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HDU 1348 Wall-计算几何-[解题报告] C++


问题描述 :

Once upon a time there was a greedy King who ordered his chief Architect to build a wall around the King’s castle. The King was so greedy, that he would not listen to his Architect’s proposals to build a beautiful brick wall with a perfect shape and nice tall towers. Instead, he ordered to build the wall around the whole castle using the least amount of stone and labor, but demanded that the wall should not come closer to the castle than a certain distance. If the King finds that the Architect has used more resources to build the wall than it was absolutely necessary to satisfy those requirements, then the Architect will loose his head. Moreover, he demanded Architect to introduce at once a plan of the wall listing the exact amount of resources that are needed to build the wall.
Your task is to help poor Architect to save his head, by writing a program that will find the minimum possible length of the wall that he could build around the castle to satisfy King’s requirements.

The task is somewhat simplified by the fact, that the King’s castle has a polygonal shape and is situated on a flat ground. The Architect has already established a Cartesian coordinate system and has precisely measured the coordinates of all castle’s vertices in feet.


The first line of the input file contains two integer numbers N and L separated by a space. N (3 <= N <= 1000) is the number of vertices in the King’s castle, and L (1 <= L <= 1000) is the minimal number of feet that King allows for the wall to come close to the castle.

Next N lines describe coordinates of castle’s vertices in a clockwise order. Each line contains two integer numbers Xi and Yi separated by a space (-10000 <= Xi, Yi <= 10000) that represent the coordinates of ith vertex. All vertices are different and the sides of the castle do not intersect anywhere except for vertices.


Write to the output file the single number that represents the minimal possible length of the wall in feet that could be built around the castle to satisfy King’s requirements. You must present the integer number of feet to the King, because the floating numbers are not invented yet. However, you must round the result in such a way, that it is accurate to 8 inches (1 foot is equal to 12 inches), since the King will not tolerate larger error in the estimates.

This problem contains multiple test cases!

The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between output blocks.



9 100
200 400
300 400
300 300
400 300
400 400
500 400
500 200
350 200
200 200



 *  凸包
 *  注意:给出的点为整点数,不要设某一精度值! 
 #include <cmath>
 #include <cstdio>
 #include <cstdlib>
 #include <iostream>
 using namespace std;
 const int N = 1005;
 const double PI = 3.1415927;
 struct point {
     double x;
     double y;
 }p[N], stack[N];
 double dis(point A, point B) {
     return sqrt((A.x-B.x)*(A.x-B.x)+(A.y-B.y)*(A.y-B.y));
 double crossProd(point A, point B, point C) {
     return (B.x-A.x)*(C.y-A.y) - (B.y-A.y)*(C.x-A.x);
 int cmp(const void *a, const void *b) {
     point *c = (point *)a;
     point *d = (point *)b;
     double k = crossProd(p[0], *c, *d);//极角大小转化为求叉乘
     if (k<0 || !k && dis(p[0], *c)>dis(p[0], *d)) return 1;
     return -1;
 double Graham(int n) {
     double x = p[0].x;
     double y = p[0].y;
     int mi = 0;
     for (int i=1; i<n; ++i) {//找到最左下的一个点
         if (p[i].x<x || (p[i].x==x && p[i].y<y)) {
             x = p[i].x;
             y = p[i].y;
             mi = i;
     point tmp = p[mi];
     p[mi] = p[0];
     p[0] = tmp;
     qsort(p+1, n-1, sizeof(point), cmp);
     p[n] = p[0];
     stack[0] = p[0];
     stack[1] = p[1];
     stack[2] = p[2];
     int top = 2;
     for (int i=3; i<=n; ++i) {//加入一个点后,向右偏拐或共线,则上一个点不在凸包内,则--top,该过程直到不向右偏拐或没有三点共线的点 
         while (crossProd(stack[top-1], stack[top], p[i])<=0 && top>=2) --top;
         stack[++top] = p[i];//在当前情况下符合凸包的点,入栈
     double len = 0;
     for (int i=0; i<top; ++i) len += dis(stack[i], stack[i+1]);
     return len;
 int main() {
     int t;
     while (scanf("%d", &t) != EOF) {
         while (t--) {
             int n, l;
             scanf ("%d%d", &n, &l);
             for (int i=0; i<n; ++i) scanf ("%lf%lf", &p[i].x, &p[i].y);
             double ans = Graham(n);
             ans += PI * (l + l);
             printf ("%.0lf\n", ans);
             if (t) printf ("\n");
     return 0;



  1. #include <stdio.h>
    int main()
    int n,p,t[100]={1};
    for(int i=1;i<100;i++)
    t =i;
    printf("Printing order for 1 pages:nSheet 1, front: Blank, 1n");
    else {
    if(n%4) p=n/4+1;
    else p=n/4;
    int q=4*p;
    printf("Printing order for %d pages:n",n);
    for(int i=0;i<p;i++){
    printf("Sheet %d, front: ",i+1);
    if(q>n) {printf("Blank, %dn",t[2*i+1]);}
    else {printf("%d, %dn",q,t[2*i+1]);}
    printf("Sheet %d, back : ",i+1);
    if(q>n) {printf("%d, Blankn",t[2*i+2]);}
    else {printf("%d, %dn",t[2*i+2],q);}
    return 0;

  2. L(X [0 .. M-1],Y [0 .. N-1])= 1 + L(X [0 .. M-2],Y [0 .. N-1])这个地方也也有笔误
    应改为L(X [0 .. M-1],Y [0 .. N-1])= 1 + L(X [0 .. M-2],Y [0 .. N-2])

  3. 有一点问题。。后面动态规划的程序中
    int dp[n+1][W+1];
    会报错 提示表达式必须含有常量值。该怎么修改呢。。

  4. 我没看懂题目
    5 6 -1 5 4 -7
    7 0 6 -1 1 -6 7 -5
    我觉得第一个应该是5 6 -1 5 4 输出是19 5 4
    第二个是7 0 6 -1 1 -6 7输出是14 7 7

  5. 这道题目虽然简单,但是小编做的很到位,应该会给很多人启发吧!对于面试当中不给开辟额外空间的问题不是绝对的,实际上至少是允许少数变量存在的。之前遇到相似的问题也是恍然大悟,今天看到小编这篇文章相见恨晚。