CodeForces 442 div2 記錄

這次CF感覺挺簡單的，但是我思路不夠寬

A. Fake NP

Tavak and Seyyed are good friends. Seyyed is very funny and he told Tavak to solve the following problem instead of longest-path.

You are given l and r. For all integers from l to r, inclusive, we wrote down all of their integer divisors except 1. Find the integer that we wrote down the maximum number of times.

Solve the problem to show that it's not a NP problem.

Input
The first line contains two integers l and r (2 ≤ l ≤ r ≤ 109).

Output
Print single integer, the integer that appears maximum number of times in the divisors.

If there are multiple answers, print any of them.

這題簽到題，如果 l==r ，那麼出現次數最多爲1，如果 l!=r 那麼出現次數最多的爲0

int main() {
    int l, r;
    cin >> l >> r;
    if (l == r) {
        cout << l << endl;
    }
    else {
        cout << 2 << endl;
    }

    return 0;
}

---

B. 3-palindrome
time limit per test1 second
memory limit per test256 megabytes
inputstandard input
outputstandard output
In the beginning of the new year Keivan decided to reverse his name. He doesn't like palindromes, so he changed Naviek to Navick.

He is too selfish, so for a given n he wants to obtain a string of n characters, each of which is either 'a', 'b' or 'c', with no palindromes of length 3 appearing in the string as a substring. For example, the strings "abc" and "abca" suit him, while the string "aba" doesn't. He also want the number of letters 'c' in his string to be as little as possible.

Input
The first line contains single integer n (1 ≤ n ≤ 2·105) — the length of the string.

Output
Print the string that satisfies all the constraints.

If there are multiple answers, print any of them.

這題題目要求輸出滿足條件的字符串，C經可能小，那麼只用不斷的輸出aa，bb，即可

int main(){

    int n;
    cin >> n;
    string fuck = "aabb";
    for(int i = 0;i < n; i++){
        putchar(fuck[i%4]);
    }
    puts("");

    return 0;
}

---

C. Find Amir
time limit per test1 second
memory limit per test256 megabytes
inputstandard input
outputstandard output
A few years ago Sajjad left his school and register to another one due to security reasons. Now he wishes to find Amir, one of his schoolmates and good friends.

There are n schools numerated from 1 to n. One can travel between each pair of them, to do so, he needs to buy a ticket. The ticker between schools i and j costs  and can be used multiple times. Help Sajjad to find the minimum cost he needs to pay for tickets to visit all schools. He can start and finish in any school.

Input
The first line contains a single integer n (1 ≤ n ≤ 105) — the number of schools.

Output
Print single integer: the minimum cost of tickets needed to visit all schools

題目要求輸出最少的花費來經過全部學校，其中票可以複用。我們 先分析下，票的花費函數是這樣的：Cost=(i+j)mod(n+1)

那麼第一種情況就是i=1，j=n ，這樣花費爲0，然後i，j不斷的向n/2逼近，保證每次消耗都是最少的。
以1，2，3 爲例

Cost1=(1+3)mod(1+3)

Cost2=(3+2)mod(1+3)

Cost=Cost1+Cost2

消耗就爲1

int main()
{
        int n;
        cin>>n;
        cout<<(n+1)/2-1<<endl;
}

---

D. Minimum number of steps
time limit per test1 second
memory limit per test256 megabytes
inputstandard input
outputstandard output
We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7.

The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string.

Input
The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106.

Output
Print the minimum number of steps modulo 109 + 7.

這題是輸出按照要求變換字符串所需的最小次數