uva10622 Perfect P-th Powers

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<cstdlib>
 4 #include<algorithm>
 5 #include<iostream>
 6 
 7 using namespace std;
 8 
 9 void setIO(const string& s) {
10     freopen((s + ".in").c_str(), "r", stdin);
11     freopen((s + ".out").c_str(), "w", stdout);
12 }
13 template<typename Q> Q read(Q& x) {
14     static char c, f;
15     for(f = 0; c = getchar(), !isdigit(c); ) if(c == ‘-‘) f = 1;
16     for(x = 0; isdigit(c); c = getchar()) x = x * 10 + c - ‘0‘;
17     if(f) x = -x;
18     return x;
19 }
20 template<typename Q> Q read() {
21     static Q x; read(x); return x;
22 }
23 
24 typedef long long LL;
25 
26 LL qpow(LL a, LL b, LL Lim = ~0ull >> 1) {
27     for(LL c = 1; ; a *= a) {
28         if(b & 1) c *= a;
29         if(!(b >>= 1)) return c;
30         if(c > Lim || a > Lim) return -1;
31     }
32 }
33 
34 bool exist(LL x, LL p) {
35     int l = 0, r = ~0u >> 1;
36     while(l <= r) {
37         int mid = l + (r - l) / 2;
38         LL res = qpow(mid, p, x);
39         if(res == x) return 1;
40         else if(res == -1 || res > x) r = mid - 1;
41         else l = mid + 1;
42     }
43     return 0;
44 }
45 
46 int solve(LL n) {
47     if(n == 1) return 1;
48     int sign = 1;
49     if(n < 0) sign = -1, n = -n;
50     for(int p = 31; p >= 2; p -= (sign > 0 ? 1 : 2)) {
51         if(exist(n, p)) return p;
52     }
53     return 1;
54 }
55 
56 int main() {
57 #ifdef DEBUG
58     freopen("in.txt", "r", stdin);
59     freopen("out.txt", "w", stdout);
60 #endif
61     int n;
62     while(read(n)) {
63         printf("%d\n", solve(n));
64     }
65     
66     return 0;
67 }