Valleys and Hills VANDH Solution

Valleys and Hills VANDH Solution Codechef

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Valleys and Hills VANDH Solution

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

  • A 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.
  • A 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

Subtasks

Subtask 1 (10 points):

  • 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.

Subtask 2 (90 points):

  • 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;
}

December Long Challenge 2021 Solution

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