Pair development----Find a

First, title:

Given a positive integer in decimal, write down all integers starting with 1, to N, and then count the number of "1" that appears. Requirements: 1. Write a function f (n) and return the number of "1" that appears between 1 and N. For example F (12) = 5. 2. In the range of 32-bit integers, the maximum n of "f (n) =n" satisfying the condition is what.

second, the idea:This problem is biased toward mathematical reasoning, its fundamental is to find the law, and the law is to be given to the number of decomposition, divided into a Chichong equal number of individuals, and then from each to find the law. Through the collation, each of the number of 1 only with its two-bit relationship, the specific algorithm program is as follows: third, the source program

1 #include <iostream.h> 2 #include <stdlib.h> 3 int main () 4 {5     int num; 6     int count=0;  7     int flog=1;  8     int low=0; 9     int now=0;10     int high=0;11     cout<< "Please enter Number:   ";     cin>>num;13 While     (num/flog!=0)     {         low=num-(num/flog) *flog;16         now= (num/flog)%10;17         high= num/(flog*10),         switch (now),         0:21             count=count+high*flog;22             break;23         Case 1:24             count=count+high*flog+low+1;25             break;26         default:27             count=count+ (high+1) *flog;28             break;29         } The number of     digits 1 in flog=flog*10;31}32 cout<<num<< "is:" <<count<<endl;33     Return 0;34}

Four: Experiment

V. Summary of the Experiment

At first, our idea was to find a general formula, but after thinking about it for a while, it was not a formula to solve, so the best way is to find the law. After summing up with our companions, we discovered the law and finally realized the program.

Pair development----Find a