Problem J
Triple-Free Binary Strings
Input: Standard Input
Output: Standard Output
A binary string consists of ones and zeros. Given a binary string T, if there is no binary string S such that SSS (concatenate three copies of S together) is a substring of T, we say T is triple-free.
A pattern consists of ones, zeros and asterisks, where an asterisk(*) can be replaced by either one or zero. For example, the pattern 0**1 contains strings 0001, 0011, 0101, 0111, but not 1001 or 0000.
Given a pattern P, how many triple-free binary strings does it contain?
Input
Each line of the input represents a test case, which contains the length of pattern, n(0<n<31), and the pattern P. There can be maximum 35 test cases.
The input terminates when n=0.
Output
For each test case, print the case number and the answer, shown below.
Sample Input Output for Sample Input
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题意:给定一个串,*可以代表0,1有多少字串,没有3个连续相同的串。
思路:深搜加位运算,每次判断当前串如果有重复3个
#include <stdio.h>
#include <string.h>
const int N = 35;
int n;
char str[N];
bool judge(int state, int len) {
int m = (1<<len) - 1;
int s = (state&m);
state = ((state&(~m))>>len);
int ss = (state&m);
state = ((state&(~m))>>len);
if (s == ss && ss == state) return true;
return false;
}
int dfs(int state, int len) {
int ans = 0, s = state;
for (int i = 0; i <= len - 3; i ++) {
if ((len - i) % 3 == 0 && judge(s, (len - i) / 3)) return 0;
s = ((s&(~1))>>1);
}
if (len == n) return 1;
if (str[len] == '0')
ans += dfs(state, len + 1);
else if (str[len] == '1')
ans += dfs(state^(1<<len), len + 1);
else {
ans += dfs(state, len + 1);
ans += dfs(state^(1<<len), len + 1);
}
return ans;
}
int main() {
int cas = 0;
while (~scanf("%d",&n) && n) {
scanf("%s", str);
printf("Case %d: %d\n", ++cas, dfs(0, 0));
}
return 0;
}
字串就返回,然后数字可以用二进制数表示。
代码: