시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 54 15 14 43.750%

문제

x에 x를 30번 곱하면 x31이 된다.

x2 = x × x, x3 = x2 × x, x4 = x3 × x, ..., x31 = x30 × x

만약, 결과를 제곱할 수 있다면, 8번만에 x31을 구할 수 있다.

x2 = x × x, x3 = x2 × x, x6 = x3 × x3, x7 = x6 × x, x14 = x7 × x7, x15 = x14 × x, x30 = x15 × x15, x31 = x30 × x

이전에 나온 계산 결과를 곱하는 방법도 같이 사용한다면 x31은 7번만에 구할 수 있다.

x2 = x × x, x4 = x2 × x2, x8 = x4 × x4, x10 = x8 × x2, x20 = x10 × x10, x30 = x20 × x10, x31 = x30 × x

위의 방법이 곱셈만으로 x31을 구하는 가장 효율적인 방법이다.

만약 나눗셈을 사용할 수 있다면, 연산의 수를 더 줄일 수 있다. x31을 5번의 곱셈과 1번의 나눗셈으로 구할 수 있다.

x2 = x × x, x4 = x2 × x2, x8 = x4 × x4, x16 = x8 × x8, x32 = x16 × x16, x31 = x32 ÷ x

이 방법은 나눗셈이 곱셈만큼 빠를 때 x31을 계산하는 가장 효율적인 방법이다.

x로 시작해서 xn을 만드는데 드는 연산 회수의 최솟값을 구하는 프로그램을 작성하시오. 문제에서 설명한 곱셈과 나눗셈만 사용할 수 있다. 연산의 결과는 항상 x의 양의 제곱수 이어야 한다. 즉, x-3은 나오면 안 된다.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스는 한 줄로 구성되어 있고, 정수 n이 주어진다. n은 양의 정수이며, 1000보다 작거나 같다.

출력

각각의 테스트 케이스에 대해서, 한 줄에 하나씩 xn을 만드는데 필요한 곱셈과 나눗셈의 최소 회수를 출력한다.

예제 입력 1

8
1
31
70
91
473
512
811
953

예제 출력 1

0
6
8
9
11
9
13
12
[{"problem_id":"3910","problem_lang":"0","title":"\uac70\ub4ed\uc81c\uacf1 \uacc4\uc0b0","description":"<p>\r\n\tx\uc5d0 x\ub97c 30\ubc88 \uacf1\ud558\uba74 x<sup>31<\/sup>\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\r\n\tx<sup>2<\/sup> = x &times; x, x<sup>3<\/sup> = x<sup>2<\/sup> &times; x, x<sup>4<\/sup> = x<sup>3<\/sup> &times; x, ..., x<sup>31<\/sup> = x<sup>30<\/sup> &times; x<\/p>\r\n\r\n<p>\r\n\t\ub9cc\uc57d, \uacb0\uacfc\ub97c \uc81c\uacf1\ud560 \uc218 \uc788\ub2e4\uba74, 8\ubc88\ub9cc\uc5d0 x<sup>31<\/sup>\uc744 \uad6c\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\r\n\tx<sup>2<\/sup> = x &times; x, x<sup>3<\/sup> = x<sup>2<\/sup> &times; x, x<sup>6<\/sup> = x<sup>3<\/sup> &times; x<sup>3<\/sup>, x<sup>7<\/sup> = x<sup>6<\/sup> &times; x, x<sup>14<\/sup> = x<sup>7<\/sup> &times; x<sup>7<\/sup>, x<sup>15<\/sup> = x<sup>14<\/sup> &times; x, x<sup>30<\/sup> = x<sup>15<\/sup> &times; x<sup>15<\/sup>, x<sup>31<\/sup> = x<sup>30<\/sup> &times; x<\/p>\r\n\r\n<p>\r\n\t\uc774\uc804\uc5d0 \ub098\uc628 \uacc4\uc0b0 \uacb0\uacfc\ub97c \uacf1\ud558\ub294 \ubc29\ubc95\ub3c4 \uac19\uc774 \uc0ac\uc6a9\ud55c\ub2e4\uba74 x<sup>31<\/sup>\uc740 7\ubc88\ub9cc\uc5d0 \uad6c\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\r\n\tx<sup>2<\/sup> = x &times; x, x<sup>4<\/sup> = x<sup>2<\/sup> &times; x<sup>2<\/sup>, x<sup>8<\/sup> = x<sup>4<\/sup> &times; x<sup>4<\/sup>, x<sup>10<\/sup> = x<sup>8<\/sup> &times; x<sup>2<\/sup>, x<sup>20<\/sup> = x<sup>10<\/sup> &times; x<sup>10<\/sup>, x<sup>30<\/sup> = x<sup>20<\/sup> &times; x<sup>10<\/sup>, x<sup>31<\/sup> = x<sup>30<\/sup> &times; x<\/p>\r\n\r\n<p>\r\n\t\uc704\uc758 \ubc29\ubc95\uc774 \uacf1\uc148\ub9cc\uc73c\ub85c x<sup>31<\/sup>\uc744 \uad6c\ud558\ub294 \uac00\uc7a5 \ud6a8\uc728\uc801\uc778 \ubc29\ubc95\uc774\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ub9cc\uc57d \ub098\ub217\uc148\uc744 \uc0ac\uc6a9\ud560 \uc218 \uc788\ub2e4\uba74, \uc5f0\uc0b0\uc758 \uc218\ub97c \ub354 \uc904\uc77c \uc218 \uc788\ub2e4. x<sup>31<\/sup>\uc744 5\ubc88\uc758 \uacf1\uc148\uacfc 1\ubc88\uc758 \ub098\ub217\uc148\uc73c\ub85c \uad6c\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\r\n\tx<sup>2<\/sup> = x &times; x, x<sup>4<\/sup> = x<sup>2<\/sup> &times; x<sup>2<\/sup>, x<sup>8<\/sup> = x<sup>4<\/sup> &times; x<sup>4<\/sup>, x<sup>16<\/sup> = x<sup>8<\/sup> &times; x<sup>8<\/sup>, x<sup>32<\/sup> = x<sup>16<\/sup> &times; x<sup>16<\/sup>, x<sup>31<\/sup> = x<sup>32&nbsp;<\/sup>&divide; x<\/p>\r\n\r\n<p>\r\n\t\uc774 \ubc29\ubc95\uc740 \ub098\ub217\uc148\uc774 \uacf1\uc148\ub9cc\ud07c \ube60\ub97c \ub54c x<sup>31<\/sup>\uc744 \uacc4\uc0b0\ud558\ub294 \uac00\uc7a5 \ud6a8\uc728\uc801\uc778 \ubc29\ubc95\uc774\ub2e4.<\/p>\r\n\r\n<p>\r\n\tx\ub85c \uc2dc\uc791\ud574\uc11c x<sup>n<\/sup>\uc744 \ub9cc\ub4dc\ub294\ub370 \ub4dc\ub294 \uc5f0\uc0b0 \ud68c\uc218\uc758 \ucd5c\uc19f\uac12\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \ubb38\uc81c\uc5d0\uc11c \uc124\uba85\ud55c \uacf1\uc148\uacfc \ub098\ub217\uc148\ub9cc \uc0ac\uc6a9\ud560 \uc218 \uc788\ub2e4. \uc5f0\uc0b0\uc758 \uacb0\uacfc\ub294 \ud56d\uc0c1 x\uc758 \uc591\uc758 \uc81c\uacf1\uc218 \uc774\uc5b4\uc57c \ud55c\ub2e4. \uc989, x<sup>-3<\/sup>\uc740 \ub098\uc624\uba74 \uc548 \ub41c\ub2e4.<\/p>\r\n","input":"<p>\r\n\t\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ud55c \uc904\ub85c \uad6c\uc131\ub418\uc5b4 \uc788\uace0, \uc815\uc218 n\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. n\uc740 \uc591\uc758 \uc815\uc218\uc774\uba70, 1000\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\ub2e4.<\/p>\r\n","output":"<p>\r\n\t\uac01\uac01\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \ud55c \uc904\uc5d0 \ud558\ub098\uc529 xn\uc744 \ub9cc\ub4dc\ub294\ub370 \ud544\uc694\ud55c \uacf1\uc148\uacfc \ub098\ub217\uc148\uc758 \ucd5c\uc18c \ud68c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3910","problem_lang":"1","title":"Power Calculus","description":"<p>Starting with x and repeatedly multiplying by x, we can compute x<sup>31<\/sup> with thirty multiplications:<\/p>\r\n\r\n<p>x<sup>2<\/sup>&nbsp;= x &times; x, x<sup>3<\/sup>&nbsp;= x<sup>2<\/sup>&nbsp;&times; x, x<sup>4<\/sup>&nbsp;= x<sup>3<\/sup>&nbsp;&times; x, ..., x<sup>31<\/sup>&nbsp;= x<sup>30<\/sup>&nbsp;&times; x<\/p>\r\n\r\n<p>The operation of squaring can appreciably shorten the sequence of multiplications. The following is a way to compute x<sup>31<\/sup> with eight multiplications:<\/p>\r\n\r\n<p>x<sup>2<\/sup>&nbsp;= x &times; x, x<sup>3<\/sup>&nbsp;= x<sup>2<\/sup>&nbsp;&times; x, x<sup>6<\/sup>&nbsp;= x<sup>3<\/sup>&nbsp;&times; x<sup>3<\/sup>, x<sup>7<\/sup>&nbsp;= x<sup>6<\/sup>&nbsp;&times; x, x<sup>14<\/sup>&nbsp;= x<sup>7<\/sup>&nbsp;&times; x<sup>7<\/sup>, x<sup>15<\/sup>&nbsp;= x<sup>14<\/sup>&nbsp;&times; x, x<sup>30<\/sup>&nbsp;= x<sup>15<\/sup>&nbsp;&times; x<sup>15<\/sup>, x<sup>31<\/sup>&nbsp;= x<sup>30<\/sup>&nbsp;&times; x<\/p>\r\n\r\n<p>This is not the shortest sequence of multiplications to compute x<sup>31<\/sup>. There are many ways with only seven multiplications. The following is one of them:<\/p>\r\n\r\n<p>x<sup>2<\/sup>&nbsp;= x &times; x, x<sup>4<\/sup>&nbsp;= x<sup>2<\/sup>&nbsp;&times; x<sup>2<\/sup>, x<sup>8<\/sup>&nbsp;= x<sup>4<\/sup>&nbsp;&times; x<sup>4<\/sup>, x<sup>10<\/sup>&nbsp;= x<sup>8<\/sup>&nbsp;&times; x<sup>2<\/sup>, x<sup>20<\/sup>&nbsp;= x<sup>10<\/sup>&nbsp;&times; x<sup>10<\/sup>, x<sup>30<\/sup>&nbsp;= x<sup>20<\/sup>&nbsp;&times; x<sup>10<\/sup>, x<sup>31<\/sup>&nbsp;= x<sup>30<\/sup>&nbsp;&times; x<\/p>\r\n\r\n<p>There however is no way to compute x<sup>31<\/sup> with fewer multiplications. Thus this is one of the most efficient ways to compute x<sup>31<\/sup> only by multiplications.<\/p>\r\n\r\n<p>If division is also available, we can find a shorter sequence of operations. It is possible to compute x<sup>31<\/sup> with six operations (five multiplications and one division):<\/p>\r\n\r\n<p>x<sup>2<\/sup>&nbsp;= x &times; x, x<sup>4<\/sup>&nbsp;= x<sup>2<\/sup>&nbsp;&times; x<sup>2<\/sup>, x<sup>8<\/sup>&nbsp;= x<sup>4<\/sup>&nbsp;&times; x<sup>4<\/sup>, x<sup>16<\/sup>&nbsp;= x<sup>8<\/sup>&nbsp;&times; x<sup>8<\/sup>, x<sup>32<\/sup>&nbsp;= x<sup>16<\/sup>&nbsp;&times; x<sup>16<\/sup>, x<sup>31<\/sup>&nbsp;= x<sup>32&nbsp;<\/sup>&divide; x<\/p>\r\n\r\n<p>This is one of the most efficient ways to compute x<sup>31<\/sup> if a division is as fast as a multiplication.<\/p>\r\n\r\n<p>Your mission is to write a program to find the least number of operations to compute x<sup>n<\/sup> by multiplication and division starting with x for the given positive integer n. Products and quotients appearing in the sequence of operations should be x to a positive integer&#39;s power. In other words, x<sup>-3<\/sup>, for example, should never appear.<\/p>\r\n","input":"<p>The input is a sequence of one or more lines each containing a single integer n. n is positive and less than or equal to 1000. The end of the input is indicated by a zero.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","output":"<p>Your program should print the least total number of multiplications and divisions required to compute x<sup>n<\/sup> starting with x for the integer n. The numbers should be written each in a separate line without any superfluous characters such as leading or trailing spaces.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]