CF1463F-Max Correct Set
题目:
题目描述:
Let’s call the set of positive integers $ S $ correct if the following two conditions are met:
- $ S \subseteq {1, 2, \dots, n} $ ;
- if $ a \in S $ and $ b \in S $ , then $ |a-b| \neq x $ and $ |a-b| \neq y $ .
For the given values $ n $ , $ x $ , and $ y $ , you have to find the maximum size of the correct set.
输入格式:
A single line contains three integers $ n $ , $ x $ and $ y $ ( $ 1 \le n \le 10^9 $ ; $ 1 \le x, y \le 22 $ ).
输出格式:
Print one integer — the maximum size of the correct set.
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| // Problem: CF1463F Max Correct Set
// Contest: Luogu
// URL: https://www.luogu.com.cn/problem/CF1463F
// Memory Limit: 250 MB
// Time Limit: 4000 ms
// Author: Ybw051114
//
// Powered by CP Editor (https://cpeditor.org)
#include "ybwhead/ios.h"
const int ImaxnF = 1e9;
const int maxn = 22;
int dp[2][1 << maxn];
int val[2 * maxn];
int main()
{
int n, x, y;
yin >> n >> x >> y;
int k = x + y;
int m = max(x, y);
int FULL = (1 << m) - 1;
for (int i = 0; i < k; ++i)
val[i] = n / k + (i < n % k);
for (int mask = 0; mask < (1 << m); ++mask)
dp[0][mask] = -ImaxnF;
dp[0][0] = 0;
for (int i = 0; i < k; ++i)
{
for (int mask = 0; mask < (1 << m); ++mask)
dp[1][mask] = -ImaxnF;
for (int mask = 0; mask < (1 << m); ++mask)
{
if (dp[0][mask] == -ImaxnF)
continue;
int nmask = (mask << 1) & FULL;
dp[1][nmask] = max(dp[1][nmask], dp[0][mask]);
if (((mask >> (x - 1)) & 1) | ((mask >> (y - 1)) & 1))
continue;
nmask |= 1;
dp[1][nmask] = max(dp[1][nmask], dp[0][mask] + val[i]);
}
swap(dp[0], dp[1]);
}
int ans = 0;
for (int mask = 0; mask < (1 << m); ++mask)
ans = max(ans, dp[0][mask]);
yout << ans << endl;
}
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