# Valleys and Hills VANDH Solution Codechef

## Valleys and Hills VANDH Solution

Chef built a binary string S that has exactly N hills and M valleys.

• hill is any index 1<i<|S| such that both its neighbors are strictly smaller than it, i.e, Si−1<Si and Si+1<Si.
• valley is any index 1<i<|S| such that both its neighbors are strictly larger than it, i.e, Si−1>Si and Si+1>Si.

Chef thinks that his string S is the shortest among all binary strings with N hills and M valleys. You don’t quite trust his words, so to verify his claim you would like to find the shortest binary string with exactly N hills and M valleys.

If there are multiple possible binary strings of the least length satisfying the given condition, you may print any of them.

Input Format

• The first line of input will contain a single integer T, denoting the number of test cases. The description of T test cases follows.
• The first and only line of each test case contains two space-separated integers N and M, the required number of hills and valleys respectively.

Output Format

For each test case, output two lines.

• The first line contains the length of the binary string you constructed to satisfy the given conditions.
• The second line contains the string itself.

Constraints

• 1≤T≤2500
• 1≤N≤500
• 1≤M≤500
• The sum of lengths of the answer strings across all test cases does not exceed 2⋅105

• 1≤N≤50
• 1≤M≤50
• You may output any string of length not exceeding 320 containing exactly N hills and M valleys: it need not be shortest by length. It is guaranteed that at least one such string with length ≤320 exists.

• Original constraints
• The binary string you construct must be shortest by length.

Sample Input 1

``````3
3 2
2 3
3 3``````

Sample Output 1

``````7
0101010
7
1010101
8
01010101``````

Explanation

Test case 1: The given string has hills at indices 2,4,6 and valleys at indices 3,5. It can be verified that there is no string of length 6 or less with 3 hills and 2 valleys. Note that for subtask 1, a binary string like 001010100 will also be accepted as a valid output, even though it is not shortest by length.

Test case 3: Apart from the given string, another possible string of length 8 that has 3 hills and 3 valleys is 10101010. You may print any of them.

### SOLUTION

Program Python: Valleys and Hills VANDH Solution in Python

``````for i in range (int(input())):
n,m = map(int,input().split())
x = ''
if m==n:
for i in range (n+1):
x+="01"
elif m>n:
for i in range(n+1):
x+="10"
for i in range(m-n-1):
x+="110"
x+="1"
else:
for i in range(m):
x+="01"
for i in range(n-m):
x+="010"
print(len(x))
print(x)``````

Program C++: Valleys and Hills VANDH Solution in C++

``````#include<bits/stdc++.h>
using namespace std;

int main()
{
int t;
cin>>t;
while(t--)
{
int n,m;
cin>>n>>m;
string ans = "";
if(m==n)
{
for(int i=0;i<n+1;i++)
{
ans+="01";
}
}
else if(m>n)
{
for(int i=0;i<n+1;i++)
{
ans+="10";
}
for(int i=0;i<m-n-1;i++)
{
ans+="110";
}
ans+="1";
}
else
{
for(int i=0;i<m;i++)
{
ans+="01";
}
for(int i=0;i<n-m;i++)
{
ans+="010";
}
}
cout<<ans.size()<<endl;
cout<<ans<<endl;
}
return 0;
}``````