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Algorithm_Python_2021/algorithm/dynamic1463.cpp at master · SoniaComp/Algorithm_Python_2021 · GitHub
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#
include
<
iostream
>
int
d[
1000001
];
using
namespace
std
;
//
1로 만들기
//
N을 1로 만드는 **최소** 연산 횟수
//
3으로 나누는 것이 빠르므로, 2보다 3을 먼저 나눈다. -- 그리디 알고리즘. 예외.
//
** 점화식의 정의를 세워보자 **
//
D[N] : N을 작게 만들 수 있는 방법
//
큰문제 단계와 나머지 다시 전체 문제로 나누면 좋다.
//
N -> N/3 (1번) 과 N/3 -> 1 (D[N/3])
//
N -> N/2 (1번) 과 N/2 -> 1 (D[N/2])
//
N -> N-1 (1번) 과 N-1 -> 1 (D[N-1])
//
D[N] = min(D[N/3], D[N/2], D[N-1])
//
D[1] = 0 // 1->1
//
--------- TOP DOWN ----------//
//
n에서부터 내려가면서.. 재귀호출
int
go
(
int
n)
{
if
(n ==
1
)
return
0
;
if
(d[n] >
0
)
return
d[n];
//
memoization 기억하고 있는 건 그대로 사용
//
D[n-1] : **아무때나** 가능함으로, 아무때나 를 먼저 해서, **비교의 기준**으로 만들어준다.
d[n] =
go
(n -
1
) +
1
;
//
D[n/2]
if
(n %
2
==
0
)
{
int
temp =
go
(n /
2
) +
1
;
if
(d[n] > temp)
d[n] = temp;
}
//
D[n/3]
if
(n %
3
==
0
)
{
int
temp =
go
(n /
3
) +
1
;
if
(d[n] > temp)
d[n] = temp;
}
return
d[n];
}
int
main
()
{
int
n;
cin >> n;
//
cout << go(n) << '\n';
//
--------- BOTTOM UP ----------//
d[
1
] =
0
;
for
(
int
i =
2
; i <= n; i++)
{
d[i] = d[i -
1
] +
1
;
if
(i %
2
==
0
&& d[i] > d[i /
2
] +
1
)
{
d[i] = d[i /
2
] +
1
;
}
if
(i %
3
==
0
&& d[i] > d[i /
3
] +
1
)
{
d[i] = d[i /
3
] +
1
;
}
}
cout << d[n] <<
'
\n
'
;
return
0
;
}
//
시간 복잡도
//
함수의 호출 횟수 * 함수의 시간 복잡도
//
- 문제의 개수 - -문제 1개 푸는데 필요한 시간-
//
점화식: D[N] = min(D[N/3], D[N/2], D[N-1])
//
N * O(1)
//
따라서 시간 복잡도: O(n)
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