nbut [1223] Friends number 好题，打表法的求每个数的因子和

• [1223] Friends number

• 时间限制: 1000 ms　内存限制: 131072 K
• 问题描述

• Paula and Tai are couple. There are many stories between them. The day Paula left by airplane, Tai send one message to telephone [phone], then, everything is changing… (The story in “the snow queen”).

  
  

  After a long time, Tai tells Paula, the number 220 and 284 is a couple of friends number, as they are special, all divisors of 220’s sum is 284, and all divisors of 284’s sum is 220. Can you find out there are how many couples of friends number less than 10,000. Then, how about 100,000, 200,000 and so on.

  
  

  The task for you is to find out there are how many couples of friends number in given closed interval [a,b]。

  
  

  
  

  
  

  
  

  
  

  
  

  
  

  
  

• 输入
• There are several cases.
  Each test case contains two positive integers a, b(1<= a <= b <=5,000,000).
  Proceed to the end of file.
• 输出
• For each test case, output the number of couples in the given range. The output of one test case occupied exactly one line.
  
• 样例输入

• 1 1001 1000

• 样例输出

• 01

• 提示

• 6 is a number whose sum of all divisors is 6. 6 is not a friend number, these number is called Perfect Number.

• 来源

• 辽宁省赛2010

• 操作

 

这个题目真心好极了，看了一个上午了，用了很多种办法进行打表，都不能打出来，终于再问了山理工的大神之后学会了正确的

打表办法，原理非常类似于素数打表，真的好牛啊，我这种小菜真是佩服极了

 

#include <iostream>#include <cstdlib>#include <cstdio>#include <time.h>#include <queue>#include <cstring>#include <algorithm>/*#include<iostream>#include<cstdio>#include<cstring>#include<cmath>using namespace std;int ans[5000010];int main(){    ans[0] = ans[1] = 1;    memset(ans,0,sizeof(ans));    int i,j;    for(i = 2; i <= 5000000; ++i)    {        ++ans[i];        for(j = i+i; j <= 5000000; j += i)        {            ans[j] += i;        }    }    //for(i=2;i<=1000;i++)    //printf("ans %d \n",ans[i]);    int sum = 0;    for(i = 2; i <= 5000000; ++i)    {        if(ans[i] <= 5000000 && i == ans[ans[i]] && i != ans[i])        {                cout<<min(i,ans[i])<<","<<endl;        }    }    //cout<<"asdfasdfasdfasdfasdfasdf\n";    for(i = 2; i <= 5000000; ++i)    {        if(ans[i] <= 5000000 && i == ans[ans[i]] && i != ans[i])        {            cout<<max(i,ans[i])<<","<<endl;        }    }}*/using namespace std;int l[500] = {220,              220,              1184,              1184,              2620,              2620,              5020,              5020,              6232,              6232,              10744,              10744,              12285,              12285,              17296,              17296,              63020,              66928,              66928,              67095,              69615,              67095,              63020,              79750,              69615,              79750,              100485,              122265,              122368,              122368,              100485,              122265,              141664,              142310,              141664,              142310,              171856,              176272,              171856,              176272,              185368,              196724,              196724,              185368,              280540,              308620,              319550,              356408,              280540,              308620,              356408,              319550,              437456,              437456,              469028,              469028,              503056,              503056,              522405,              522405,              600392,              609928,              624184,              635624,              643336,              643336,              667964,              600392,              609928,              624184,              635624,              726104,              667964,              726104,              802725,              802725,              879712,              898216,              879712,              947835,              898216,              998104,              998104,              1077890,              1077890,              947835,              1154450,              1156870,              1175265,              1185376,              1154450,              1280565,              1185376,              1156870,              1328470,              1280565,              1358595,              1392368,              1175265,              1392368,              1466150,              1468324,              1328470,              1358595,              1511930,              1511930,              1669910,              1466150,              1468324,              1798875,              1798875,              1669910,              2082464,              2082464,              2236570,              2236570,              2652728,              2723792,              2728726,              2739704,              2802416,              2803580,              2723792,              2739704,              2652728,              2802416,              2728726,              3276856,              3606850,              2803580,              3276856,              3786904,              3805264,              3606850,              3805264,              4238984,              4246130,              4259750,              3786904,              4238984,              4259750,              4246130,              -1             };int r[500] ={    284,    284,    1210,    1210,    2924,    2924,    5564,    5564,    6368,    6368,    10856,    10856,    14595,    14595,    18416,    18416,    76084,    66992,    66992,    71145,    87633,    71145,    76084,    88730,    87633,    88730,    124155,    139815,    123152,    123152,    124155,    139815,    153176,    168730,    153176,    168730,    176336,    180848,    176336,    180848,    203432,    202444,    202444,    203432,    365084,    389924,    430402,    399592,    365084,    389924,    399592,    430402,    455344,    455344,    486178,    486178,    514736,    514736,    525915,    525915,    669688,    686072,    691256,    712216,    652664,    652664,    783556,    669688,    686072,    691256,    712216,    796696,    783556,    796696,    863835,    863835,    901424,    980984,    901424,    1125765,    980984,    1043096,    1043096,    1099390,    1099390,    1125765,    1189150,    1292570,    1438983,    1286744,    1189150,    1340235,    1286744,    1292570,    1483850,    1340235,    1486845,    1464592,    1438983,    1464592,    1747930,    1749212,    1483850,    1486845,    1598470,    1598470,    2062570,    1747930,    1749212,    1870245,    1870245,    2062570,    2090656,    2090656,    2429030,    2429030,    2941672,    2874064,    3077354,    2928136,    2947216,    3716164,    2874064,    2928136,    2941672,    2947216,    3077354,    3721544,    3892670,    3716164,    3721544,    4300136,    4006736,    3892670,    4006736,    4314616,    4488910,    4445050,    4300136,    4314616,    4445050,    4488910,    -1};struct N{    int x,y;} st[11000];bool cmp(N s1,N s2){    return s1.x < s2.x;}int main(){    int i,L,R,ans;    for(i = 0; l[i] != -1; ++i)    {        st[i].x = l[i];        st[i].y = r[i];    }    int Top = i;    sort(st,st+Top,cmp);        while(scanf("%d %d",&L,&R) != EOF)        {            ans = 0;            for(i = 0; i < Top; ++i)            {                if(L <= st[i].x && st[i].y <= R && st[i].x != st[i-1].x && st[i].y != st[i-1].y)                {                    ans++;                }            }            printf("%d\n",ans);        }        return 0;}