题意:

给出n, k,求UVa 1363 (数论 数列求和) Joseph's Problem

分析:

假设UVa 1363 (数论 数列求和) Joseph's Problem,则k mod (i+1) = k - (i+1)*p = k - i*p - p = k mod i - p

则对于某个区间,i∈[l, r],k/i的整数部分p相同,则其余数成等差数列,公差为-p

 

然后我想到了做莫比乌斯反演时候有个分块加速,在区间[i, n / (n / i)],n/i的整数部分相同,于是有了这份代码。

 1 #include <cstdio>
 2 #include <algorithm>
 3 using namespace std;
 4 typedef long long LL;
 5 
 6 int main()
 7 {
 8     LL n, k;
 9     while(scanf("%lld%lld", &n, &k) == 2)
10     {
11         LL ans = 0;
12         LL i, j, r = min(n, k);
13         for(i = 1; i <= r; i = j + 1)
14         {
15             j = k / (k / i);
16             if(j > r) j = r;
17 
18             LL d = -k / i;
19             LL l = j - i + 1;
20             LL a1 = k % i;
21             ans += (LL) (a1*l + l*(l-1)/2*d);
22         }
23         if(n > k)
24             ans += (LL) (n-k) * k;
25 
26         printf("%lld\n", ans);
27     }
28 
29     return 0;
30 }
代码君

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