }; void check() { if (root==NULL) return; // tree is correct root->checkBST(-1000000000, 1000000000); root->checkAVL(); }; long treeSize() { if (root==NULL) return 0; return root->treeSize(); } private: void ensureTraceEmpty() // Ensures that stack "trace" is empty. { while (!trace.empty()) trace.pop(); }; bool findValue(AvlElem &pValue) //Finds given pValue in the tree. //Returns true if the value is found. { ensureTraceEmpty(); AvlTreeNode<AvlElem> *current=root; while (current!=NULL) { trace.push(current); if (current->value==pValue) return true; if (pValue<current->value) current=current->left; else current=current->right; }; return false; }; void fixAfterInsert(AvlTreeNode<AvlElem> *child) // Fixes AVL property after insertion. // delta=-1 means: left tree is higher // delta=+1 means: right tree is higher. { AvlTreeNode<AvlElem> *current = trace.top(); trace.pop(); long delta; while (current!=NULL) { if (current->left==child) delta=-1; else delta=+1; current->w += delta; if (current->w==0) return; // the tree does not change height if (current->w==delta) { // the tree changes height, but rotation is not required child=current; if (trace.empty()) return; current=trace.top(); trace.pop(); } else { AvlTreeNode<AvlElem> *parent; if (trace.empty()) parent=NULL; else parent = trace.top(); AvlTreeNode<AvlElem> *newTop; if (current->w==-2) { if (current->left->w==-1) newTop=current->rotateSingleToTheRight(); else if (current->left->w==+1) newTop=current->rotateDoubleToTheRight(); else throw new Error("Error 002"); } else if (current->w==+2) { if (current->right->w==+1) newTop=current->rotateSingleToTheLeft(); else if (current->right->w==-1) newTop=current->rotateDoubleToTheLeft(); else throw new Error("Error 002"); } else throw new Error("Error 001"); if (parent==NULL) root=newTop; else { if (current==parent->left) parent->left=newTop; else parent->right=newTop; }; return; // no further action is required. }; }; }; void reallyDeleteNode() // Removes a node from the tree - node found by findValue(). { if (trace.empty()) throw new Error("15"); AvlTreeNode<AvlElem> *toDelete=trace.top(); if ((toDelete->left!=NULL)&&(toDelete->right!=NULL)) { // go to the greatest value in left subtree: AvlTreeNode<AvlElem> *current=toDelete->left; trace.push(current); while (current->right!=NULL) { current=current->right; trace.push(current); }; toDelete->value=current->value; toDelete->count=current->count; toDelete->count2=current->count2; toDelete->o=current->o; toDelete=current; }; // now really remove "toDelete" from the tree // we know it has at most one child AvlTreeNode<AvlElem> *child=toDelete->left; if (child==NULL) child=toDelete->right; trace.pop(); // pop "toDelete" from the trace; AvlTreeNode<AvlElem> *parent; long delta; if (trace.empty()) { // "toDelete" is a root root=child; delete toDelete; return; } else { parent=trace.top(); if (toDelete==parent->left) { parent->left=child; delta=+1; } else { parent->right=child; delta=-1; }; delete toDelete; }; fixAfterDeletion(delta); }; void fixAfterDeletion(long delta) // Fixes AVL property after deletion { AvlTreeNode<AvlElem> *current=trace.top(); trace.pop(); while (current!=NULL) { current->w += delta; if (current->w==delta) return; if (current->w==0) { // just pass it higher; if (trace.empty()) return; AvlTreeNode<AvlElem> *child=current; current=trace.top(); trace.pop(); if (current->left==child) delta=+1; else delta=-1; } else { // we will have to rotate: bool stop=false; AvlTreeNode<AvlElem> *parent=NULL; AvlTreeNode<AvlElem> *newTop; if (!trace.empty()) parent=trace.top(); if (current->w==-2) { // rotations to the right if (current->left->w==-1) newTop=current->rotateSingleToTheRight(); else if (current->left->w==+1) newTop=current->rotateDoubleToTheRight(); else if (current->left->w==0) { newTop=current->rotateGammaSingleToTheRight(); stop=true; } else throw new Error("Error 002"); } else if (current->w==+2) { // rotations to the left if (current->right->w==+1) newTop=current->rotateSingleToTheLeft(); else if (current->right->w==-1) newTop=current->rotateDoubleToTheLeft(); else if (current->right->w==0) { newTop=current->rotateGammaSingleToTheLeft(); stop=true; } else throw new Error("Error 002"); } else throw new Error("14"); if (parent==NULL) root=newTop; else { if (current==parent->left) { parent->left=newTop; delta=+1; } else { parent->right=newTop; delta=-1; }; }; if (stop) return; current=parent; if (!trace.empty()) trace.pop(); }; }; }; }; AvlTree<Zakres> t; void showInfo(AvlTreeNode<Zakres> *node) { cout << "Info: "; if (node==NULL) cout << "Empty\n"; else cout << node->value.pocz << ".." << node->value.kon << ": " << node->value.value << "\n"; } void ulepsz(LL f, LL valu) { Zakres zf(f,0,0); AvlTreeNode<Zakres> *node = t.greatestSmallerOrEqualThanNode(zf); //showInfo(node); LL po,ko; po=f; if (node==NULL) { node = t.smallestNode(); ko=node->value.pocz-1; } else { if (node->value.value<=valu) return; // nic interesujacego ko=node->value.kon; if (node->value.pocz!=f) { // kawalek zostaje: node->value.kon=f-1; } else { // ten node jest caly do usuniecia: t.deleteValue(zf); } } bool koniec=false; while (!koniec && ko<SMALLER_INF) { // szukaj wezla do usuniecia: zf.pocz=ko+1; node = t.greatestSmallerOrEqualThanNode(zf); if (node->value.value>=valu) { // do usuniecia ko=node->value.kon; t.deleteValue(zf); } else koniec=true; // dalej nie usuwamy } zf.pocz=po; zf.kon=ko; zf.value=valu; t.insertValue(zf); } int main() { // magic formula, which makes streams work faster: ios_base::sync_with_stdio(0); INF=INF*INF; SMALLER_INF=SMALLER_INF*SMALLER_INF; delta_zakres=0; delta_value=0; LL pop_delta_zakres; LL pop_delta_value; long n; cin >> n; Zakres z; LL kp=0; LL p; long pos=1; cin >> p; while (p==0) { pos++; if (pos>n) { // same 0: cout << "0\n"; return 0; } cin >> p; } z.pocz=-p; z.kon=INF; z.value=0; t.insertValue(z); //cout << "--- After first step at: " << pos << "\n"; //t.displayValues(); AvlTreeNode<Zakres> *node = NULL; FOR(i,pos+1,n) { kp++; cin >> p; if (p==0) { continue; }; z.pocz=0-delta_zakres; node = t.greatestSmallerOrEqualThanNode(z); pop_delta_zakres=delta_zakres; pop_delta_value=delta_value; LL k3=0; if (node!=NULL) k3=node->value.value; delta_zakres-=p; delta_value+=kp; kp=0; //cout << "--- Step " << i << " before bettering:\n"; t.displayValues(); if (node!=NULL) { //cout << " ulepszanie: " << -p << " " << k3+pop_delta_value << "\n"; ulepsz(-p-delta_zakres, k3+pop_delta_value-delta_value); } //cout << "--- Step " << i << " after bettering:\n"; t.displayValues(); //cout << "\n"; } z.pocz=0-delta_zakres; node = t.greatestSmallerOrEqualThanNode(z); if (node==NULL) cout << "-1\n"; else cout << node->value.value+delta_value << "\n"; return 0; }; |