April 28 Tuesday Classroom Exercise: Number of "1"

First, the topic requirements

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), returns the number of "1" that occurs 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, design ideas (1) One-time f (0) =0;f (1) =1;f (2-9) = 1;　　　　(2) Two digits F (10) =1+ (0+1) = 2;　　　　F (11) = (+) + (+) = 4;　　　　F (12) = (+) + (2+1) = 5;　　　　F (13) = (+) + (3+1) = 6;　　　　F (23) = (2+1) +10=13;　　　　F (33) = (3+1) +10=14;　　F (93) = (9+1) +10=20;　　　　(3) Three digits f (123) = digit number of 1 + 10 digits appearing 1 number + hundred occurrences 1 Number (4) N = ABCDE with C bit as example if (c==0) num=ab*100;　　　　if (c==1) num=ab*100+de+1; if (c>=2) num= (ab+1) *100 three, source program

#include <iostream> #include <math.h>using namespace std;int count1num (int Digit) {int figure=1;// Number of digits in Mark Count 1 (1 digit, 10 10 bit) int curofdigit=0;//current digit int lowerofdigit=0;//lower bit number size (can be multi-bit) int higherofdigit=0;//higher bit number size int Count=0;while (digit/figure!=0) {//Get digital curofdigit= (digit/figure)%10;lowerofdigit=digit-(digit/figure*figure); higherofdigit=digit/(FIGURE*10); if (digit<=0) return 0;if (0==curofdigit)//Current number is 0 o'clock count {count+=higherofdigit* Figure;} else if (1==curofdigit)//The current number is 1 o'clock count {count+=higherofdigit*figure+lowerofdigit+1;} else{count+= (higherofdigit+1) *figure;} figure=figure*10;//number left one}return count;} void Main () {int digit;int max=0;while ((cout<<) Enter the value to be tested (enter-1 end test): "<<endl" && (cin>>digit ) {if (digit==-1) break;cout<< "1 to" <<Digit<< contains 1 numbers: "<<count1num (Digit) <<endl;}}

Four, the operation

V. Summary of the Experiment

The difficulty of the topic is mainly to find the law of "1", and then write the corresponding algorithm according to the finding. The topic is not difficult, but the law is still difficult to find.

April 28 Tuesday Classroom Exercise: Number of "1"