Q:

integer to string

The strutils.h library contains a function IntegerToString. (You might have wondered how
the computer actually goes about the process of converting an integer into its string representation.)
As it turns out, the easiest way to implement this function is to use the recursive decomposition of an integer. 
Someone wrote a recursive implementation of IntegerToString so that it operates recursively without using any of the iterative constructs such as while and for.
Although it helped me ... i m not able to understand the code :S  
#include <iostream>
#include <string>

using namespace std;

const char digit_pairs[201] = {
  "00010203040506070809"
  "10111213141516171819"
  "20212223242526272829"
  "30313233343536373839"
  "40414243444546474849"
  "50515253545556575859"
  "60616263646566676869"
  "70717273747576777879"
  "80818283848586878889"
  "90919293949596979899"
};

std::string& itostr(int n, std::string& s)
{
    if(n==0)
    {
        s="0";
        return s;
    }

    int sign = -(n<0);
    unsigned int val = (n^sign)-sign;

    int size;
    if(val>=10000)
    {
        if(val>=10000000)
        {
            if(val>=1000000000)
                size=10;
            else if(val>=100000000)
                size=9;
            else 
                size=8;
        }
        else
        {
            if(val>=1000000)
                size=7;
            else if(val>=100000)
                size=6;
            else
                size=5;
        }
    }
    else 
    {
        if(val>=100)
        {
            if(val>=1000)
                size=4;
            else
                size=3;
        }
        else
        {
            if(val>=10)
                size=2;
            else
                size=1;
        }
    }
    size -= sign;
    s.resize(size);
    char* c = &s[0];
    if(sign)
        *c='-';

    c += size-1;
    while(val>=100)
    {
       int pos = val % 100;
       val /= 100;
       *(short*)(c-1)=*(short*)(digit_pairs+2*pos); 
       c-=2;
    }
    while(val>0)
    {
        *c--='0' + (val % 10);
        val /= 10;
    }
    return s;
}

just want to get better understanding of this code.

A:

I think the "recursive decomposition" is
N = T * 10 + O

This leads to a recursive algorithm
string(N) = let T = idiv(N, 10),
            let O = mod(N, 10),
            concat(T? string(T): empty_string, todigit(O))

Now you just have to write that up in C++, figuring out the little details along the way.
Then if you want to see more efficient ways, read

C++ performance challenge: integer to std::string conversion

