hdu1147:pick up sticks-优快云博客

本文介绍了一个计算机编程问题——挑棍问题，该问题涉及通过算法确定哪些棍子在一系列随机投掷后位于顶部。文章详细解释了输入输出要求，并提供了一段示例代码，用于解决如何判断两根棍子是否相交及如何找出所有顶部棍子的问题。

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Pick-up sticks

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2044 Accepted Submission(s): 769

Problem Description

Stan has n sticks of various length. He throws them one at a time on the floor in a random way. After finishing throwing, Stan tries to find the top sticks, that is these sticks such that there is no stick on top of them. Stan has noticed that the last thrown stick is always on top but he wants to know all the sticks that are on top. Stan sticks are very, very thin such that their thickness can be neglected.

Input

Input consists of a number of cases. The data for each case start with 1 ≤ n ≤ 100000, the number of sticks for this case. The following n lines contain four numbers each, these numbers are the planar coordinates of the endpoints of one stick. The sticks are listed in the order in which Stan has thrown them. You may assume that there are no more than 1000 top sticks. The input is ended by the case with n=0. This case should not be processed.

Output

For each input case, print one line of output listing the top sticks in the format given in the sample. The top sticks should be listed in order in which they were thrown.
The picture to the right below illustrates the first case from input.

Sample Input

Sample Output

Top sticks: 2, 4, 5.
Top sticks: 1, 2, 3.

#include<iostream>
#include<cstdio>
#include<string>
#include<algorithm>
#include<queue>
#include<vector>
#include<map>
#include<cmath>
using namespace std;

const int MAXN = 100001;
bool top[MAXN];
struct Point{
    double x, y;
};

struct Line{
    Point st, ed;
}line[MAXN];
double max(double a, double b){
    return a > b ? a : b;
}
double min(double a, double b){
    return a < b ? a : b;
}
double dist(Point &a1, Point &a2){
    return sqrt((a1.x - a2.x)*(a1.x - a2.x) + (a1.y - a2.y)*(a1.y - a2.y));
}

bool kpc(Line l1, Line l2){
    return min(l1.st.x, l1.ed.x) <= max(l2.st.x, l2.ed.x) && min(l1.st.y, l1.ed.y) <= max(l2.st.y, l2.ed.y)
        && min(l2.st.x, l2.ed.x) <= max(l1.st.x, l1.ed.x) && min(l2.st.y, l2.ed.y) <= max(l1.st.y, l1.ed.y);
}

bool kual(Line l1, Line l2){
    Point A, B;
    Point C, D;
    bool flag1, flag2;
    flag1 = flag2 = false;
    A = l1.st;
    B = l1.ed;
    C = l2.st;
    D = l2.ed;
    double t1 = (C.x - A.x)*(B.y - A.y) - (C.y - A.y)*(B.x - A.x);
    double t2 = (D.x - A.x)*(B.y - A.y) - (D.y - A.y)*(B.x - A.x);
    if (t1*t2 <= 0)
    {
        flag1 = true;
    }
    t1 = (B.x - C.x)*(D.y - C.y) - (B.y - C.y)*(D.x - C.x);
    t2 = (A.x - C.x)*(D.y - C.y) - (A.y - C.y)*(D.x - C.x);
    if (t1*t2 <= 0){
        flag2 = true;
    }
    if (flag1&&flag2){
        return true;
    }
    return false;
}
int main(){
    int n;
    int i, j;
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
    while (cin >> n, n){
        for (i = 0; i < n; i++){
            cin >> line[i].st.x >> line[i].st.y;
            cin >> line[i].ed.x >> line[i].ed.y;
            top[i] = true;
        }

	//注意到

/*

	效率低若n>1000则会超时

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

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

		if(top[j]){

		    if(kpc(line[i],line[j]){

                    	if(kual(line[i],line[j]){

			     top[j]=false;

*/


        for (i = 0; i < n; i++){
            for (j = i+1; j < n; j++){
                if (kpc(line[i], line[j])){
                    if (kual(line[i], line[j])){
                        top[i] = false;
                        break;
                    }
                }
            }
        }
        bool flag = false;
        j = -1;
        cout << "Top sticks: ";
        for (i = 0; i < n; i++){
            if (top[i] && flag){
                cout << j + 1 << ", ";
                j = i;
            }
            else if (top[i]){
                j = i;
                flag = true;
            }
        }
        cout << j + 1 << "." << endl;
    }

    return 0;
}