URAL 2037 Richness of binary words （回文子串，找规律）

Richness of binary words

题目链接：

http://acm.hust.edu.cn/vjudge/contest/126823#problem/B

Description

For each integer i from 1 to n, you must print a string s i of length n consisting of letters ‘a’ and ‘b’ only. The string s i must contain exactly i distinct palindrome substrings. Two substrings are considered distinct if they are different as strings.

Input

The input contains one integer n (1 ≤ n ≤ 2000).

Output

You must print n lines. If for some i, the answer exists, print it in the form “ i : s i” where s i is one of possible strings. Otherwise, print “ i : NO”.

Sample Input

input output

4

1 : NO

2 : NO

3 : NO

4 : aaaa

##题意：

要求输出n个长度为n的字符串(只能放a或b)：
要求Si中不同回文子串的个数恰为i.


##题解：

本质就是找出一种构造方式使得回文子串个数不会再增加.
参考2015-ICPC合肥现场赛H题：
http://blog.****.net/snowy_smile/article/details/49870109
http://blog.****.net/keshuai19940722/article/details/49839359


##代码：
``` cpp
#include
#include
#include
#include
#include
#include
#include
#include
#include
#define LL long long
#define eps 1e-8
#define maxn 210000
#define mod 100000007
#define inf 0x3f3f3f3f
#define IN freopen("in.txt","r",stdin);
using namespace std;

int n;

int main(int argc, char const *argv[])

{

//IN;

while(scanf("%d", &n) != EOF)
{
    if(n == 1) {
        printf("1 : a\n");
        continue;
    }
    if(n == 2) {
        printf("1 : NO\n");
        printf("2 : ab\n");
        continue;
    }

    if(n < 8) {
        for(int i=1; i<n; i++)
            printf("%d : NO\n", i);
        printf("%d : ", n);
        for(int i=1; i<=n; i++)
            putchar('a');
        printf("\n");
        continue;
    }

    if(n == 8) {
        for(int i=1; i<7; i++)
            printf("%d : NO\n", i);
        printf("7 : aababbaa\n");
        printf("8 : ");
        for(int i=1; i<=n; i++)
            putchar('a');
        printf("\n");
        continue;
    }

    char str[] = "abaabb";
    for(int i=1; i<=7; i++)
        printf("%d : NO\n", i);
    for(int i=8; i<=n; i++) {
        printf("%d : ", i);
        for(int j=1,cur=0; j<=n; j++) {
            if(j <= i-8) putchar('a');
            else {
                if(cur == 6) cur = 0;
                putchar(str[cur++]);
            }
        }
        printf("\n");
    }
}

return 0;

}