HDU 1099 Lottery (数学问题模拟)

Lottery

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 2420 Accepted Submission(s): 1097



[align=left]Problem Description[/align]
Eddy's company publishes a kind of lottery.This set of lottery which are numbered 1 to n, and a set of one of each is required for a prize .With one number per lottery, how many lottery on average are required to make a complete set
of n coupons?

[align=left]Input[/align]
Input consists of a sequence of lines each containing a single positive integer n, 1<=n<=22, giving the size of the set of coupons.

[align=left]Output[/align]
For each input line, output the average number of lottery required to collect the complete set of n coupons. If the answer is an integer number, output the number. If the answer is not integer, then output the integer part of the
answer followed by a space and then by the proper fraction in the format shown below. The fractional part should be irreducible. There should be no trailing spaces in any line of ouput.

[align=left]Sample Input[/align]

2
5
17

[align=left]Sample Output[/align]

3
5
11 --
12
340463
58 ------
720720

有题意可推出n/n+n/(n-1)+n/(n-2)+……n/2+n/1

AC代码：

#include <stdio.h>
#define ll __int64
//author:XXYY
ll gcd(ll a,ll b)
{
if(b==0)
return a;
return gcd(b,a%b);
}
int main(){
ll n,i,m,z,len1,len2,x,n1,n2,y;
while(~scanf("%I64d",&n)){
m=0;
z=1;
for(i=n;i>0;i--){//通分
m=n*z+m*i;
z*=i;
x=gcd(m,z);
m/=x;
z/=x;
}
if(m%z){
y=m/z;
m=m%z;
n1=y;
len1=len2=0;
while(n1){
len1++;
n1/=10;
}
n2=z;
while(n2){
len2++;
n2/=10;
}
for(i=0;i<=len1;i++)
printf(" ");
printf("%I64d\n",m);
printf("%I64d ",y);
for(i=0;i<len2;i++)
printf("-");
printf("\n");
for(i=0;i<=len1;i++)
printf(" ");
printf("%I64d\n",z);
}
else
printf("%I64d\n",m/z);
}
return 0;
}

看到这么小的范围，暴力打表也是可以的：

#include<stdio.h>
int main(){
int n;
while(~scanf("%d",&n)){
switch(n){
case 1:
printf("1\n");
break;
case 2:
printf("3\n");
break;
case 3:
printf("  1\n5 -\n  2\n");
break;
case 4:
printf("  1\n8 -\n  3\n");
break;
case 5:
printf("   5\n11 --\n   12\n");
break;
case 6:
printf("   7\n14 --\n   10\n");
break;
case 7:
printf("   3\n18 --\n   20\n");
break;
case 8:
printf("   26\n21 --\n   35\n");
break;
case 9:
printf("   129\n25 ---\n   280\n");
break;
case 10:
printf("   73\n29 ---\n   252\n");
break;
case 11:
printf("   551\n33 ----\n   2520\n");
break;
case 12:
printf("   551\n37 ----\n   2310\n");
break;
case 13:
printf("   9473\n41 -----\n   27720\n");
break;
case 14:
printf("   13433\n45 -----\n   25740\n");
break;
case 15:
printf("   18581\n49 -----\n   24024\n");
break;
case 16:
printf("   4129\n54 -----\n   45045\n");
break;
case 17:
printf("   340463\n58 ------\n   720720\n");
break;
case 18:
printf("   620743\n62 ------\n   680680\n");
break;
case 19:
printf("   1662439\n67 -------\n   4084080\n");
break;
case 20:
printf("   3704479\n71 -------\n   3879876\n");
break;
case 21:
printf("   408335\n76 ------\n   739024\n");
break;
case 22:
printf("   46533\n81 ------\n   235144\n");
break;
}
}
return 0;
}