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

 1 /*
 2    题意：这题就是求b+1到a的因子个数和。
 3    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
 4 */
 5 /************************************************
 6 Author        :Running_Time
 7 Created Time  :2015-8-1 14:08:34
 8 File Name     :B.cpp
 9  *************************************************/
10 
11 #include <cstdio>
12 #include <algorithm>
13 #include <iostream>
14 #include <sstream>
15 #include <cstring>
16 #include <cmath>
17 #include <string>
18 #include <vector>
19 #include <queue>
20 #include <deque>
21 #include <stack>
22 #include <list>
23 #include <map>
24 #include <set>
25 #include <bitset>
26 #include <cstdlib>
27 #include <ctime>
28 using namespace std;
29 
30 typedef long long ll;
31 const int MAXN = 5e6 + 10;
32 const int INF = 0x3f3f3f3f;
33 const int MOD = 1e9 + 7;
34 int cnt[MAXN];
35 int a[MAXN];
36 bool is_prime[MAXN];
37 int prime[MAXN/10];
38 ll dp[MAXN];
39 ll sum[MAXN];
40 
41 void solve(void)    {
42     memset (is_prime, true, sizeof (is_prime));
43     for (int i=2; i<=5000000; ++i)  a[i] = i;
44     int tot = 0;
45     for (int i=2; i<=5000000; ++i)  {
46         if (is_prime[i])    prime[++tot] = i;
47         for (int j=1; j<=tot && i*prime[j]<=5000000; ++j)   {
48             int tmp = i * prime[j];
49             is_prime[tmp] = false;
50             if (a[tmp] > prime[j])  a[tmp] = prime[j];
51             if (i % prime[j] == 0)  break;
52         }
53     }
54     dp[2] = 1;
55     for (int i=3; i<=5000000; ++i)  {
56         dp[i] = dp[i/a[i]] + 1;
57     }
58     for (int i=2; i<=5000000; ++i)  {
59         sum[i] = sum[i-1] + dp[i];
60     }
61 }
62 
63 int main(void)    {       //Codeforces Round #304 (Div. 2) D. Soldier and Number Game
64     solve ();
65     int T;  scanf ("%d", &T);
66     while (T--) {
67         int l, r;   scanf ("%d%d", &r, &l);
68         if (l == r) {
69             puts ("0"); continue;
70         }
71         printf ("%I64d\n", sum[r] - sum[l]);
72     }
73 
74     return 0;
75 }