Convex packet Problem--graham Scan

Graham Scan Overview:

The definition of convex polygon is not described in detail here, the implementation principle of the algorithm is given here.

Step 1:

Find the set of points with the lowest x value, and find the point with the lowest Y value as the initial point

Step 2:

After acquiring a new sequence, p[n]=p[1]

Step 3:

Put p[0],p[1],p[2] into a stack, from i=3 Loop to i=n-1, take stack top two elements and P[i] line, if not formed left-hand, stack top element back stack, until the stack of elements only two left.

Press P[i] into the stack.

C + + code:

#include <algorithm>#defineMax_n 100000000intTop//number of vertices in convex hulltypedef std::p air<int,int>Point ;intDis (point p1, point p2)//The square of the distance of two points{    return(P1.first-p2.first) * (P1.first-p2.first) + (p1.second-p2.second) * (P1.second-p2.second);} Point P[max_n];//cross product of vector p0p1 and vector p0p2intmulti (Point P1, point P2, point p0) {//x1*y2-x2*y1    return(P1.first-p0.first) * (P2.second-p0.second)-(P2.first-p0.first) * (P1.second-p0.second);}BOOLCMP (Point A, point B) {//Point B has a greater angle.    if(multi (A, B, p[0]) >0)        return true; //co-line    if(multi (A, B, p[0]) ==0&& Dis (A, p[0]) < dis (b, p[0]))        return true; return false;}//the essence of Graham_scanvoidGraham_scan (Point p[], point stack[],intN) {    intI, k =0; Top=2; //find the bottom and left point     for(i =1; I < n;i++)        if(P[i].second < P[k].second | | (P[i].second = = P[k].second) && (P[i].first <P[k].first)))  K=i; //Specify the point as p[0];Std::swap (p[0], p[k]); //Sort by polar angle from small to large, short distances, note p[0]Std::sort (p[1], P[n-1], CMP); //Core, for convenience, use our self-built stackstack[0] = p[0], stack[1] = p[1], stack[2] = p[2];  for(i =3; I < n;i++)    {         while(Top >1&& multi (P[i], stack[top], stack[top-1]) >=0) Top--; stack[++top] =P[i]; }} 

Convex packet Problem--graham Scan