Graham Scan Algorithm -> sqrt and arctan2 huge values

Question

I have to implement Graham Scan Algorithm. This is my code:

    /*
    Graham's algorithm'
    */

    #include <stdio.h>
    #include <stdlib.h>
    #include <conio.h>

    #include <stack>
    #include <vector>
    #include <math.h>

    #include <algorithm>
    #include <cstdlib>

    using namespace std;
    struct Tpoint
    {
        int x;
        int y;
    };

    struct AR{
        double alpha;
        double r;
        int i;
    }; 


    bool operator<(AR p, AR q){
        if(p.alpha != p.alpha){
            return p.alpha < p.alpha;
        } else {
            return p.r < p.r;
        }
    }



    int det(Tpoint p1, Tpoint p2, Tpoint p3){
        return p1.x*p2.y + p2.x*p3.y + p3.x*p1.y - p3.x*p2.y - p1.x*p3.y - p2.x*p1.y;
    }


    int right_turn(stack<Tpoint,vector<Tpoint> > S,Tpoint p3){
        Tpoint p2;
        Tpoint p1;


        p2=S.top();
        S.pop();
        p1=S.top();
        S.push(p2);


        if (det(p1,p2,p3)>0)
        return 0;


        if (det(p1,p2,p3)<0)
        return 1;
    }

    int main(){

        vector<Tpoint> Q;

        //Stos pointów, na końcu zawiera wynik
        stack<Tpoint,vector<Tpoint> > S;

        Tpoint point;


    Tpoint array[]={3,-2, -3,-2, 6,4, -6,1, 4,5, 0,0, 3,4, -3,3, -2,2, 0,6};
    Tpoint point00=array[0];
    int xMax = array[0].x;
    int yMin = array[0].y;
    int i;
    for (i=0; i<10; i++){
        if (array[i].y<yMin){
            if(array[i].x>xMax){
                xMax=array[i].x;
                yMin=array[i].y;
                point00=array[i];


            }
        }
    }

    //sorting section start

    printf("%d %d \n \n",point00.x, point00.y);
    Q.push_back(point00);

    Tpoint arrayCLONE[10];
    AR arrayAR[10];
    for (i=0; i<10; i++){
                arrayAR[i].alpha=0.0;
                arrayAR[i].r=0.0;
                arrayAR[i].i=i;
                arrayCLONE[i] = array[i]; 

                array[i].x-=point00.x;
                array[i].y-=point00.y;

    }



    for (i=0; i<10; i++){
        if ((array[i].x != point00.x) && (array[i].y != point00.y)) {
            arrayAR[i].alpha=atan2(array[i].y, array[i].x);
            arrayAR[i].r=sqrt(array[i].x*array[i].x+array[i].y*array[i].y);


            printf("alpha= %d, r= %d \n",arrayAR[i].alpha,arrayAR[i].r);
            printf("x= %d, y= %d\n",array[i].x, array[i].y);
        }else{

        arrayAR[i].alpha=9999;
        arrayAR[i].r=9999;
        arrayAR[i].i=0;
        }

    }

    sort (arrayAR, arrayAR + 10);

    for (i=0; i<10; i++){
        if (arrayAR[i].alpha<1000){
            Q.push_back(arrayCLONE[arrayAR[i].i]);
        //  printf("i =%d \n",i);
            printf("x =%d \n",arrayCLONE[arrayAR[i].i].x);
            printf("y =%d \n",arrayCLONE[arrayAR[i].i].y);
            printf("_____ \n");

        //  printf("index i =%d \n",arrayAR[i].i);
        }
    }


    //sorting section end


    S.push(Q[0]);
    S.push(Q[1]);
    S.push(Q[2]);

    for (int i=3;i<10; i++){
    while (right_turn(S,Q[i])==1)
        S.pop();
        S.push(Q[i]);
    }


    printf("points: \n");
    while (!(S.empty()))
    {
        point=S.top();
        S.pop();
        printf("(%d,%d) ",point.x,point.y);
    }
        printf("\n..");
        getch();
        return 0;
    }

It's not working in sorting section. Functions _arctan2() and _sqrt() have returning large values. I.e sqrt returns -1464986461. Why it happens? As a result, points are not sorted by alfa, but in not known way. If I manual set order of points, algorithm work properly.

Could you tell me way it is not working?

I did some Graham scan implementations back in my younger days, and you don't actually need to compute either sqrt or atan (just int operations if points have int coords). Remember that det(A,B,C)=0 if and only if A, B and C are colinear (I used the function you have already defined). In other words, in your operator, you can just check the sign of det instead of the sign of (alpha1-alpha2) which you are currently doing. In case the det is zero, check the square of the distances (sqrt preserves i equalities, so you can just skip the extra, costly, unneeded floating point operation) — Catalin Pol, Dec 10 '13 at 02:12

score 1 · Answer 1 · answered Dec 09 '13 at 23:54

1

You're trying to print a floating point value as a decimal (int) value.

Do this instead:

printf("alpha= %f, r= %f \n",arrayAR[i].alpha,arrayAR[i].r);

%d means signed decimal integer. Review the documentation for printf

%f means decimal floating point

answered Dec 09 '13 at 23:54

AndyG

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score 0 · Answer 2 · answered Dec 14 '13 at 14:24

Ok, now it works:

    /*
    Graham's algorithm'
    */

    #include <stdio.h>
    #include <stdlib.h>
    #include <conio.h>

    #include <stack>
    #include <vector>
    #include <math.h>

    #include <algorithm>
    #include <cstdlib>

    using namespace std;
    struct Tpoint
    {
        int x;
        int y;
    };

    struct AR{
        double alpha;
        double r;
        int i;
    }; 


    bool operator<(AR p, AR q){
        if(p.alpha != q.alpha){
            return p.alpha < q.alpha;
        } else {
            return p.r < q.r;
        }
    }



    int det(Tpoint p1, Tpoint p2, Tpoint p3){
        return p1.x*p2.y + p2.x*p3.y + p3.x*p1.y - p3.x*p2.y - p1.x*p3.y - p2.x*p1.y;
    }


    int right_turn(stack<Tpoint,vector<Tpoint> > S,Tpoint p3){
        Tpoint p2;
        Tpoint p1;


        p2=S.top();
        S.pop();
        p1=S.top();
        S.push(p2);


        if (det(p1,p2,p3)>0)
        return 0;


        if (det(p1,p2,p3)<0)
        return 1;
    }

    int main(){

        vector<Tpoint> Q;

        //Stos pointów, na końcu zawiera wynik
        stack<Tpoint,vector<Tpoint> > S;

        Tpoint point;


    Tpoint array[]={-3,-2, 6,4, -6,1, 4,5, 0,6, 3,4, -3,5, 3,-2,  -2,2, 0,0, 1,1};
    Tpoint point00=array[0];
    int xMax = array[0].x;
    int yMin = array[0].y;
    int i;
    for (i=1; i<9; i++){

        if (array[i].y<yMin){
            yMin=array[i].y;


            }
        }


    for (i=1; i<9; i++){

        if (array[i].y==yMin){
                if(array[i].x>xMax){
                xMax=array[i].x;

                point00=array[i];


            }
        }
    }


    //sorting section start

    printf("point00 x=%d y=%d \n \n",point00.x, point00.y);
    Q.push_back(point00);

    Tpoint arrayCLONE[11];
    AR arrayAR[11];
    for (i=0; i<10; i++){
                arrayAR[i].alpha=0.0;
                arrayAR[i].r=0.0;
                arrayAR[i].i=i;
                arrayCLONE[i] = array[i]; 


                array[i].x-=point00.x;
                array[i].y-=point00.y;

        //printf("x2= %d, y2= %d\n",array[i].x, array[i].y);
    }



    for (i=0; i<11; i++){

        if (((array[i].x != 0) || (array[i].y != 0))) {

            arrayAR[i].alpha=atan2(array[i].y, array[i].x);
            arrayAR[i].r=sqrt(array[i].x*array[i].x+array[i].y*array[i].y);

            arrayAR[i].i=i;
            printf("alpha= %f, r= %f , x= %d, y=%d\n",arrayAR[i].alpha,arrayAR[i].r,array[i].x, array[i].y);

        }else{

        arrayAR[i].alpha=9999;
        arrayAR[i].r=9999;
        arrayAR[i].i=16;
        }

    }

    sort (arrayAR, arrayAR +10);
    Tpoint temp;
    for (i=0; i<10; i++){
        if (arrayAR[i].alpha<1000 && arrayAR[i].alpha>0.0){

            Q.push_back(arrayCLONE[arrayAR[i].i]);
        //  printf("i =%d \n",i);
            printf("x =%d \n",arrayCLONE[arrayAR[i].i].x);
            printf("y =%d \n",arrayCLONE[arrayAR[i].i].y);
            printf("_____ \n");

        //  temp.x=arrayCLONE[arrayAR[i].i].x;
        //  temp.y=arrayCLONE[arrayAR[i].i].y;
        //  printf("index i =%d \n",arrayAR[i].i);
        }
    }

    //Q.push_back(temp);
    //sorting section end


    S.push(Q[0]);
    S.push(Q[1]);
    S.push(Q[2]);

    for (int i=3;i<10; i++){
    while (right_turn(S,Q[i])==1)
        S.pop();
        S.push(Q[i]);
    }

    //  S.push(Q[5]);


    printf("points: \n");
    while (!(S.empty()))
    {
        point=S.top();
        S.pop();
        printf("(%d,%d) ",point.x,point.y);
    }
        printf("\n...");
        getch();
        return 0;
    }

Why did you change your for-loops to be `for (i=1; i<9; i++)`? You realize that `array[0]` is a valid index, right? It would be nice to mention *what* you changed as well: Your `operator<` was wrong, and you were indeed printing floating points as decimals as my answer pointed out. — AndyG, Dec 17 '13 at 16:43

Graham Scan Algorithm -> sqrt and arctan2 huge values

2 Answers2