本文涉及知識點
數學C++二分查找
P12261 [藍橋杯 2024 國 Java B] 激光炮
題目描述
小明在二維平面上放置了 門激光炮,第
門激光炮位於座標
,射向靶點
,形成
條線段。他想使用一條垂直於
軸且其中一個端點在
輸入格式
輸入共
第一行為一個正整數 。
後面 行,每行 2 個由空格分開的非負整數表示
。
輸出格式
輸出共 行,一個浮點數表示答案(輸出四捨五入到
輸入輸出樣例 #1
輸入 #1
3
0 100000
100000 200000
200000 0
輸出 #1
133333.33
説明/提示
樣例説明
第 門激光炮發射路線的交點為
,因此,只需要在
處放置一條長度為
評測用例規模與約定
- 對於
的評測用例,保證
。
- 對於
的評測用例,保證
,
。
計算幾何
沒有激光線平行與y軸,故可以用一元一次方程表示激光線
令
如果隔板是x = x0,則本題的答案是fm(x0)。
如果g(-1e5) >=h(-1e5),則答案是g(-1e5)
如果h(1e5) >= g(1e5),則答案是h(1e5)
排除以上兩種情況後:存在x0。 g(x0) >= h(x0) 且
二分查找出x0,fm(x0)便是答案。
代碼
核心代碼
#include <iostream>
#include <sstream>
#include <vector>
#include<map>
#include<unordered_map>
#include<set>
#include<unordered_set>
#include<string>
#include<algorithm>
#include<functional>
#include<queue>
#include <stack>
#include<iomanip>
#include<numeric>
#include <math.h>
#include <climits>
#include<assert.h>
#include<cstring>
#include<list>
#include<array>
#include <bitset>
using namespace std;
template<class T1, class T2>
std::istream& operator >> (std::istream& in, pair<T1, T2>& pr) {
in >> pr.first >> pr.second;
return in;
}
template<class T1, class T2, class T3 >
std::istream& operator >> (std::istream& in, tuple<T1, T2, T3>& t) {
in >> get<0>(t) >> get<1>(t) >> get<2>(t);
return in;
}
template<class T1, class T2, class T3, class T4 >
std::istream& operator >> (std::istream& in, tuple<T1, T2, T3, T4>& t) {
in >> get<0>(t) >> get<1>(t) >> get<2>(t) >> get<3>(t);
return in;
}
template<class T1, class T2, class T3, class T4, class T5, class T6, class T7 >
std::istream& operator >> (std::istream& in, tuple<T1, T2, T3, T4,T5,T6,T7>& t) {
in >> get<0>(t) >> get<1>(t) >> get<2>(t) >> get<3>(t) >> get<4>(t) >> get<5>(t) >> get<6>(t);
return in;
}
template<class T = int>
vector<T> Read() {
int n;
cin >> n;
vector<T> ret(n);
for (int i = 0; i < n; i++) {
cin >> ret[i];
}
return ret;
}
template<class T = int>
vector<T> ReadNotNum() {
vector<T> ret;
T tmp;
while (cin >> tmp) {
ret.emplace_back(tmp);
if ('\n' == cin.get()) { break; }
}
return ret;
}
template<class T = int>
vector<T> Read(int n) {
vector<T> ret(n);
for (int i = 0; i < n; i++) {
cin >> ret[i];
}
return ret;
}
template<int N = 1'000'000>
class COutBuff
{
public:
COutBuff() {
m_p = puffer;
}
template<class T>
void write(T x) {
int num[28], sp = 0;
if (x < 0)
*m_p++ = '-', x = -x;
if (!x)
*m_p++ = 48;
while (x)
num[++sp] = x % 10, x /= 10;
while (sp)
*m_p++ = num[sp--] + 48;
AuotToFile();
}
void writestr(const char* sz) {
strcpy(m_p, sz);
m_p += strlen(sz);
AuotToFile();
}
inline void write(char ch)
{
*m_p++ = ch;
AuotToFile();
}
inline void ToFile() {
fwrite(puffer, 1, m_p - puffer, stdout);
m_p = puffer;
}
~COutBuff() {
ToFile();
}
private:
inline void AuotToFile() {
if (m_p - puffer > N - 100) {
ToFile();
}
}
char puffer[N], * m_p;
};
template<int N = 1'000'000>
class CInBuff
{
public:
inline CInBuff() {}
inline CInBuff<N>& operator>>(char& ch) {
FileToBuf();
while (('\r' == *S) || ('\n' == *S) || (' ' == *S)) { S++; }//忽略空格和回車
ch = *S++;
return *this;
}
inline CInBuff<N>& operator>>(int& val) {
FileToBuf();
int x(0), f(0);
while (!isdigit(*S))
f |= (*S++ == '-');
while (isdigit(*S))
x = (x << 1) + (x << 3) + (*S++ ^ 48);
val = f ? -x : x; S++;//忽略空格換行
return *this;
}
inline CInBuff& operator>>(long long& val) {
FileToBuf();
long long x(0); int f(0);
while (!isdigit(*S))
f |= (*S++ == '-');
while (isdigit(*S))
x = (x << 1) + (x << 3) + (*S++ ^ 48);
val = f ? -x : x; S++;//忽略空格換行
return *this;
}
template<class T1, class T2>
inline CInBuff& operator>>(pair<T1, T2>& val) {
*this >> val.first >> val.second;
return *this;
}
template<class T1, class T2, class T3>
inline CInBuff& operator>>(tuple<T1, T2, T3>& val) {
*this >> get<0>(val) >> get<1>(val) >> get<2>(val);
return *this;
}
template<class T1, class T2, class T3, class T4>
inline CInBuff& operator>>(tuple<T1, T2, T3, T4>& val) {
*this >> get<0>(val) >> get<1>(val) >> get<2>(val) >> get<3>(val);
return *this;
}
template<class T = int>
inline CInBuff& operator>>(vector<T>& val) {
int n;
*this >> n;
val.resize(n);
for (int i = 0; i < n; i++) {
*this >> val[i];
}
return *this;
}
template<class T = int>
vector<T> Read(int n) {
vector<T> ret(n);
for (int i = 0; i < n; i++) {
*this >> ret[i];
}
return ret;
}
template<class T = int>
vector<T> Read() {
vector<T> ret;
*this >> ret;
return ret;
}
private:
inline void FileToBuf() {
const int canRead = m_iWritePos - (S - buffer);
if (canRead >= 100) { return; }
if (m_bFinish) { return; }
for (int i = 0; i < canRead; i++)
{
buffer[i] = S[i];//memcpy出錯
}
m_iWritePos = canRead;
buffer[m_iWritePos] = 0;
S = buffer;
int readCnt = fread(buffer + m_iWritePos, 1, N - m_iWritePos, stdin);
if (readCnt <= 0) { m_bFinish = true; return; }
m_iWritePos += readCnt;
buffer[m_iWritePos] = 0;
S = buffer;
}
int m_iWritePos = 0; bool m_bFinish = false;
char buffer[N + 10], * S = buffer;
};
template<class INDEX_TYPE>
class CBinarySearch
{
public:
CBinarySearch(INDEX_TYPE iMinIndex, INDEX_TYPE iMaxIndex, INDEX_TYPE tol = 1) :m_iMin(iMinIndex), m_iMax(iMaxIndex), m_iTol(tol) {}
template<class _Pr>
INDEX_TYPE FindFrist(_Pr pr)
{
auto left = m_iMin - m_iTol;
auto rightInclue = m_iMax;
while (rightInclue - left > m_iTol)
{
const auto mid = left + (rightInclue - left) / 2;
if (pr(mid))
{
rightInclue = mid;
}
else
{
left = mid;
}
}
return rightInclue;
}
template<class _Pr>
INDEX_TYPE FindEnd(_Pr pr)
{
INDEX_TYPE leftInclude = m_iMin;
INDEX_TYPE right = m_iMax + m_iTol;
while (right - leftInclude > m_iTol)
{
const auto mid = leftInclude + (right - leftInclude) / 2;
if (pr(mid))
{
leftInclude = mid;
}
else
{
right = mid;
}
}
return leftInclude;
}
protected:
const INDEX_TYPE m_iMin, m_iMax, m_iTol;
};
class Solution {
public:
double Ans(vector<pair<int, int>>& ab) {
vector<pair<double, double>> vg, vh;
for (const auto& [a, b] : ab) {
double c = (a - b) / 2e5;
double d = (a + b) / 2.0;
if (c >= 0) {
vg.emplace_back(c, d);
}
else {
vh.emplace_back(c, d);
}
}
auto GH = [&](vector<pair<double, double>>& v, double x) {
double ret = -1;
for (const auto& [c, d] : v) {
ret = max(ret, c * x + d);
}
return ret;
};
auto G = [&](double x) {return GH(vg, x); };
auto H = [&](double x) {return GH(vh, x); };
auto F = [&](double x) {return max(G(x), H(x)); };
if (G(-1e5) >= H(-1e5)) { return F(-1e5); }
if (H(1e5) >= G(1e5)) { return F(1e5); }
auto Check = [&](double mid) {return G(mid) >= H(mid); };
auto x0 = CBinarySearch<double>(-1e5, 1e5, 0.0001).FindFrist(Check);
return F(x0);
}
};
int main() {
#ifdef _DEBUG
freopen("a.in", "r", stdin);
#endif // DEBUG
ios::sync_with_stdio(0); cin.tie(nullptr);
//CInBuff<> in; COutBuff<10'000'000> ob;
auto ab = Read<pair<int, int>>();
#ifdef _DEBUG
//printf("s=\"%s\"", N,K);
Out(ab, ",ab=");
//Out(edge, ",edge=");
//Out(xyzw, ",xyzw=");
//Out(a, ",a=");
//Out(que, ",que=");
// //Out(ab, ",ab=");
// //Out(par, "par=");
// //Out(que, "que=");
// //Out(B, "B=");
#endif // DEBUG
auto res = Solution().Ans(ab);
printf("%.2lf", res);
return 0;
};
單元測試
vector<pair<int, int>> ab;
TEST_METHOD(TestMethod1)
{
ab = { {0,100000},{100000,200000},{200000,0} };
auto res = Solution().Ans(ab);
AssertEx(133333.33, res, 0.01);
}
TEST_METHOD(TestMethod2)
{
ab = { {5,6},{4,3} };
auto res = Solution().Ans(ab);
AssertEx(5.0, res, 0.01);
}
TEST_METHOD(TestMethod3)
{
ab = { {1,2},{4,3} };
auto res = Solution().Ans(ab);
AssertEx(3, res, 0.01);
}
測試環境
操作系統:win7 開發環境: VS2019 C++17
或者 操作系統:win10 開發環境: VS2022 C++17
如無特殊説明,本算法用**C++**實現。