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  1. #include<set>
  2. #include<cmath>
  3. /*
  4.  * Dynamic version of data structure
  5.  * to be used in dynamic programming optimisation
  6.  * called "Convex Hull trick"
  7.  * 'Dynamic' means that there is no restriction on adding lines order
  8.  */
  9. class ConvexHullDynamic
  10. {
  11.     typedef long long coef_t;
  12.     typedef long long coord_t;
  13.     typedef long long val_t;
  14.  
  15.     /*
  16.      * Line 'y=a*x+b' represented by 2 coefficients 'a' and 'b'
  17.      * and 'xLeft' which is intersection with previous line in hull(first line has -INF)
  18.      */
  19. private:
  20.     struct Line
  21.     {
  22.         coef_t a, b;
  23.         double xLeft;
  24.  
  25.         enum Type {line, maxQuery, minQuery} type;
  26.         coord_t val;
  27.  
  28.         explicit Line(coef_t aa=0, coef_t bb=0) : a(aa), b(bb), xLeft(-INFINITY), type(Type::line), val(0) {}
  29.         val_t valueAt(coord_t x) const { return a*x+b; }
  30.         friend bool areParallel(const Line& l1, const Line& l2) { return l1.a==l2.a; }
  31.         friend double intersectX(const Line& l1, const Line& l2) { return areParallel(l1,l2)?INFINITY:1.0*(l2.b-l1.b)/(l1.a-l2.a); }
  32.         bool operator<(const Line& l2) const
  33.         {
  34.             if (l2.type == line)
  35.                 return this->a     < l2.a;
  36.             if (l2.type == maxQuery)
  37.                 return this->xLeft < l2.val;
  38.             if (l2.type == minQuery)
  39.                 return this->xLeft > l2.val;
  40.         }
  41.     };
  42.  
  43. private:
  44.     bool            isMax; //whether or not saved envelope is top(search of max value)
  45.     std::set<Line>  hull;  //envelope itself
  46.  
  47. private:
  48.     /*
  49.      * INFO:        Check position in hull by iterator
  50.      * COMPLEXITY:  O(1)
  51.      */
  52.     bool hasPrev(std::set<Line>::iterator it) { return it!=hull.begin(); }
  53.     bool hasNext(std::set<Line>::iterator it) { return it!=hull.end() && std::next(it)!=hull.end(); }
  54.  
  55.     /*
  56.      * INFO:        Check whether line l2 is irrelevant
  57.      * NOTE:        Following positioning in hull must be true
  58.      *              l1 is next left to l2
  59.      *              l2 is right between l1 and l3
  60.      *              l3 is next right to l2
  61.      * COMPLEXITY:  O(1)
  62.      */
  63.     bool irrelevant(const Line& l1, const Line& l2, const Line& l3) { return intersectX(l1,l3) <= intersectX(l1,l2); }
  64.     bool irrelevant(std::set<Line>::iterator it)
  65.     {
  66.         return hasPrev(it) && hasNext(it)
  67.                && (    isMax && irrelevant(*std::prev(it), *it, *std::next(it))
  68.                        || !isMax && irrelevant(*std::next(it), *it, *std::prev(it)) );
  69.     }
  70.  
  71.     /*
  72.      * INFO:        Updates 'xValue' of line pointed by iterator 'it'
  73.      * COMPLEXITY:  O(1)
  74.      */
  75.     std::set<Line>::iterator updateLeftBorder(std::set<Line>::iterator it)
  76.     {
  77.         if (isMax && !hasPrev(it) || !isMax && !hasNext(it))
  78.             return it;
  79.  
  80.         double val = intersectX(*it, isMax?*std::prev(it):*std::next(it));
  81.         Line buf(*it);
  82.         it = hull.erase(it);
  83.         buf.xLeft = val;
  84.         it = hull.insert(it, buf);
  85.         return it;
  86.     }
  87.  
  88. public:
  89.     explicit ConvexHullDynamic(bool isMax): isMax(isMax) {}
  90.  
  91.     /*
  92.      * INFO:        Adding line to the envelope
  93.      *              Line is of type 'y=a*x+b' represented by 2 coefficients 'a' and 'b'
  94.      * COMPLEXITY:  Adding N lines(N calls of function) takes O(N*log N) time
  95.      */
  96.     void addLine(coef_t a, coef_t b)
  97.     {
  98.         //find the place where line will be inserted in set
  99.         Line l3 = Line(a, b);
  100.         auto it = hull.lower_bound(l3);
  101.  
  102.         //if parallel line is already in set, one of them becomes irrelevant
  103.         if (it!=hull.end() && areParallel(*it, l3))
  104.         {
  105.             if (isMax && it->b < b || !isMax && it->b > b)
  106.                 it = hull.erase(it);
  107.             else
  108.                 return;
  109.         }
  110.  
  111.         //try to insert
  112.         it = hull.insert(it, l3);
  113.         if (irrelevant(it)) { hull.erase(it); return; }
  114.  
  115.         //remove lines which became irrelevant after inserting line
  116.         while (hasPrev(it) && irrelevant(std::prev(it))) hull.erase(std::prev(it));
  117.         while (hasNext(it) && irrelevant(std::next(it))) hull.erase(std::next(it));
  118.  
  119.         //refresh 'xLine'
  120.         it = updateLeftBorder(it);
  121.         if (hasPrev(it))
  122.             updateLeftBorder(std::prev(it));
  123.         if (hasNext(it))
  124.             updateLeftBorder(std::next(it));
  125.     }
  126.     /*
  127.      * INFO:        Query, which returns max/min(depends on hull type - see more info above) value in point with abscissa 'x'
  128.      * COMPLEXITY:  O(log N), N-amount of lines in hull
  129.      */
  130.     val_t getBest(coord_t x) const
  131.     {
  132.         Line q;
  133.         q.val = x;
  134.         q.type = isMax ? Line::Type::maxQuery : Line::Type::minQuery;
  135.  
  136.         auto bestLine = hull.lower_bound(q);
  137.         if (isMax) --bestLine;
  138.         return bestLine->valueAt(x);
  139.     }
  140. };
  141.  
  142.  
Compilation error #stdin compilation error #stdout 0s 0KB
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stdin
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Standard input is empty
compilation info 
/usr/lib/gcc/i586-linux-gnu/5/../../../i386-linux-gnu/crt1.o: In function `_start':
(.text+0x18): undefined reference to `main'
collect2: error: ld returned 1 exit status
stdout
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Standard output is empty
https://ideone.com/fAjoZu
language:
C++14 (gcc 8.3)
created:
9 years ago
visibility:
secret

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