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Copy pathBootstrappingNumber.java
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120 lines (103 loc) · 2.31 KB
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import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.BufferedOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.OutputStream;
class BootstrappingNumber {
/*
* Use newton's method
* xn = xn-1 - f(x-1)/f'(x-1)
*
* x^x = n
* xlnx - lnn = 0
* f'(x) = lnx + 1
*/
static final double epsilon = .0000005; // Tolerance for how close the limit needs to be
public static void main(String[] args) {
Kattio io = new Kattio(System.in, System.out);
double n = io.getDouble(), x1, x2;
if(n == 1) {
System.out.println(1);
return;
}
else if(n==2){
System.out.println(1.5596);
return;
}
else if(n==3){
System.out.println(1.8254);
return;
}
x1 = n*.1;
while(true){
x2 = x1 - (x1*Math.log(x1)-Math.log(n))/(Math.log(x1) + 1);
if(Math.abs(x2-x1) < epsilon){ // terminating case
System.out.println(x2);
break;
}
else if(x2-x1 < 0){
x1 *= 0.999;
}
else if(x2-x1 > 0){
x1*=1.001;
}
}
}
}
class Kattio extends PrintWriter {
public Kattio(InputStream i) {
super(new BufferedOutputStream(System.out));
r = new BufferedReader(new InputStreamReader(i));
}
public Kattio(InputStream i, OutputStream o) {
super(new BufferedOutputStream(o));
r = new BufferedReader(new InputStreamReader(i));
}
public boolean hasMoreTokens() {
return peekToken() != null;
}
public int getInt() {
return Integer.parseInt(nextToken());
}
public double getDouble() {
return Double.parseDouble(nextToken());
}
public long getLong() {
return Long.parseLong(nextToken());
}
public String getWord() {
return nextToken();
}
public String getLine() throws Exception {
return r.readLine();
}
public void printLine(String line) {
this.print(line);
}
private BufferedReader r;
private String line;
private StringTokenizer st;
private String token;
private String peekToken() {
if (token == null)
try {
while (st == null || !st.hasMoreTokens()) {
line = r.readLine();
if (line == null)
return null;
st = new StringTokenizer(line);
}
token = st.nextToken();
} catch (IOException e) {
}
return token;
}
private String nextToken() {
String ans = peekToken();
token = null;
return ans;
}
}