Codeforces 1133C

本文详细解析了Codeforces比赛中的C题目,通过尺取法解决最大子序列问题,分享了一种快速求解策略并附带AC代码。文章对比了个人解法与官方题解,展示了如何优化查找过程。

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题目链接

http://codeforces.com/contest/1133/problem/C

题意

n n n个数字,求最多能选出多少个数,使得他们之间两两相差不超过5。

思路

官方题解是尺取法。

说说我的做法吧,跑出来比标程快一点(雾

先排序,然后开一个数组 b b b记录当前位置连续向右取,满足条件的情况下能取到的最大下标。

如下图所示:

下标i012345
数组a1210121517
数组b114555

如果已知 b [ i ] b[i] b[i],那么求 b [ i + 1 ] b[i + 1] b[i+1]的时候直接从 a [ b [ i − 1 ] ] a[b[i - 1]] a[b[i1]]开始找,会快很多。

最后遍历一遍数组 b ​ b​ b,最大的就是答案。

AC代码
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<vector>
#include<set>
#include<string>
#include<sstream>
#include<cctype>
#include<map>
#include<stack>
#include<queue>
#include<list>
#include<cstdlib>
#include<ctime>
using namespace std;
typedef long long ll;
const double PI = atan(1.0)*4;
const int INF = 0x7ffffff;
const ll MOD = 1000000007;
const int maxn = 200010;
				//i0 1 2  3  4  5
int a[maxn];	// 1 2 10 12 15 17
int b[maxn];	// 1 1 4  5  5  5

int main()
{
//	freopen("input.txt", "r", stdin);
//  freopen("output.txt", "w", stdout);
	int n, ans = 0, j;
	scanf("%d", &n);
	for(int i = 0; i < n; i++)
		scanf("%d", &a[i]);
	sort(a, a + n);
	b[n - 1] = n - 1;
	for(j = 1; j < n; j++)
		if(a[j] - a[0] > 5)
			break;
	b[0] = j;
	for(int i = 1; i < n; i++)
	{
		for(j = b[i - 1]; j < n; j++)
		{
			if(a[j] - a[i] > 5)
				break;
		}
		b[i] = j;
	}
	for(int i = 0; i < n; i++)
	{
		if(b[i] - i > ans)
			ans = b[i] - i;
	}
	printf("%d\n", ans);
	return 0;
}

附上官方题解:

#include <bits/stdc++.h>

using namespace std;

int main() {
#ifdef _DEBUG
	freopen("input.txt", "r", stdin);
//	freopen("output.txt", "w", stdout);
#endif
	
	int n;
	cin >> n;
	vector<int> a(n);
	for (int i = 0; i < n; ++i) {
		cin >> a[i];
	}
	sort(a.begin(), a.end());
	int ans = 0;
	int j = 0;
	for (int i = 0; i < n; ++i) {
		while (j < n && a[j] - a[i] <= 5) {
			++j;
			ans = max(ans, j - i);
		}
	}
	
	cout << ans << endl;
	
	return 0;
}
### Codeforces Problem 1332C Explanation The provided references pertain specifically to problem 742B on Codeforces rather than problem 1332C. For an accurate understanding and solution approach for problem 1332C, it's essential to refer directly to its description and constraints. However, based on general knowledge regarding competitive programming problems found on platforms like Codeforces: Problem 1332C typically involves algorithmic challenges that require efficient data structures or algorithms such as dynamic programming, graph theory, greedy algorithms, etc., depending upon the specific nature of the task described within this particular question[^6]. To provide a detailed explanation or demonstration concerning **Codeforces problem 1332C**, one would need direct access to the exact statement associated with this challenge since different tasks demand tailored strategies addressing their unique requirements. For obtaining precise details about problem 1332C including any sample inputs/outputs along with explanations or solutions, visiting the official Codeforces website and navigating to contest number 1332 followed by examining section C is recommended. ```python # Example pseudo-code structure often seen in solving competitive coding questions. def solve_problem_1332C(input_data): # Placeholder function body; actual logic depends heavily on the specifics of problem 1332C. processed_result = process_input(input_data) final_answer = compute_solution(processed_result) return final_answer input_example = "Example Input" print(solve_problem_1332C(input_example)) ```
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