Problem A. Oversized Pancake Flipper(googlejam资格赛)

本文介绍了一个有趣的算法问题——翻转煎饼问题。问题要求使用一个特定长度的煎饼翻转工具,将所有煎饼翻转到笑脸朝上的一面。文章提供了一段C++代码示例,展示了如何通过迭代检查并翻转不符合要求的煎饼,从而解决这个问题。

Problem

Last year, the Infinite House of Pancakes introduced a new kind of pancake. It has a happy face made of chocolate chips on one side (the “happy side”), and nothing on the other side (the “blank side”).

You are the head cook on duty. The pancakes are cooked in a single row over a hot surface. As part of its infinite efforts to maximize efficiency, the House has recently given you an oversized pancake flipper that flips exactly K consecutive pancakes. That is, in that range of K pancakes, it changes every happy-side pancake to a blank-side pancake, and vice versa; it does not change the left-to-right order of those pancakes.

You cannot flip fewer than K pancakes at a time with the flipper, even at the ends of the row (since there are raised borders on both sides of the cooking surface). For example, you can flip the first K pancakes, but not the first K - 1 pancakes.

Your apprentice cook, who is still learning the job, just used the old-fashioned single-pancake flipper to flip some individual pancakes and then ran to the restroom with it, right before the time when customers come to visit the kitchen. You only have the oversized pancake flipper left, and you need to use it quickly to leave all the cooking pancakes happy side up, so that the customers leave feeling happy with their visit.

Given the current state of the pancakes, calculate the minimum number of uses of the oversized pancake flipper needed to leave all pancakes happy side up, or state that there is no way to do it.

Input

The first line of the input gives the number of test cases, T. T test cases follow. Each consists of one line with a string S and an integer K. S represents the row of pancakes: each of its characters is either + (which represents a pancake that is initially happy side up) or - (which represents a pancake that is initially blank side up).

Output

For each test case, output one line containing Case #x: y, where x is the test case number (starting from 1) and y is either IMPOSSIBLE if there is no way to get all the pancakes happy side up, or an integer representing the the minimum number of times you will need to use the oversized pancake flipper to do it.

Limits

1 ≤ T ≤ 100.
Every character in S is either + or -.
2 ≤ K ≤ length of S.
Small dataset

2 ≤ length of S ≤ 10.
Large dataset

2 ≤ length of S ≤ 1000.
Sample

Input

Output

3
—+-++- 3
+++++ 4
-+-+- 4

Case #1: 3
Case #2: 0
Case #3: IMPOSSIBLE
In Case #1, you can get all the pancakes happy side up by first flipping the leftmost 3 pancakes, getting to ++++-++-, then the rightmost 3, getting to ++++—+, and finally the 3 pancakes that remain blank side up. There are other ways to do it with 3 flips or more, but none with fewer than 3 flips.

In Case #2, all of the pancakes are already happy side up, so there is no need to flip any of them.

In Case #3, there is no way to make the second and third pancakes from the left have the same side up, because any flip flips them both. Therefore, there is no way to make all of the pancakes happy side up.

引用块内容

从左往右推,没什么难度吧,读懂题就好

#include<iostream>
#include<string>
using namespace std;
void f(int t)
{
    string s;
    int K;
    int num = 0;
    cin >> s >> K;
    int len = s.size();
    int i;
    for (i = 0; i <= len-K; ++i)
    {
        if (s[i] == '-')
        {
            ++num;
            for (int j = 0; j < K; ++j)
                s[i+j]=s[i + j] == '-' ? '+' : '-';
        }
    }
    for (; i < len; ++i)
    {
        if (s[i] == '-')
        {
            printf("Case #%d: IMPOSSIBLE\n", t);
            return;
        }
    }
    printf("Case #%d: %d\n", t, num);
}
int main()
{

    freopen("file.txt", "w", stdout);
    int T;

    cin >> T;
    for (int t = 1; t <= T; ++t)
    {
        f(t);
    }

}
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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