B. Gerald is into Art

本文探讨了如何判断两张矩形画是否可以不重叠地放在另一张矩形板上,通过旋转和调整位置,确保画作的一边平行于地面,并提供了一个C++实现方案。

B. Gerald is into Art
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Gerald bought two very rare paintings at the Sotheby’s auction and he now wants to hang them on the wall. For that he bought a special board to attach it to the wall and place the paintings on the board. The board has shape of an a1 × b1 rectangle, the paintings have shape of a a2 × b2 and a3 × b3 rectangles.

Since the paintings are painted in the style of abstract art, it does not matter exactly how they will be rotated, but still, one side of both the board, and each of the paintings must be parallel to the floor. The paintings can touch each other and the edges of the board, but can not overlap or go beyond the edge of the board. Gerald asks whether it is possible to place the paintings on the board, or is the board he bought not large enough?
Input

The first line contains two space-separated numbers a1 and b1 — the sides of the board. Next two lines contain numbers a2, b2, a3 and b3 — the sides of the paintings. All numbers ai, bi in the input are integers and fit into the range from 1 to 1000.
Output

If the paintings can be placed on the wall, print “YES” (without the quotes), and if they cannot, print “NO” (without the quotes).
Examples
Input

3 2
1 3
2 1

Output

YES

Input

5 5
3 3
3 3

Output

NO

Input

4 2
2 3
1 2

Output

YES

Note

That’s how we can place the pictures in the first test:

And that’s how we can do it in the third one.

两个矩形能否不重叠的放入第三个矩形中、暴力枚举

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <cstdlib>
#include <algorithm>
#include <set>
#include <stack>
#include <cmath>
#include <queue>
#include <map>
using namespace std;

typedef long long int llint;
#define ite ::iterator
#define mem(a) memset(a, 0, sizeof(a))
#define pi acos(-1)
const llint maxn = 2e5+100;
/*-------------------模板-----------------------------------------*/
template <typename T>
int com(const T& v1, const T& v2) {
    if (v1 < v2)    return -1;
    else if (v1 > v2)   return 1;
    return 0;
}

int a[1100][1100];

int main() {
    mem(a);
    //freopen("text.in", "r", stdin);
    //freopen("text.out", "w", stdout);
    int a1, b1, a2, b2, a3, b3;
    cin >> a1 >> b1 >> a2 >> b2 >> a3 >> b3;
    int flag = 0;
    int a11 = max(a1, b1), b11 = min(a1, b1);
    int a22 = max(a2, b2), b22 = min(a2, b2);
    //int a33 = max(a3, b3), b33 = min(a3, b3);
    int n1 = a11 - a22, n2 = b11 - b22;
    if (n1 >= 0 && n2 >= 0) {
        if ((n1>=a3 && b11>=b3) || (n1>=b3 && b11>=a3)) flag = 1;
        if ((n2>=a3 && a11>=b3) || (n2>=b3 && a11>=a3)) flag = 1;
    }
    n1 = a11 - b22, n2 = b11 - a22;
    if (n1 >= 0 && n2 >= 0) {
        if ((n1>=a3 && b11>=b3) || (n1>=b3 && b11>=a3)) flag = 1;
        if ((n2>=a3 && a11>=b3) || (n2>=b3 && a11>=a3)) flag = 1;
    }
    if (flag)   cout << "YES" << endl;
    else    cout << "NO" << endl;
    return 0;
}

转载于:https://www.cnblogs.com/Tovi/p/6194799.html

内容概要:本文系统介绍了算术优化算法(AOA)的基本原理、核心思想及Python实现方法,并通过图像分割的实际案例展示了其应用价值。AOA是一种基于种群的元启发式算法,其核心思想来源于四则运算,利用乘除运算进行全局勘探,加减运算进行局部开发,通过数学优化器加速函数(MOA)和数学优化概率(MOP)动态控制搜索过程,在全局探索与局部开发之间实现平衡。文章详细解析了算法的初始化、勘探与开发阶段的更新策略,并提供了完整的Python代码实现,结合Rastrigin函数进行测试验证。进一步地,以Flask框架搭建前后端分离系统,将AOA应用于图像分割任务,展示了其在实际工程中的可行性与高效性。最后,通过收敛速度、寻优精度等指标评估算法性能,并提出自适应参数调整、模型优化和并行计算等改进策略。; 适合人群:具备一定Python编程基础和优化算法基础知识的高校学生、科研人员及工程技术人员,尤其适合从事人工智能、图像处理、智能优化等领域的从业者;; 使用场景及目标:①理解元启发式算法的设计思想与实现机制;②掌握AOA在函数优化、图像分割等实际问题中的建模与求解方法;③学习如何将优化算法集成到Web系统中实现工程化应用;④为算法性能评估与改进提供实践参考; 阅读建议:建议读者结合代码逐行调试,深入理解算法流程中MOA与MOP的作用机制,尝试在不同测试函数上运行算法以观察性能差异,并可进一步扩展图像分割模块,引入更复杂的预处理或后处理技术以提升分割效果。
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