最大约数和

题目大意：

选若干个正整数，和不小于S，使每个数的因数（不包括本身）之和最大

样例输入

11

样例输出

9

数据范围限制

对于30%的数据， S<=10；

对于100%的数据， S <=1000。

提示

样例说明:

取数字4和6，可以得到最大值(1 + 2) + (1 + 2 + 3) = 9。

解题思路：

这道题先求出每个数的因数和（我是打表的），然后用01背包判断没见物品选和不选的最优

打表代码：

#include<cstdio>
#include<iostream>
using namespace std;
int a[1005]; 
int main()
{freopen("dabiao.txt","w",stdout);//输进一个文件for (int i=1;i<=1000;i++)//每一个数for (int j=1;j<i;j++)//小于他的所有数if (i%j==0)//判断是否为因数a[i]+=j;//累加printf("{0");//方便写常量for (int i=1;i<=1000;i++)printf(",%d",a[i]);//输出printf("};");
}

解题代码：

#include<cstdio>
#include<iostream>
using namespace std;
int n,f[1005];
const int dj[1001]={0,0,1,1,3,1,6,1,7,4,8,1,16,1,10,9,15,1,21,1,22,11,14,1,36,6,16,13,28,1,42,1,31,15,20,13,55,1,22,17,50,1,54,1,40,33,26,1,76,8,43,21,46,1,66,17,64,23,32,1,108,1,34,41,63,19,78,1,58,27,74,1,123,1,40,49,64,19,90,1,106,40,44,1,140,23,46,33,92,1,144,21,76,35,50,25,156,1,73,57,117,1,114,1,106,87,56,1,172,1,106,41,136,1,126,29,94,65,62,25,240,12,64,45,100,31,186,1,127,47,122,1,204,27,70,105,134,1,150,1,196,51,74,25,259,35,76,81,118,1,222,1,148,81,134,37,236,1,82,57,218,31,201,1,130,123,86,1,312,14,154,89,136,1,186,73,196,63,92,1,366,1,154,65,176,43,198,29,148,131,170,1,316,1,100,141,203,1,270,1,265,71,104,37,300,47,106,105,226,31,366,1,166,75,110,49,384,39,112,77,284,31,234,1,280,178,116,1,332,1,202,153,218,1,312,53,184,83,194,1,504,1,157,121,190,97,258,33,232,87,218,1,476,35,130,177,255,1,270,45,328,129,134,1,456,59,214,93,208,1,450,1,286,175,140,97,396,1,142,137,440,1,294,1,220,195,218,49,531,18,250,101,226,1,390,65,274,183,152,37,568,51,154,105,316,67,396,1,364,107,266,1,528,1,160,309,244,1,330,41,442,111,254,37,523,109,166,113,302,55,534,1,256,161,170,73,656,1,211,117,416,43,438,57,316,231,176,1,492,1,394,209,404,1,366,77,274,219,182,1,810,20,184,169,420,79,378,1,376,177,314,61,524,1,274,249,344,43,582,1,460,131,194,1,636,191,196,185,298,1,618,41,463,135,200,85,696,1,202,241,561,1,414,45,310,321,314,49,672,1,346,141,316,67,522,89,466,143,302,1,924,1,214,201,386,133,438,69,328,243,362,1,808,1,334,285,334,43,450,1,640,300,314,1,620,95,226,153,568,1,759,53,346,155,230,217,744,1,232,261,548,1,690,1,466,303,236,1,806,75,394,161,428,55,486,145,532,225,242,1,1032,51,244,285,447,103,606,1,442,167,536,1,684,47,346,441,496,79,510,1,592,171,254,1,1056,107,358,225,388,1,786,81,511,287,260,109,716,59,394,177,740,1,648,1,400,467,266,49,960,24,442,249,588,55,546,113,484,183,272,145,1140,1,274,185,590,115,798,1,418,257,566,49,888,87,280,357,424,1,690,57,928,303,284,1,780,119,286,401,512,1,870,1,604,195,434,169,1075,1,343,197,680,91,594,65,526,507,296,1,1008,51,490,201,586,1,846,269,454,203,410,1,1260,1,454,281,460,193,618,1,652,351,506,61,1026,1,310,393,824,1,630,1,724,339,314,97,1112,156,316,333,478,55,1242,1,568,215,320,133,876,161,442,297,890,1,654,1,700,411,434,1,1167,71,652,373,496,1,666,137,646,305,494,1,1356,1,334,345,596,295,816,53,508,227,554,73,1344,1,340,565,605,1,690,105,940,231,470,1,1136,143,514,233,676,67,1038,1,526,555,350,145,1104,59,352,237,1036,1,978,57,820,447,356,109,972,1,586,329,638,55,1014,293,544,243,362,1,1698,111,421,245,550,205,870,1,952,364,602,61,1004,1,370,633,776,79,900,1,856,379,554,1,1176,155,376,345,764,115,1122,1,736,255,506,157,1484,1,382,393,1040,1,774,117,580,639,386,73,1276,1,958,261,586,1,942,217,694,439,392,61,1572,83,514,417,983,163,798,1,598,267,650,121,1548,75,400,501,604,1,1122,65,1153,369,404,85,1100,347,538,273,722,1,1368,1,868,275,554,169,1416,63,412,637,944,1,834,1,736,663,614,1,1356,1,682,281,946,193,846,173,844,443,422,1,2040,30,424,285,640,253,1026,217,826,287,824,61,1164,1,634,705,764,1,1158,1,988,483,434,1,1656,179,436,361,924,91,1290,81,778,401,566,373,1196,1,442,297,1352,1,1341,1,880,555,446,1,1392,135,730,561,676,67,906,185,1144,447,452,61,1921,71,610,505,806,187,918,1,688,417,1106,1,1568,95,460,573,694,139,1242,1,1240,311,464,85,1764,253,466,425,962,1,1374,209,706,315,470,361,1794,1,694,317,1076,1,954,65,916,975,638,1,1292,87,910,321,1208,1,1152,197,724,483,482,145,2088,32,634,441,730,199,1338,1,1027,471,794,1,1576,147,490,761,946,1,990,101,1414,449,494,1,1536,203,634,549,972,67,1818,1,1024,335,734,205,1356,1,502,521,1340};
int main()//上为常量
{scanf("%d",&n);for (int i=1;i<=n;++i)//01背包for (int j=n;j>=i;--j)f[j]=max(f[j],f[j-i]+dj[i]);//求最优的printf("%d",f[n]);//输出return 0;
}