// Find the number of 1 in an integer with radix 10

　　// Input: strN - a string, which represents an integer

　　// Output: the number of 1 in n with radix

　　/////////////////////////////////////////////////////////////////////////////

　　int NumberOf1(const char* strN)

　　{

　　if(!strN || *strN < '0' || *strN > '9' || *strN == '\0')

　　return 0;

　　int firstDigit = *strN - '0';

　　unsigned int length = static_cast(strlen(strN));

　　// the integer contains only one digit

　　if(length == 1 && firstDigit == 0)

　　return 0;

　　if(length == 1 && firstDigit > 0)

　　return 1;

　　// suppose the integer is 21345

　　// numFirstDigit is the number of 1 of 10000-19999 due to the first digit

　　int numFirstDigit = 0;

　　// numOtherDigits is the number of 1 01346-21345 due to all digits

　　// except the first one

　　int numOtherDigits = firstDigit * (length - 1) * PowerBase10(length - 2);

　　// numRecursive is the number of 1 of integer 1345

　　int numRecursive = NumberOf1(strN + 1);

　　// if the first digit is greater than 1, suppose in integer 21345

　　// number of 1 due to the first digit is 10^4. It's 10000-19999

　　if(firstDigit > 1)

　　numFirstDigit = PowerBase10(length - 1);

　　// if the first digit equals to 1, suppose in integer 12345

　　// number of 1 due to the first digit is 2346. It's 10000-12345

　　else if(firstDigit == 1)

　　numFirstDigit = atoi(strN + 1) + 1;

　　return numFirstDigit + numOtherDigits + numRecursive;

　　}

　　/////////////////////////////////////////////////////////////////////////////

　　// Calculate 10^n

　　/////////////////////////////////////////////////////////////////////////////

　　int PowerBase10(unsigned int n)

　　{

　　int result = 1;

　　for(unsigned int i = 0; i < n; ++ i)

　　result *= 10;

　　return result;

　　}

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