uva 10940 Throwing cards away II

我打印出了1 - 100

n = 1, ans = 1

n = 2 ans = 2

n = 3 ans = 2

n = 4 ans = 4

n = 5 ans = 2

n = 6 ans = 4

n = 7 ans = 6

n = 8 ans = 8

n = 9 ans = 2

n = 10 ans = 4

n = 11 ans = 6

n = 12 ans = 8

n = 13 ans = 10

n = 14 ans = 12

n = 15 ans = 14

n = 16 ans = 16

n = 17 ans = 2

n = 18 ans = 4

n = 19 ans = 6

n = 20 ans = 8

n = 21 ans = 10

n = 22 ans = 12

n = 23 ans = 14

n = 24 ans = 16

n = 25 ans = 18

n = 26 ans = 20

n = 27 ans = 22

n = 28 ans = 24

n = 29 ans = 26

n = 30 ans = 28

n = 31 ans = 30

n = 32 ans = 32

n = 33 ans = 2

n = 34 ans = 4

n = 35 ans = 6

n = 36 ans = 8

n = 37 ans = 10

n = 38 ans = 12

n = 39 ans = 14

n = 40 ans = 16

n = 41 ans = 18

n = 42 ans = 20

n = 43 ans = 22

n = 44 ans = 24

n = 45 ans = 26

n = 46 ans = 28

n = 47 ans = 30

n = 48 ans = 32

n = 49 ans = 34

n = 50 ans = 36

n = 51 ans = 38

n = 52 ans = 40

n = 53 ans = 42

n = 54 ans = 44

n = 55 ans = 46

n = 56 ans = 48

n = 57 ans = 50

n = 58 ans = 52

n = 59 ans = 54

n = 60 ans = 56

n = 61 ans = 58

n = 62 ans = 60

n = 63 ans = 62

n = 64 ans = 64

n = 65 ans = 2

n = 66 ans = 4

n = 67 ans = 6

n = 68 ans = 8

n = 69 ans = 10

n = 70 ans = 12

n = 71 ans = 14

n = 72 ans = 16

n = 73 ans = 18

n = 74 ans = 20

n = 75 ans = 22

n = 76 ans = 24

n = 77 ans = 26

n = 78 ans = 28

n = 79 ans = 30

n = 80 ans = 32

n = 81 ans = 34

n = 82 ans = 36

n = 83 ans = 38

n = 84 ans = 40

n = 85 ans = 42

n = 86 ans = 44

n = 87 ans = 46

n = 88 ans = 48

n = 89 ans = 50

n = 90 ans = 52

n = 91 ans = 54

n = 92 ans = 56

n = 93 ans = 58

n = 94 ans = 60

n = 95 ans = 62

n = 96 ans = 64

n = 97 ans = 66

n = 98 ans = 68

n = 99 ans = 70

n = 100 ans = 72

首先发现有重复，于是把所有的ans 第一次出现的 n 和 ans 单独列出来。

n = 1 ans = 1

n = 2, ans = 2

n = 7 ans = 6

n = 8, ans = 8;

n = 13, ans = 10;

n = 14, ans = 12;

n = 15, ans = 14;

n = 16 ans = 16;

n = 25 ans = 18

n = 26 ans = 20

n = 27 ans = 22

n = 28 ans = 24

n = 29 ans = 26

n = 30 ans = 28

n = 31 ans = 30

n = 32 ans = 32

于是规律便得出来了， 2 ^ (i -1) < n <= 2^(i) , 那么 ans 便为 (n - 2 ^ (i-1)) * 2;

#include <cstdio>
#include <algorithm>
using namespace std;

int a[21];

int main(){
    int n;
    a[0] = 1;
    for (int i = 1; i <= 20; i++)a[i] = 2 * a[i - 1];
    while (scanf("%d", &n) == 1 && n){
          if (n == 1)puts("1");
          else {
               for (int i = 0; i < 20; i++){
                   if (n > a[i] && n <= a[i+1]){
                         printf("%d\n", 2*(n - a[i]));
                         break; 
                   }
               }
          }
    } 
    
    return 0;
}