Aggregated Counting-----hdu5439(2015 长春网络赛 找规律)

#include<stdio.h>
#include<string.h>
#include<iostream>
#include<math.h>
#include<stdlib.h>
#include<algorithm>
using namespace std;
#define N 500000
#define mod 1000000007

__int64 a[N], b[N], ans[N];

void Init()
{
    int i;
    a[1] = b[1] = 1;
    a[2] = 2;
    b[2] = 3;
    for(i=1; i<N; i++)
    {
        a[i] = lower_bound(b+1, b+i, i) - b;
        b[i] = b[i-1] + a[i];
    }
    ans[1] = 1;
    for(i=2; i<N; i++)
    {
        ans[i] = ans[i-1] + (b[i]-b[i-1])*(b[i-1]+1 + b[i]) / 2 % mod * i % mod;
    }
}

int main()
{
    int T, n, i;
    Init();
    scanf("%d", &T);
    while(T--)
    {
        scanf("%d", &n);
        int pos = lower_bound(b+1, b+N+1, n) - b;
        __int64 Ans = ans[pos-1];
        for(i=b[pos-1]+1; i<=n; i++)
            Ans = (Ans + (__int64)i*pos) % mod;
        printf("%I64d\n", Ans);
    }
    return 0;
}

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