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详细代码可以fork下Github上leetcode项目,不定期更新。
练习题如下:
此题的难点在于如何解决溢出问题,这里用到数论的一个知识点,没办法只能照葫芦画瓢。
具体利用了欧拉函数,算法如下:
public long f(int b, int i, int mod){
if (i == 0) return 1;
else if (mod == 1) return 0;
else if (fbx[b][i] < 0){
int euler = (int) euler_phi(mod);
return pow(b, f(b, i - 1, euler) + euler, mod);
}
else{
return fbx[b][i] % mod;
}
}
好了,f函数编写完成之后,我们用快速幂来实现pow函数,先打表fbx把能算的算出来。
最后再用一个cache把已经算出的值缓存起来,因为后续输出变动的原因在于n的变化。
代码如下:
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
public class Main{
String INPUT = "./data/judge/201708/P2720.txt";
public static void main(String[] args) throws IOException {
new Main().run();
}
static final int MAX_N = 101;
int[][] fbx = new int[MAX_N][MAX_N];
int[] ten_power = new int[8];
public int power_of(int x, int y){
if (y < 0) return -1;
int res = 1;
while (y > 0){
if ((y & 1) != 0){
res = res * x;
if (res >= ten_power[7] || res <= 0) return -1;
}
y >>= 1;
x = x * x;
}
return res;
}
public void prepare(){
ten_power[0] = 1;
for (int i = 1; i < 8; ++i){
ten_power[i] = ten_power[i - 1] * 10;
}
for (int i = 0; i < MAX_N; ++i) Arrays.fill(fbx[i], -1);
for (int i = 1; i < MAX_N; ++i){
fbx[i][0] = 1;
for (int j = 1; j < MAX_N; ++j){
fbx[i][j] = power_of(i, fbx[i][j - 1]);
}
}
}
int[][] cache = new int[MAX_N][MAX_N];
void solve() {
prepare();
for (int i = 0; i < MAX_N; ++i) Arrays.fill(cache[i], -1);
while (true){
int b = ni();
if (b == 0) break;
int i = ni();
int n = ni();
int ans = 0;
if (cache[b][i] < 0){
if (b == 1){
ans = 1;
}
else ans = (int) f(b, i, ten_power[7]);
cache[b][i] = ans;
}
ans = cache[b][i] % ten_power[n];
StringBuilder sb = new StringBuilder();
for (int j = 0; j < n - String.valueOf(ans).length(); ++j){
sb.append("0");
}
out.println(sb.toString() + ans);
}
}
public long euler_phi(int m){
long res = m;
for (int i = 2; i <= m / i; ++i){
if (m % i == 0){
res = res / i * (i - 1);
for (; m % i == 0; m /= i);
}
}
if (m != 1){
res = res / m * (m - 1);
}
return res;
}
public long f(int b, int i, int mod){
if (i == 0) return 1;
else if (mod == 1) return 0;
else if (fbx[b][i] < 0){
int euler = (int) euler_phi(mod);
return pow(b, f(b, i - 1, euler) + euler, mod);
}
else{
return fbx[b][i] % mod;
}
}
public long pow(long base, long n, long mod){
long res = 1;
while (n > 0){
if ((n & 1) != 0){
res = res * base % mod;
}
n >>= 1;
base = base * base % mod;
}
return res;
}
FastScanner in;
PrintWriter out;
void run() throws IOException {
boolean oj;
try {
oj = ! System.getProperty("user.dir").equals("F:\\java_workspace\\leetcode");
} catch (Exception e) {
oj = System.getProperty("ONLINE_JUDGE") != null;
}
InputStream is = oj ? System.in : new FileInputStream(new File(INPUT));
in = new FastScanner(is);
out = new PrintWriter(System.out);
long s = System.currentTimeMillis();
solve();
out.flush();
if (!oj){
System.out.println("[" + (System.currentTimeMillis() - s) + "ms]");
}
}
public boolean more(){
return in.hasNext();
}
public int ni(){
return in.nextInt();
}
public long nl(){
return in.nextLong();
}
public double nd(){
return in.nextDouble();
}
public String ns(){
return in.nextString();
}
public char nc(){
return in.nextChar();
}
class FastScanner {
BufferedReader br;
StringTokenizer st;
boolean hasNext;
public FastScanner(InputStream is) throws IOException {
br = new BufferedReader(new InputStreamReader(is));
hasNext = true;
}
public String nextToken() {
while (st == null || !st.hasMoreTokens()) {
try {
st = new StringTokenizer(br.readLine());
} catch (Exception e) {
hasNext = false;
return "##";
}
}
return st.nextToken();
}
String next = null;
public boolean hasNext(){
next = nextToken();
return hasNext;
}
public int nextInt() {
if (next == null){
hasNext();
}
String more = next;
next = null;
return Integer.parseInt(more);
}
public long nextLong() {
if (next == null){
hasNext();
}
String more = next;
next = null;
return Long.parseLong(more);
}
public double nextDouble() {
if (next == null){
hasNext();
}
String more = next;
next = null;
return Double.parseDouble(more);
}
public String nextString(){
if (next == null){
hasNext();
}
String more = next;
next = null;
return more;
}
public char nextChar(){
if (next == null){
hasNext();
}
String more = next;
next = null;
return more.charAt(0);
}
}
}