2013
11-13

# Persistent Bits

WhatNext Software creates sequence generators that they hope will produce fairly random sequences of 16-bit unsigned integers in the range 0–65535. In general a sequence is specified by integers A, B, C, and S, where 1 ≤ A < 32768, 0 ≤ B < 65536, 2 ≤ C < 65536, and 0 ≤ S < C. S is the first element (the seed) of the sequence, and each later element is generated from the previous element. If X is an element of the sequence, then the next element is

(A * X + B) % C

where ‘%’ is the remainder or modulus operation. Although every element of the sequence will be a 16-bit unsigned integer less than 65536, the intermediate result A * X + B may be larger, so calculations should be done with a 32-bit int rather than a 16-bit short to ensure accurate results.

Some values of the parameters produce better sequences than others. The most embarrassing sequences to WhatNext Software are ones that never change one or more bits. A bit that never changes throughout the sequence is persistent. Ideally, a sequence will have no persistent bits. Your job is to test a sequence and determine which bits are persistent.

For example, a particularly bad choice is A = 2, B = 5, C = 18, and S = 3. It produces the sequence 3, (2*3+5)%18 = 11, (2*11+5)%18 = 9, (2*9+5)%18 = 5, (2*5+5)%18 = 15, (2*15+5)%18 = 17, then (2*17+5)%18 = 3 again, and we’re back at the beginning. So the sequence repeats the the same six values over and over:

 Decimal 16-Bit Binary 3 0000000000000011 11 0000000000001011 9 0000000000001001 5 0000000000000101 15 0000000000001111 17 0000000000010001 overall 00000000000????1

The last line of the table indicates which bit positions are always 0, always 1, or take on both values in the sequence. Note that 12 of the 16 bits are persistent. (Good random sequences will have no persistent bits, but the converse is not necessarily true. For example, the sequence defined by A = 1, B = 1, C = 64000, and S = 0 has no persistent bits, but it’s also not random: it just counts from 0 to 63999 before repeating.)  Note that a sequence does not need to return to the seed: with A = 2, B = 0, C = 16, and S = 2, the sequence goes 2, 4, 8, 0, 0, 0, ….

There are from one to sixteen datasets followed by a line containing only 0. Each dataset is a line containing decimal integer values for A, B, C, and S, separated by single blanks.

There is one line of output for each data set, each containing 16 characters, either ’1′, ’0′, or ‘?’ for each of the 16 bits in order, with the most significant bit first, with ’1′ indicating the corresponding bit is always 1, ’0′ meaning the corresponding bit is always 0, and ‘?’ indicating the bit takes on values of both 0 and 1 in the sequence.

2 5 18 3
1 1 64000 0
2 0 16 2
256 85 32768 21845
1 4097 32776 248
0

00000000000????1
????????????????
000000000000???0
0101010101010101
0???000011111???

import java.util.Arrays;
import java.util.Scanner;

public class Main {

int a;
int b;
int c;
int s;
int x;
char[] result;
int flg;
boolean[] dup;

public Main() {
Scanner scan = new Scanner(System.in);
while ((a = scan.nextInt()) != 0) {
b = scan.nextInt();
c = scan.nextInt();
s = scan.nextInt();
result = new char[16];
Arrays.fill(result, '0');
initFlg(Integer.toBinaryString(s));
dup = new boolean[c];
dup[s] = true;
x = (a * s + b) % c;
while (!dup[x]) {
dup[x] = true;
if (setFlg(Integer.toBinaryString(x))) {
break;
}
x = (a * x + b) % c;
}
System.out.println(result);
}
}

public void initFlg(String str) {
for (int i = 15, k = str.length() - 1; k >= 0; i--, k--) {
if (str.charAt(k) == '1') {
result[i] = '1';
}
}
}

public boolean setFlg(String str) {
flg = 0;
for (int i = 15, k = str.length() - 1; k >= 0; i--, k--) {
if (result[i] == '?') {
flg++;
if (flg == 16) {
return true;
}
continue;
} else {
if (str.charAt(k) != result[i]) {
result[i] = '?';
}
}
}
return false;
}

public static void main(String[] args) {
new Main();
}

}

1. 第23行：
hash = -1是否应该改成hash[s ] = -1

因为是要把从字符串s的start位到当前位在hash中重置

修改提交后能accept，但是不修改居然也能accept

2. 第一句可以忽略不计了吧。从第二句开始分析，说明这个花色下的所有牌都会在其它里面出现，那么还剩下♠️和♦️。第三句，可以排除2和7，因为在两种花色里有。现在是第四句，因为♠️还剩下多个，只有是♦️B才能知道答案。

3. 在方法1里面：

//遍历所有的边，计算入度
for(int i=0; i<V; i++)
{
degree = 0;