K-th Beautiful String CodeForces - 1328B（二分+数学）

For the given integer n (n>2) let’s write down all the strings of length n which contain n−2 letters ‘a’ and two letters ‘b’ in lexicographical (alphabetical) order.

Recall that the string s of length n is lexicographically less than string t of length n, if there exists such i (1≤i≤n), that si<ti, and for any j (1≤j<i) sj=tj. The lexicographic comparison of strings is implemented by the operator < in modern programming languages.

For example, if n=5 the strings are (the order does matter):

aaabb
aabab
aabba
abaab
ababa
abbaa
baaab
baaba
babaa
bbaaa
It is easy to show that such a list of strings will contain exactly n⋅(n−1)2 strings.

You are given n (n>2) and k (1≤k≤n⋅(n−1)2). Print the k-th string from the list.

Input
The input contains one or more test cases.

The first line contains one integer t (1≤t≤104) — the number of test cases in the test. Then t test cases follow.

Each test case is written on the the separate line containing two integers n and k (3≤n≤105,1≤k≤min(2⋅109,n⋅(n−1)2).

The sum of values n over all test cases in the test doesn’t exceed 105.

Output
For each test case print the k-th string from the list of all described above strings of length n. Strings in the list are sorted lexicographically (alphabetically).

Example
Input
7
5 1
5 2
5 8
5 10
3 1
3 2
20 100
Output
aaabb
aabab
baaba
bbaaa
abb
bab
aaaaabaaaaabaaaaaaaa
思路：考虑两个b的位置，左边的b右边有几个位置，对于这个b来说，就有几种情况，二分去找这个区间，然后再判断第二个b的位置就可以了。
代码如下：

#include<bits/stdc++.h>
#define ll long long
using namespace std;int n;ll k;int main()
{int t;scanf("%d",&t);while(t--){scanf("%d%lld",&n,&k);ll l=1,r=n-1,mid;while(l<=r){int mid=l+r>>1;if((1ll+mid)*mid/2<=k) l=mid+1;else r=mid-1;}ll pos1,pos2;if((r+1)*r/2==k){pos1=n-r;pos2=pos1+1;} else{pos1=n-l;pos2=n-(k-(r+1)*r/2-1);}for(int i=1;i<=n;i++) {if(i==pos1||i==pos2) cout<<'b';else cout<<'a';}cout<<endl;}return 0;
}

努力加油a啊，(^o)/~

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K-th Beautiful String CodeForces - 1328B（二分+数学）

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