Given a string consisting of integers 0 to 9. The task is to count the number of substrings which when converted into integer are divisible by 4. Substring may contain leading zeroes.
Input : "124" Output : 4 Substrings divisible by 4 are "12", "4", "24", "124" . Input : "04" Output : 3 Substring divisible by 4 are "0", "4", "04" .
Efficient solution : A number is divisible by 4 if its last two digits are divisible by 4 and single-digit numbers divisible by 4 are 4, 8 and 0. So, to calculate the number of substrings divisible by 4 we first count number of 0’s, 4’s and 8’s in the string. Then, we make all pairs of two consecutive characters and convert it into an integer. After converting it into integer we check that whether it is divisible by 4 or not. If it is divisible by 4 then all such substring ending with this last two characters are divisible by 4. Now, the number of such substrings are basically the index of 1st character of pair. To make it more clear, consider string “14532465” then possible pairs are “14”, “45”, “53”, “32”, “24”, “46”, “65” . In these pairs only “32” and “24” when converted into integer are divisible by 4. Then, substrings ( length >= 2 ) divisible by 4 must end with either “32” or “24” So, number of substrings ending with “32” are “14532”, “4532”, “532”, “32” i.e 4 and index of ‘3’ is also 4 . Similarly, the number of substrings ending with “24” is 5.
Thus we get an O(n) solution. Below is the implementation of this approach .
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