[Careercup] 18.4 count number of 2

18.4 Write a method to count the number of 2s between 0 and N.

This problem gives us an integer n, let us find all 2 occurrences of the [0,n] interval, such as if n=20, then meet test instructions is 2, 12, 20, then return 3. Leetcode on a very similar topic factorial Trailing zeroes, but the number of the question to 5 also includes the factor of 5, such as 10 inside there are 5, which is the difference between the two questions. So first this problem can be solved with brute force, we call a function for each number within the interval, to count the number of 2 occurrences in that figure. and statistics a number of people on the number is very simple, is the flat shift, to 10, if 2, then the counter increases by 1, and then this number is divided by 10, until 0 stop, see the code as follows:

Solution One:

intCount_number_2 (intnum) {    intres =0;  while(Num >0) {        if(num%Ten==2) ++Res; Num/=Ten; }    returnRes;}intCount_in_range (intnum) {    intres =0;  for(inti =2; I <= num; ++i) {res+=count_number_2 (i); }    returnRes;}

In fact, there is a better way to do this problem, we are not in the interval of a number of 2, but the bitwise to find, for example, we first to list some of the sequence:

0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
...
110 111 112 113 114 115 116 117 118 119

We found that the minimum number of occurrences of the 2 frequency is 1 per 10 digits, and we can probably be divided into three scenarios to discuss, digit < 2, Digti = 2, and digit > 2.

Solution Two:

intCount_in_range_as_digit (intNumintd) {intPower_of_10 = POW (Ten, D); intNEXT_POWER_OF_10 = power_of_10 *Ten; intright = num%power_of_10; intRound_down = num-num%next_power_of_10; intROUND_UP = Round_down +next_power_of_10; intdigit = (num/power_of_10)%Ten; if(Digit <2)returnRound_down/Ten; Else if(Digit = =2)returnRound_down/Ten+ Right +1; Else returnROUND_UP/Ten;}intCount_in_range (intnum) {    intres =0; intLen =to_string (num). Size ();  for(inti =0; i < Len; ++i) {res+=count_in_range_as_digit (num, i); }    returnRes;}

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[Careercup] 18.4 count number of 2