POJ 1113 凸包2 Graham-scan 入门题（极角序，水平序）

题意：

国王想建一个周长最短的城墙，使墙的任意一点到城墙的距离都 > l。求这面墙的周长。

不难发现题目要求的就是    凸包的周长+半径为l圆的周长。

不清楚Graham-scan算法的两种排序概念的可以去看看lrj的黑书，黑书介绍了两种排序方法来实现Graham-scan算法。

1. 极角序 （看了lrj的黑书就知道这个排序不能解决某些共线问题，有一定的缺陷，但这题反映不出它的缺陷）

#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<math.h>
using namespace std;
#define eps 1e-8
#define inf 1<<29
const double pi = acos(-1.0);

struct point
{
    int x, y;
}p[1002], stack[1002];

int det(int x1, int y1, int x2, int y2)
{
    return x1 * y2 - x2 * y1;
}

int cross(point o, point a, point b)
{
    return det(a.x - o.x, a.y - o.y, b.x - o.x, b.y - o.y);
}

double f(int x)
{
    return x * x * 1.0;
}

double dis(point a, point b)
{
    return sqrt( f(a.x - b.x) + f(a.y - b.y) );
}

bool cmp(point a, point b) //极角排序
{
    int tmp = cross(p[0], a, b);
    if(tmp > 0 || ( tmp == 0 && dis(p[0], a) < dis(p[0], b) ) ) return 1;
    return 0;
}
int n;
int l;

int main()
{
    int i, j;
    while( ~scanf("%d%d", &n, &l) )
    {
        for(i = 0; i < n; i++)
        {
            scanf("%d%d", &p[i].x, &p[i].y);
            if(p[i].y < p[0].y || (p[i].y == p[0].y && p[i].x < p[0].x))
                swap(p[i], p[0]); //使0变为起始点
        }
        sort(p + 1, p + n, cmp);
        int top = 0;
        for(i = 0; i < n; i++)
        {
            while(top >= 2 && cross(stack[top-2], stack[top-1], p[i]) < 0)
                top--;
            stack[top++] = p[i];
        }
        double ans = pi * 2.0 * l;
        stack[top++] = stack[0]; //把起始点再次加入，形成一个环，方便以下的计算
        for(i = 0; i < top - 1; i++)
            ans += dis(stack[i], stack[i+1]);
        printf("%d\n", (int) (ans + 0.5));
    }
    
}

2.水平序

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<algorithm>
using namespace std;

#define eps 1e-8
#define inf 1<<29
const double pi = acos(-1.0);

struct point
{
    int x, y;
}p[1002], stack[1002];

int det(int x1, int y1, int x2, int y2)
{
    return x1 * y2 - x2 * y1;
}

int cross(point o, point a, point b)
{
    return det(a.x - o.x, a.y - o.y, b.x - o.x, b.y - o.y);
}

double f(int x)
{
    return x * x * 1.0;
}

double dis(point a, point b)
{
    return sqrt( f(a.x - b.x) + f(a.y - b.y) );
}

bool cmp(point a, point b) //水平排序
{
    if(a.y == b.y) return a.x < b.x;
    return a.y < b.y;
}

int n, l;

int main()
{
    int i, j;
    while( ~scanf("%d%d", &n, &l) )
    {
        for(i = 0; i < n; i++)
            scanf("%d%d", &p[i].x, &p[i].y);
        sort(p, p + n, cmp);
        int top = 0;
        for(i = 0; i < n; i++)
        {
            while(top >= 2 && cross(stack[top-2], stack[top-1], p[i]) < 0 )
                top --;
            stack[top++] = p[i];
        }
        int t = top + 1;
        for(i = n - 2; i >= 0; i--)
        {
            while(top >= t && cross(stack[top-2], stack[top-1], p[i]) < 0)
                top--;
            stack[top++] = p[i];
        }
        double ans = l* 2 * pi;
        for(i = 0; i < top - 1; i++)
            ans += dis(stack[i], stack[i+1]);
        printf("%d\n", (int) (ans + 0.5) );
    }
    return 0;
}

 

 水平序Graham-scan写成函数

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<algorithm>
using namespace std;

#define eps 1e-8
#define inf 1<<29
const double pi = acos(-1.0);

struct point
{
    int x, y;
}p[1002], conbag[1002];

int det(int x1, int y1, int x2, int y2)
{
    return x1 * y2 - x2 * y1;
}

int cross(point o, point a, point b)
{
    return det(a.x - o.x, a.y - o.y, b.x - o.x, b.y - o.y);
}

double f(int x)
{
    return x * x * 1.0;
}

double dis(point a, point b)
{
    return sqrt( f(a.x - b.x) + f(a.y - b.y) );
}

bool cmp(point a, point b)
{
    if(a.y == b.y) return a.x < b.x;
    return a.y < b.y;
}

int n, l;

double graham(point p[], int n)
{
    //if(n < 3) return;
    int i;
    sort(p, p + n, cmp);
    int top = 0;
    point res[1003];
    for(i = 0; i < n; i++)
    {
        while(top >= 2 && cross(res[top-2], res[top-1], p[i]) < 0)
            top--;
        res[top++] = p[i];
    }
    int t = top + 1;
    for(i = n - 2; i >= 0; i--)
    {
        while(top >= t && cross(res[top-2], res[top-1], p[i]) < 0)
            top--;
        res[top++] = p[i];
    }
    res[top++] = p[0];
    double ans = 0;
    for(i = 0; i < top - 1; i++)
        ans += dis(res[i], res[i+1]);
    return ans;
}
int main()
{
    int i, j;
    while( ~scanf("%d%d", &n, &l) )
    {
        for(i = 0; i < n; i++)
            scanf("%d%d", &p[i].x, &p[i].y);
        double ans = graham(p, n) + 2 * pi * l;
        printf("%d\n", (int) (ans + 0.5) );
    }
    return 0;
}