Bouncy numbers
Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468.
Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420.
We shall call a positive integer that is neither increasing nor decreasing a “bouncy” number; for example, 155349.
Clearly there cannot be any bouncy numbers below one-hundred, but just over half of the numbers below one-thousand (525) are bouncy. In fact, the least number for which the proportion of bouncy numbers first reaches 50% is 538.
Surprisingly, bouncy numbers become more and more common and by the time we reach 21780 the proportion of bouncy numbers is equal to 90%.
Find the least number for which the proportion of bouncy numbers is exactly 99%.
彈跳數
從左往右，如果每一位數字都大於等於其左邊的數字，這樣的數被稱爲上升數，比如134468。
同樣地，如果每一位數字都大於等於其右邊的數字，這樣的數被稱爲下降數，比如66420。
如果一個正整數既不是上升數也不是下降數，我們就稱之爲“彈跳”數，比如155349。
顯然不存在小於一百的彈跳數，而在小於一千的數中有略超過一半（525）的彈跳數。事實上，使得彈跳數的比例恰好達到50%的最小數是538。
令人驚奇的是，彈跳數將變得越來越普遍，到21780時，彈跳數的比例恰好等於90%。
找出使得彈跳數的比例恰好爲99%的最小數。
package projecteuler;
import junit.framework.TestCase;
public class Prj112 extends TestCase {
public void testBouncyNumbers() {
int n = Integer.MAX_VALUE;
int count = 0;
for (int i = 1; i <= n; i++) {
if (isBouncyNumber(i)) {
count++;
}
if (i * 99 == 100 * count) {
System.out.println("i==" + i);
System.out.println("count=" + count);
return;
}
}
System.out.println("count=" + (n - count));
}
boolean isBouncyNumber(int val) {
int[] arr = int2Arr(val);
boolean isDesc = true;
boolean isAsec = true;
for (int i = 1; i < arr.length; i++) {
if (arr[i - 1] < arr[i]) {
isDesc = false;
} else if (arr[i - 1] > arr[i]) {
isAsec = false;
}
if (!isDesc && !isAsec) {
return true;
}
}
return false;
}
private int[] int2Arr(int val) {
String str = Integer.toString(val);
int[] ret = new int[str.length()];
for (int i = 0; i < str.length(); i++) {
ret[i] = Integer.parseInt(String.valueOf(str.charAt(i)));
}
return ret;
}
}