BZOJ1257: [CQOI2007] and the number of I - divisible block

The meaning of problems

求 $ \ sum _ {i = 1} ^ nk \ mod \ i $ ($ 1 \ leq n, k \ leq 10 ^ 9 $).

analysis

Such a large data range $ O (n) $ complexity also word within ah

The modulo sense, $ k \ mod \ i = k - \ left \ lfloor \ frac {k} {i} \ right \ rfloor * i $,

Therefore it is divisible by the block, note classification and discuss the relationship between $ k $ $ $ n-of.

#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
int n, k;

ll solve()
{
    ll ret = 1LL * n * k;
    if(k <= n)   //需要分类讨论
    {
        for(int i = 1,j;i <= k;i = j+1)
        {
            j = k / (k / i);
            
            ret -= 1LL * (i+j) * (j-i+1) / 2 * (k / i);
        }
    }
    else
    {
        for(int i = 1,j;i <= n;i = j+1)
        {
            j = min(k / (k / i), n);
            ret -= 1LL * (i+j) * (j-i+1) / 2 * (k / i);
        }
    }

    return ret;
}

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

 

 

 

Reference Links: https://zhuanlan.zhihu.com/p/77687419