Codeforces - 327A - Flipping Game

本文探讨了由Iahub发明的翻转游戏的解决策略,包括输入解析、游戏规则理解、状态变化分析以及实现算法优化。通过分析游戏流程,提出了一种O(N)复杂度的解决方案,并详细阐述了关键步骤及其实现代码。

摘要生成于 C知道 ,由 DeepSeek-R1 满血版支持, 前往体验 >

题目:http://codeforces.com/problemset/problem/327/A

A. Flipping Game
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Iahub got bored, so he invented a game to be played on paper.

He writes n integers a1, a2, ..., an. Each of those integers can be either 0 or 1. He's allowed to do exactly one move: he chooses two indices i and j (1 ≤ i ≤ j ≤ n) and flips all values ak for which their positions are in range [i, j] (that is i ≤ k ≤ j). Flip the value of x means to apply operation x = 1 - x.

The goal of the game is that after exactly one move to obtain the maximum number of ones. Write a program to solve the little game of Iahub.

Input

The first line of the input contains an integer n (1 ≤ n ≤ 100). In the second line of the input there are n integers: a1, a2, ..., an. It is guaranteed that each of those n values is either 0 or 1.

Output

Print an integer — the maximal number of 1s that can be obtained after exactly one move.

Sample test(s)
input
5
1 0 0 1 0
output
4
input
4
1 0 0 1
output
4
Note

In the first case, flip the segment from 2 to 5 (i = 2, j = 5). That flip changes the sequence, it becomes: [1 1 1 0 1]. So, it contains four ones. There is no way to make the whole sequence equal to [1 1 1 1 1].

In the second case, flipping only the second and the third element (i = 2, j = 3) will turn all numbers into 1.

分析:

此题转化的比较巧妙,具体如下:(摘自http://codeforces.com/blog/entry/8274

O(N) method: For achieve this complexity, we need to make an observation. Suppose I flip an interval (it does not matter what interval, it can be any interval). Also suppose that S is the number of ones before flipiing it. What happens? Every time I flip a 0 value, S increases by 1 (I get a new 1 value). Every time I flip a 1 value, S decreases by 1 (I loose a 1 value). What would be the “gain” from a flip? I consider winning “+1” when I get a 0 value and “-1” when I get a 1 value. The “gain” would be simply a sum of +1 and -1. This gives us idea to make another vector b[]. B[i] is 1 if A[i] is 0 and B[i] is -1 if A[i] is 1. We want to maximize S + gain_after_one_move sum. As S is constant, I want to maximize gain_after_one_move. In other words, I want to find a subsequence in b[] which gives the maximal sum. If I flip it, I get maximal number of 1s too. This can be founded trivially in O(N ^ 2). How to get O(N)? A relative experienced programmer in dynamic programming will immediately recognize it as a classical problem “subsequence of maximal sum”. If you never heard about it, come back to this approach after you learn it.

代码:

#include <iostream>

int main()
{
	int n;
	int num[100];
	int a[100];
	std::cin >> n;

	int count = 0;
	for(int i = 0; i < n; ++i)
	{
		std::cin >> num[i];
		if(num[i] == 1)
		{
			a[i] = -1;
			++count;
		}
		else
		{
			a[i] = 1;
		}
	}

	int max = -2;  // less than -1 is ok
	int sum = 0;
	for(int i = 0; i < n; ++i)
	{
		sum += a[i];

		if(sum > max)
		{
			max = sum;
		}

		if(sum < 0)
		{
			sum = 0;
		}
	}

	std::cout << max + count << std::endl;

	return 0;
}
        感谢阅读!

### 关于 Codeforces Problem 1802A 目前提供的引用内容并未涉及 Codeforces 编号为 1802A 的题目详情或解决方案[^1]。然而,基于常见的竞赛编程问题模式以及可能的解决方法,可以推测该类题目通常围绕算法设计、数据结构应用或者特定技巧展开。 如果假设此题属于典型的算法挑战之一,则可以从以下几个方面入手分析: #### 可能的方向一:字符串处理 许多入门级到中级难度的问题会考察字符串操作能力。例如判断子串是否存在、统计字符频率或是执行某种转换逻辑等。以下是 Python 中实现的一个简单例子用于演示如何高效地比较两个字符串是否相匹配: ```python def are_strings_equal(s1, s2): if len(s1) != len(s2): return False for i in range(len(s1)): if s1[i] != s2[i]: return False return True ``` #### 方向二:数组与列表的操作 另一常见主题是对整数序列进行各种形式上的变换或者是查询最值等问题。下面给出一段 C++ 程序片段来展示快速寻找最大元素位置的方法: ```cpp #include <bits/stdc++.h> using namespace std; int main(){ int n; cin >> n; vector<int> a(n); for(auto &x : a){ cin>>x; } auto max_it = max_element(a.begin(),a.end()); cout << distance(a.begin(),max_it)+1; // 输出索引加一作为答案 } ``` 由于具体描述缺失,在这里仅提供通用框架供参考。对于确切解答还需要访问实际页面获取更多信息后再做进一步探讨[^3]。
评论
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包
实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值