ZOJ 1633 Big String

ZOJ 1633 Big String

Big String

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Time Limit: 2 Seconds Memory Limit: 65536 KB

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We will construct an infinitely long string from two short strings: A = "^__^" (four characters), and B = "T.T" (three characters). Repeat the following steps:

Concatenate A after B to obtain a new string C. For example, if A = "^__^" and B = "T.T", then C = BA = "T.T^__^".Let A = B, B = C -- as the example above A = "T.T", B = "T.T^__^". Your task is to find out the n-th character of this infinite string.


Input

The input contains multiple test cases, each contains only one integer N (1 <= N <= 2^63 - 1). Proceed to the end of file.


Output

For each test case, print one character on each line, which is the N-th (index begins with 1) character of this infinite string.


Sample Input

1
2
4
8


Sample Output

T
.
^
T

題意：開始時有兩個字符串，A = "^__^" (four characters),  B = "T.T" (three characters)，然後重復執行C=BA，A=B,B = C，問第n個字符是什麼。

分析：因為最終的字符串是從前往後遞推出來的，所以再求解時，我們可以把這個過程逆過去，直到字符串的長度不超過7，輸出即可。

#include
#include
using namespace std;
typedef long long LL;
LL a[95];  //保存字符串的長度
int main()
{
    string C = "T.T^__^";
    a[0] = 4;
    a[1] = 3;
    int i;
    for(i = 2; i < 90; i++)
        a[i] = a[i-1] + a[i-2];
    LL n;
    while(cin >> n)
    {
        while(n > 7)
        {
            int pos = lower_bound(a, a+89, n) - a;
            n -= a[pos-1];
        }
        cout << C[n-1] << endl;
    }
    return 0;
}