Efficiently do exactly what summation does, with comments of clarity, in C++

  • 1
    class Solution {
        string addBinary(string a, string b) {
            int i=a.size()-1,j=b.size()-1, carry=0;
            // since pass by value, find longer string and write to it
            if(i<j) { std::swap(a,b); std::swap(i,j); }
            // from LSB, sum and write to a, until b is all traversed
            for(;j>=0;--i,--j) {
                if(carry<2) { a[i]='0'+carry; carry=0; }
                else { a[i]='0'+carry-2; carry=1; }
            // if carry==1, need to modify the remaining part of a, 
            if(carry) {
                // the rightmost successive 1s would be 0s after summation, and carry remain unchanged
                for(;i>=0 && a[i]=='1';--i) { a[i]='0'; }
                if(i<0) a='1'+a; // all 1s
                else ++a[i]; // the rightmost 0 found
            return a;

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