Sawtooth
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 2272 Accepted Submission(s): 834
● One straight line can divide a plane into two regions.
● Two lines can divide a plane into at most four regions.
● Three lines can divide a plane into at most seven regions.
● And so on...
Now we have some figure constructed with two parallel rays in the same direction, joined by two straight segments. It looks like a character “M”. You are given N such “M”s. What is the maximum number of regions that these “M”s can divide a plane ?
Each case contains one single non-negative integer, indicating number of “M”s. (0 ≤ N ≤ 1012)
f(n) = 8 * n * n - 7 * n + 1
import java.io.BufferedInputStream;
import java.io.BufferedOutputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;
public class Main {
public static void main(String[] args) {
Scanner in = new Scanner(new BufferedInputStream(System.in));
PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
int T, kase;
T = in.nextInt();
kase = 0;
BigInteger n, ans;
while (T-- != 0) {
n = in.nextBigInteger();
ans = BigInteger.valueOf(8).multiply(n).multiply(n).subtract(BigInteger.valueOf(7).multiply(n))
.add(BigInteger.ONE);
out.printf("Case #%d: ", ++kase);
out.println(ans.toString());
}
in.close();
out.close();
}
}