兩數相除,判斷小數位是否有限位
You are given several queries. Each query consists of three integers p, q and b. You need to answer whether the result of p/q in notation with base b
is a finite fraction.
A fraction in notation with base b
is finite if it contains finite number of numerals after the decimal point. It is also possible that a fraction has zero numerals after the decimal point.
The first line contains a single integer n
(1≤n≤105
) — the number of queries.
Next n
lines contain queries, one per line. Each line contains three integers p, q, and b (0≤p≤1018, 1≤q≤1018, 2≤b≤1018). All numbers are given in notation with base 10
.
OutputFor each question, in a separate line, print Finite if the fraction is finite and Infinite otherwise.
2Output Copy
6 12 10
4 3 10
FiniteInput Copy
Infinite
4Output Copy
1 1 2
9 36 2
4 12 3
3 5 4
FiniteNote
Finite
Finite
Infinite
612=12=0,510
43=1,(3)10
936=14=0,012
412=13=0,13
題意 : 給兩個數,以及一個所要求的進制,詢問是否在此進制下,相除後是否為有限位小數
思路分析 : 比賽的時候想了一個模擬,不過沒有去寫,旁邊的大佬一直再和說,會超時,會超時,然後賽後才知道是用這樣的,比如 10進制下,判斷兩數是否整除,只需要讓除數已知除以 2 或者 5,當可以除到 1 的時候,代表是可以整除的,如果是換成任意進制下的一個數,則需要去除當前的數和 b進制的約數。
代碼示例 :
#define ll long long ll gcd(ll a, ll b){ return b == 0?a:gcd(b, a%b); } int main() { //freopen("in.txt", "r", stdin); //freopen("out.txt", "w", stdout); ll t; ll p, q, b; cin >> t; while(t--){ scanf("%lld%lld%lld", &p, &q, &b); ll g = gcd(p, q); ll x = q / g; ll f = gcd(b, x); while(1){ if (f == 1) break; while(x%f == 0) x /= f; f = gcd(b, x); } if (x == 1) printf("Finite\n"); else printf("Infinite\n"); } return 0; }
兩數相除,判斷小數位是否有限位