UVA 11246 - K-Multiple Free set(数论推理)

UVA 11246 - K-Multiple Free set

题目链接

题意:一个{1..n}的集合,求一个子集合,使得元素个数最多,并且不存在有两个元素x1 * k = x2,求出最多的元素个数是多少

思路:推理一下,

一开始n个

先要删除k倍的,删除为{k, 2k, 3k, 4k, 5k, 6k...},会删掉多余的k^2,因此在加回k^2倍的数

然后现在集合中会出现情况的只有k^2的倍数,因此对k^2倍的数字看成一个新集合反复做这个操作即可,因此最后答案为n - n / k + n / (k ^ 2) - n / (k ^ 3) + n / (k ^ 4)...

代码:

#include <stdio.h>
#include <string.h>

int t, n, k;

int solve(int n, int k) {
    int sign = 1, ans = 0;
    while (n) {
	ans += sign * n;
	n /= k;
	sign = - sign;
    }
    return ans;
}

int main() {
    scanf("%d", &t);
    while (t--) {
	scanf("%d%d", &n, &k);
	printf("%d\n", solve(n, k));
    }
    return 0;
}

UVA 11246 - K-Multiple Free set(数论推理)

时间: 2024-11-10 00:16:08

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