2nd Attempt DAY 1

Problem Statement (string : Largest number with given sum) easy question.

Geek lost the password of his super locker. He remembers the number of digits N as well as the sum S of all the digits of his password. He know that his password is the largest number of N digits that can be made with given sum S. As he is busy doing his homework, help him retrieving his password.

Input:
N = 5, S = 12
Output:
93000
Explanation:
Sum of elements is 12. Largest possible 
5 digit number is 93000 with sum 12.

we have to write a function that returns string which is a number.

Approach is like for every digit we check all 10 number from 9 to 0 while comparing the sum.

code

string largestNumber(int n, int sum)
    {
        string ans="";
        while(n--)
        {
           if(sum==0)
           {
               ans=ans+to_string(0);
               continue;
           }
           for(int i=9;i>=0;i--)
           {
               if(sum>=i)
               {
                   ans=ans+to_string(i);
                   sum=sum-i;
                   break;
               }
           }
        }
        return (sum==0)?ans:"-1";
    }

Problem Statement : String's Count(easy + important)

Given a length n, count the number of strings of length n that can be made using a, b and c with at-most one b and two c allowed.

Input: n = 1
Output: 3
Explanation: Possible strings are: "a",
"b" and "c"

• countA: Represents the count of strings with only 'a' at each position (1 possibility).

• countB: Represents the count of strings with only 'b' at each position (n possibilities).

• countC: Represents the count of strings with only 'c' at each position (n possibilities).

• countAB: Represents the count of strings with two distinct characters, considering 'a' and 'b' (n * (n - 1) possibilities).

• countAC: Represents the count of strings with two distinct characters, considering 'a' and 'c' (countAB / 2 possibilities).

• countBC: Represents the count of strings with two distinct characters, considering 'b' and 'c' (countAC * (n - 2) possibilities).

• total: Sum of all the counts, representing the total number of valid strings of length n with at most one 'b' and two 'c'.

long long int countStr(long long int n) {
    const long long res = 2 * n + (3 * (n - 1) * n) / 2 + (n * (n - 1) * (n - 2)) / 2 + 1;
    return res;
}

PODT Problem Statement : Sequence of Sequence(DP medium problem)

Given two integers m and n, try making a special sequence of numbers seq of length n such that

• seq_i+1 >= 2*seq_i

• seq_i \> 0

• seq_i  <= m

Your task is to determine total number of such special sequences possible.

Input: 
m = 10
n = 4
Output: 
4
Explaination: 
There should be n elements and 
value of last element should be at-most m. 
The sequences are {1, 2, 4, 8}, {1, 2, 4, 9}, 
{1, 2, 4, 10}, {1, 2, 5, 10}.

 int numberSequence(int m, int n){
        if(m<n)
            return 0;
        if(n==0)
            return 1;
        return numberSequence(m/2,n-1) + numberSequence(m-1,n);

    }

Finally outdoor activity was running 2 km .