Given two integers A and B, the task is to calculate the number of pairs (a, b) such that 1 ≤ a ≤ A, 1 ≤ b ≤ B and the equation (a * b) + a + b = concat(a, b) is true where conc(a, b) is the concatenation of a and b (for example, conc(12, 23) = 1223, conc(100, 11) = 10011). Note that a and b should not contain any leading zeroes.
Input: A = 1, B = 12
There exists only one pair (1, 9) satisfying
the equation ((1 * 9) + 1 + 9 = 19)
Input: A = 2, B = 8
There doesn’t exist any pair satisfying the equation.
Approach: It can be observed that the above (a * b + a + b = conc(a, b)) will only be satisfied when the digits of an integer ≤ b contains only 9. Simply, calculate the number of digits (≤ b) containing only 9 and multiply with the integer a.
Below is the implementation of the above approach:
- Count valid pairs in the array satisfying given conditions
- Count index pairs which satisfy the given condition
- Count triplet pairs (A, B, C) of points in 2-D space that satisfy the given condition
- Check if elements of an array can be arranged satisfying the given condition
- Count of numbers satisfying m + sum(m) + sum(sum(m)) = N
- Pairs from an array that satisfy the given condition
- Count of sub-sequences which satisfy the given condition
- Count all possible N digit numbers that satisfy the given condition
- Count of indices in an array that satisfy the given condition
- Count pairs with Odd XOR
- Count pairs with given sum | Set 2
- Count number of pairs (i, j) such that arr[i] * arr[j] = arr[i] + arr[j]
- Count pairs (a, b) whose sum of cubes is N (a^3 + b^3 = N)
- Count of pairs (x, y) in an array such that x < y
- Count of odd and even sum pairs in an array
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