Problem D - Continuous Fractions

A simple continuous fraction has the form:

where the a_i's are integer numbers.

The previous continuous fraction could be noted as [a₁, a₂,..., a_n]. It is not difficult to show that any rational number , with integers p > q > 0, can be represented in a unique way by a simple continuous fraction with n terms, such that = [a₁, a₂,..., a_n-1, 1], where n and the a_i's are positive natural numbers.

Your task is to find and print the simple continuous fraction that corresponds to a given rational number.

Input 

Input will consist of a series of cases, each one in a line. A line describing a case contains p and q, two integer numbers separated by a space, with 10²⁰ > p > q > 0.

The end of the input is indicated by a line containing 0 0.

Output 

Cases must be analyzed in the order that are read from the input. Output for each case will consist of several lines. The first line indicates the case number, starting at 1, using the format:

Case i:

replacing i by the corresponding case number. The second line displays the input data in the form p / q.

The remaining lines must contain the continuous fraction corresponding to the rational number, , specified in the given input line. The continuous fraction must be printed accordingly to the following rules:

• Horizontal bars are formed by sequences of dashes `-'.
• The width of each horizontal bar is exactly equal to the width of the denominator under it.
• Blank characters should be printed using periods `.'
• The number on a fraction numerator must be printed center justified. That is, the number of spaces at either side must be same, if possible; in other case, one more space must be added at the right side.

Sample Input 

75 34
65 60
0 0

Sample Output 

Case 1:
75 / 34
..........1......
2.+.-------------
............1....
....4.+.---------
..............1..
........1.+.-----
................1
............5.+.-
................1
Case 2:
65 / 60
......1...
1.+.------
.........1
....11.+.-
.........1

---

如果不是大數的話，這題其實很好寫。
說他是大數，其實也不然，因為數字只是比 unsigned long long 大了十倍。

但是用兩個 long long 去合併成 10^20 還是會有 overflow 的可能。

因此還是用了不算好的做法去計算，仍然是一位一位的大數記錄方式。

這裡只有實做 -*/%，這四種運算。


// 0.044 s Rank 1
#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
#define NLEN 25
class UINT70 {
    public:
        int d[NLEN], length, ZF;
        UINT70(const char *s) {
            int i, j;
            memset(d, 0, sizeof(d));
            for(i = 0; s[i]; i++)
                d[i] = s[i]-'0';
            length = i;
            for(j = i-1, i = 0; j > i; j--, i++)
                swap(d[i], d[j]);
            if(length == 1 && d[0] == 0)
                ZF = 1;
            else
                ZF = 0;
        }
        UINT70() {
            length = 1;
            memset(d, 0, sizeof(d));
            ZF = 1;
        }
        UINT70 operator-(const UINT70 &y) {
            int i;
            UINT70 ans;
            memcpy(ans.d, d, sizeof(d));
            for(i = 0; i < y.length; i++)
                ans.d[i] -= y.d[i];
            ans.carry();
            return ans;
        }
        UINT70 operator*(const UINT70 &y) {
            int i, j;
            UINT70 ans;
            for(i = 0; i < length; i++) {
                for(j = 0; j < y.length; j++) {
                    if(i+j < NLEN)
                    ans.d[i+j] += (this->d[i])*y.d[j];
                }
            }
            ans.carry();
            return ans;
        }
        UINT70 operator/(const UINT70 &y) {
            int i, j, x[NLEN];
            UINT70 ans;
            memcpy(x, d, sizeof(d));
            for(i = length-y.length; i >= 0; i--) {
                while(check(x, y.d, y.length, i)) {
                    ans.d[i]++;
                    for(j = 0; j < y.length+1; j++) {
                        x[i+j] -= y.d[j];
                        if(x[i+j] < 0) {
                            x[i+j+1]--;
                            x[i+j] += 10;
                        }
                    }
                }
            }
            ans.carry();
            return ans;
        }
        UINT70 operator%(const UINT70 &y) {
            int i, j, x[NLEN];
            UINT70 ans;
            memcpy(x, d, sizeof(d));
            for(i = length-y.length; i >= 0; i--) {
                while(check(x, y.d, y.length, i)) {
                    for(j = 0; j < y.length+1; j++) {
                        x[i+j] -= y.d[j];
                        if(x[i+j] < 0) {
                            x[i+j+1]--;
                            x[i+j] += 10;
                        }
                    }
                }
            }
            for(i = NLEN-1; i >= 0; i--)
                ans.d[i] = x[i];
            ans.carry();
            return ans;
        }
        void c_str(char *p) {
            int i;
            for(i = length-1; i >= 0; i--)
                *p++ = d[i]+'0';
            *p = '\0';
        }
    private:
        void carry() {
            int i;
            for(i = 0; i < NLEN-1; i++) {
                while(d[i] < 0)
                    d[i+1]--, d[i] += 10;
                d[i+1] += d[i]/10;
                d[i] %= 10;
            }
            for(i = NLEN-1; i > 0 && d[i] == 0; i--);
            length = i+1;
            if(length == 1 && d[0] == 0)
                ZF = 1;
            else
                ZF = 0;
        }
        int check(const int x[], const int y[], int ly, int shift) {
            int i;
            for(i = ly; i >= 0; i--) {
                if(x[i+shift] < y[i])
                    return 0;
                if(x[i+shift] > y[i])
                    return 1;
            }
            return 1;
        }
};
char g[1024][1024];
char buf[30];
int N, M;
int build(UINT70 p, UINT70 q, int x, int y) {
    UINT70 pdivq, pmodq;
    pdivq = p/q;
    pmodq = p%q;
    if(pmodq.ZF) {
        UINT70 one("1");
        pdivq = pdivq - one;
    }
    pdivq.c_str(buf);
    sprintf(g[x+1]+y, "%s.+.", buf);
    int ty = y;
    while(g[x+1][ty] != '\0')   ty++;
    g[x+1][ty] = '.';
    int i, len;
    if(!pmodq.ZF) {
        len = build(q, pmodq, x+2, ty);
        for(i = 0; i < len; i++)
            g[x+1][i+ty] = '-';
        g[x][ty+(len-1)/2] = '1';
        len = len + ty-y;
    } else {
        len = 1;
        g[x][ty] = '1';
        g[x+1][ty] = '-';
        g[x+2][ty] = '1';
        N = x+3;
        len = len + ty-y;
    }
    return len;
}
int main() {
    long long p, q;
    int cases = 0;
    char s1[150], s2[150];
    while(scanf("%s %s", s1, s2) == 2) {
        UINT70 p(s1), q(s2);
        if(p.ZF)  break;
        memset(g, '.', sizeof(g));
        printf("Case %d:\n", ++cases);
        printf("%s / %s\n", s1, s2);
        M = build(p, q, 0, 0);
        int i, j;
        for(i = 0; i < N; i++) {
            g[i][M] = '\0';
            puts(g[i]);
        }
    }
    return 0;
}
/*
99999999999999999999 99999999999999999998
*/