BestCoder Round #54 (div.2) 1003 Geometric Progression

题目传送门

题意：判断是否是等比数列

分析：高精度 + 条件：a[i] * a[i+2] == a[i+1] * a[i+1]。特殊情况：0 0 0 0 0是Yes的，1 2 0 9 2是No的

代码：

/************************************************
* Author        :Running_Time
* Created Time  :2015-9-5 20:06:46
* File Name     :C.cpp
 ************************************************/

#include <cstdio>
#include <algorithm>
#include <iostream>
#include <sstream>
#include <cstring>
#include <cmath>
#include <string>
#include <vector>
#include <queue>
#include <deque>
#include <stack>
#include <list>
#include <map>
#include <set>
#include <bitset>
#include <cstdlib>
#include <ctime>
using namespace std;

#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1
typedef long long ll;
const int N = 1e2 + 10;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
const int numlen = 2005; // 需要的位数
const int numbit = 4;   // 数组一位表示的整数
const int addbit = 10000;//进位数
const int maxn = numlen/numbit + 10;   // 数组要开的位数

int max(int a, int b) { return a>b?a:b; }
struct bign {
    int len, s[numlen];
    bign() {
        memset(s, 0, sizeof(s));
        len = 1;
    }
    bign(int num) { *this = num; }
    bign(const char *num) { *this = num; }
    bign operator = (const int num) {
        char s[numlen];
        sprintf(s, "%d", num);
        *this = s;
        return *this;
    }
    bign operator = (const char *num) {
        int clen = strlen(num);
        while(clen > 1 && num[0] == '0') num++, clen--;
        len = 0;
        for(int i = clen-1;i >= 0;i -= numbit) {
            int top = min(numbit, i+1), mul = 1;
            s[len] = 0;
            for(int j = 0;j < top; j++) {
                s[len] += (num[i-j]-'0')*mul;
                mul *= 10;
            }
            len++;
        }
        deal();
        return *this;
    }

    void deal() {
        while(len > 1 && !s[len-1]) len--;
    }

    bign operator + (const bign &a) const {
        bign ret;
        ret.len = 0;
        int top = max(len, a.len) , add = 0;
        for(int i = 0;add || i < top; i++) {
            int now = add;
            if(i < len) now += s[i];
            if(i < a.len)   now += a.s[i];
            ret.s[ret.len++] = now%addbit;
            add = now/addbit;
        }
        return ret;
    }
    bign operator - (const bign &a) const {
        bign ret;
        ret.len = 0;
        int cal = 0;
        for(int i = 0;i < len; i++) {
            int now = s[i] - cal;
            if(i < a.len)   now -= a.s[i];
            if(now >= 0)    cal = 0;
            else {
                cal = 1; now += addbit;
            }
            ret.s[ret.len++] = now;
        }
        ret.deal();
        return ret;
    }
    bign operator * (const bign &a) const {
        bign ret;
        ret.len = len + a.len;
        for(int i = 0;i < len; i++) {
            int pre = 0;
            for(int j = 0;j < a.len; j++) {
                int now = s[i]*a.s[j] + pre;
                pre = 0;
                ret.s[i+j] += now;
                if(ret.s[i+j] >= addbit) {
                    pre = ret.s[i+j]/addbit;
                    ret.s[i+j] -= pre*addbit;
                }
            }
            if(pre) ret.s[i+a.len] = pre;
        }
        ret.deal();
        return ret;
    }

    //乘以小数，直接乘快点  ***********注意计算过程可能会爆int
    bign operator * (const int num) {
        bign ret;
        ret.len = 0;
        int bb = 0;
        for(int i = 0;i < len; i++) {
            int now = bb + s[i]*num;
            ret.s[ret.len++] = now%addbit;
            bb = now/addbit;
        }
        while(bb) {
            ret.s[ret.len++] = bb % addbit;
            bb /= addbit;
        }
        ret.deal();
        return ret;
    }
    // 除以一个小整数     ***********注意计算过程可能会爆int
    bign operator / (const int a) const {
        bign ret;
        ret.len = len;
        int pre = 0;
        for(int i = len-1;i >= 0; i--) {
            ret.s[i] = (s[i] + pre*addbit)/a;
            pre = s[i] + pre*addbit - a*ret.s[i];
        }
        ret.deal();
        return ret;
    }

    bign operator % (const int a) const {
        bign b = *this / a;
        return *this - b*a;
    }

    bign operator += (const bign &a) { *this = *this + a; return *this; }
    bign operator -= (const bign &a) { *this = *this - a; return *this; }
    bign operator *= (const bign &a) { *this = *this * a; return *this; }
    bign operator /= (const int a) { *this = *this / a; return *this; }
    bign operator %= (const int a) { *this = *this % a; return *this; }

    bool operator < (const bign &a) const {
        if(len != a.len)    return len < a.len;
        for(int i = len-1;i >= 0; i--) if(s[i] != a.s[i])
            return s[i] < a.s[i];
        return false;
    }
    bool operator > (const bign &a) const  { return a < *this; }
    bool operator <= (const bign &a) const { return !(*this > a); }
    bool operator >= (const bign &a) const { return !(*this < a); }
    bool operator == (const bign &a) const { return !(*this > a || *this < a); }
    bool operator != (const bign &a) const { return *this > a || *this < a; }

    void print() {
        printf("%d", s[len-1]);
        for(int i = len-2;i >= 0; i--) {
            printf("%04d", s[i]);
        }
        puts("");
    }

    string str() const {
        string ret = "";
        for(int i = 0;i < len; i++) ret = char(s[i] + '0') + ret;
        return ret;
    }
};
istream& operator >> (istream &in, bign &x) {
    string s;
    in >> s;
    x = s.c_str();
    return in;
}
ostream& operator << (ostream &out, const bign &x) {
    printf("%d", x.s[x.len-1]);
    for(int i = x.len-2;i >= 0; i--)    printf("%04d", x.s[i]);
    return out;
}
bign a[N];

int main(void)    {
	int T;	scanf ("%d", &T);
	while (T--)	{
		int n;	scanf ("%d", &n);
		for (int i=1; i<=n; ++i)	cin >> a[i];
		bool flag = true;	int zero = 0;
		for (int i=1; i<=n; ++i)	{
			if (a[i] == 0)	{
				zero++;
			}
		}
		if (n == 1 || zero == n)	{
			puts ("Yes");	continue;
		}
		if (zero > 0)	{
			puts ("No");	continue;
		}
		else	{
            for (int i=1; i<=n-2; ++i)	{
				if (a[i] * a[i+2] != a[i+1] * a[i+1])	{
					flag = false;	break;
				}
            }
		}

		puts (flag ? "Yes" : "No");
	}

    return 0;
}