数学+DP Codeforces Round #304 (Div. 2) D. Soldier and Number Game

题目传送门

 /*
    题意：这题就是求b+1到a的因子个数和。
    数学+DP：a[i]保存i的最小因子，dp[i] = dp[i/a[i]] +１;再来一个前缀和
 */
 /************************************************
 Author        :Running_Time
 Created Time  :2015-8-1 14:08:34
 File Name     :B.cpp
  *************************************************/

 #include <cstdio>
 #include <algorithm>
 #include <iostream>
 #include <sstream>
 #include <cstring>
 #include <cmath>
 #include <string>
 #include <vector>
 #include <queue>
 #include <deque>
 #include <stack>
 #include <list>
 #include <map>
 #include <set>
 #include <bitset>
 #include <cstdlib>
 #include <ctime>
 using namespace std;

 typedef long long ll;
 const int MAXN = 5e6 + ;
 const int INF = 0x3f3f3f3f;
 const int MOD = 1e9 + ;
 int cnt[MAXN];
 int a[MAXN];
 bool is_prime[MAXN];
 int prime[MAXN/];
 ll dp[MAXN];
 ll sum[MAXN];

 void solve(void)    {
     memset (is_prime, true, sizeof (is_prime));
     for (int i=; i<=; ++i)  a[i] = i;
     int tot = ;
     for (int i=; i<=; ++i)  {
         if (is_prime[i])    prime[++tot] = i;
         for (int j=; j<=tot && i*prime[j]<=; ++j)   {
             int tmp = i * prime[j];
             is_prime[tmp] = false;
             if (a[tmp] > prime[j])  a[tmp] = prime[j];
             if (i % prime[j] == )  break;
         }
     }
     dp[] = ;
     for (int i=; i<=; ++i)  {
         dp[i] = dp[i/a[i]] + ;
     }
     for (int i=; i<=; ++i)  {
         sum[i] = sum[i-] + dp[i];
     }
 }

 int main(void)    {       //Codeforces Round #304 (Div. 2) D. Soldier and Number Game
     solve ();
     int T;  scanf ("%d", &T);
     while (T--) {
         int l, r;   scanf ("%d%d", &r, &l);
         if (l == r) {
             puts (""); continue;
         }
         printf ("%I64d\n", sum[r] - sum[l]);
     }

     return ;
 }