POJ 3122 分披萨(二分查找)
发布日期:2021-07-01 03:39:37 浏览次数:2 分类:技术文章

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题目链接:

题目大意:

有 n 块披萨(大小不一样), f 个人分,包含主人自己 f+1 人;

每人吃的披萨必须是一块披萨上切下来的。每个人吃的披萨相等,披萨可以有剩余。求每人吃的最大披萨面积。

思路:

  • 假设每人分得的披萨面积等效为半径 R的圆;
  • 每块披萨可以分给几个人呢? r[i] 表示披萨半径,则是 r[i]2/R2 取整个人
  • 然后全部累加起来,如果总和大于等于 f+1,则每个人还有分更大的披萨的可能,R取值增大
  • 如果总和小于 f+1,则每个人分的太大了,不够分的,R取值减小
  • R的取值范围在(0,max(r[i]))

Wrong Answer代码

/** * @description: 有 n 块披萨(大小不一样), f 个人分,包含主人自己 f+1 人; *                  每人吃的披萨必须是一块披萨上切下来的。求 * @author: michael ming * @date: 2019/4/20 0:23 * @modified by:  */#include 
#include
#define PI 3.14159265359using namespace std;const double error = 1e-7;double find_max_R(size_t pizza_num, int *r_pizza, double r_low, double r_high, size_t people){
double R_we_want = r_low+(r_high-r_low)/2; size_t people_get_pizza = 0; while(r_high - r_low > error) {
people_get_pizza = 0; R_we_want = r_low+(r_high-r_low)/2; for(int i = 0; i < pizza_num; ++i) people_get_pizza += (int)(r_pizza[i]*r_pizza[i]/(R_we_want*R_we_want)); if(people_get_pizza >= people) r_low = R_we_want; else r_high = R_we_want; } return R_we_want;}int main(){
size_t t, pizza_num, friend_num; double r_max_pizza = 0; cin >> t; while(t--) {
cin >> pizza_num >> friend_num; int *r_pizza = new int [pizza_num]; for(int i = 0; i < pizza_num; ++i) {
cin >> r_pizza[i]; r_max_pizza = r_pizza[i] > r_max_pizza ? r_pizza[i] : r_max_pizza; } r_max_pizza = find_max_R(pizza_num,r_pizza,0,r_max_pizza,friend_num+1); cout << setiosflags(ios::fixed) << setprecision(4) << PI*r_max_pizza*r_max_pizza << endl; delete[] r_pizza; r_pizza = NULL; } return 0;}

在这里插入图片描述

AC代码(主要修改,精度问题,把求人数的除法改成减法)

/** * @description: 有 n 块披萨(大小不一样), f 个人分,包含主人自己 f+1 人; *                  每人吃的披萨必须是一块披萨上切下来的。求 * @author: michael ming * @date: 2019/4/20 0:23 * @modified by:  */#include 
#include
#include
#include
#define PI acos(-1.0)using namespace std;const double error = 1e-7;double find_max_R(size_t pizza_num, double *s_pizza, double s_low, double s_high, size_t people){
double S_we_want = s_low+(s_high-s_low)/2.0; size_t people_get_pizza = 0; while(s_high - s_low > error) {
people_get_pizza = 0; S_we_want = s_low+(s_high-s_low)/2.0; for(int i = 0; i < pizza_num; ++i) {
double temp = s_pizza[i]; while(temp-S_we_want>=0) {
temp -= S_we_want; //改成减法,不易丢失精度 people_get_pizza++; } } if(people_get_pizza >= people) s_low = S_we_want; else s_high = S_we_want; } return S_we_want;}int main(){
size_t t, pizza_num, friend_num; double s_max_pizza = 0.0; cin >> t; while(t--) {
cin >> pizza_num >> friend_num; double *s_pizza = new double [pizza_num]; for(int i = 0; i < pizza_num; ++i) {
cin >> s_pizza[i]; s_pizza[i] *= s_pizza[i]; } sort(s_pizza, s_pizza+pizza_num); s_max_pizza = find_max_R(pizza_num,s_pizza,0,s_pizza[pizza_num-1],friend_num+1); cout << setiosflags(ios::fixed) << setprecision(4) << PI*s_max_pizza << endl; delete[] s_pizza; s_pizza = NULL; } return 0;}

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