UVa 1363 (数论 数列求和) Joseph's Problem

 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 }

 1 // UVa1363 Joseph‘s Problem
 2 // Rujia Liu
 3 #include<iostream>
 4 #include<algorithm>
 5 using namespace std;
 6 
 7 // 首项为a，公差为-d，除了首项之外还有n项
 8 // 末项为a-n*d，平均数为(2*a-n*d)/2
 9 long long sum(int a, int d, int n) {
10   return (long long)(2*a-n*d)*(n+1)/2;
11 }
12 
13 int main() {
14   int n, k;
15   while(cin >> n >> k) {
16     int i = 1;
17     long long ans = 0;
18     while(i <= n) {
19       int q = k % i, p = k / i;
20       int cnt = n - i; // 最多还有n - i项
21       if(p > 0) cnt = min(cnt, q / p); 
22       ans += sum(q, p, cnt);
23       i += cnt + 1;
24     }
25     cout << ans << "\n";
26   }
27   return 0;
28 }