string multiply(string num1, string num2){
int shift = 0;
string result = "0";
for(int i=num1.size()-1; i>=0; i--){
string s=strMulti(num2, num1[i]);
for(int j=0; j<shift; j++){
s.insert(s.end(), '0');
}
result = strPlus(result, s);
shift++;
}
return result;
}
string multiply(string num1, string num2) {
if (num1.size() <= 0 || num2.size() <= 0) return "";
string result;
for ( int i = num1.size() - 1; i >= 0; i--) {
int carry = 0;
string val;
// every digit of string 1 is multiplied with every digit of string 2 and store result from each round into val
// first round i = num1.size() - 1: right most digit of string 1 multiply every digit of string 2
// second round i = num1.size() - 2: second from right digit of string 1 multiply .....
for( int j = num2.size() - 1; j >= 0; j--) {
int v = (num2[j] - '0') * (num1[i] - '0') + carry; // convert char into int
val.insert(val.begin(), v%10 + '0'); // convert int into char and store the result one by one to val from front
carry = v/10;
}
if (carry) val.insert(val.begin(), carry + '0'); // last carry
// first round i = num1.size() - 1: shift val to left by 0 position
// second round i = num1.size() - 1: shift val to left by 1 position
for (int j = i; j < num1.size() - 1; j++) {
val.push_back('0');
}
// accumulating multiplication from each round
result = strPlus(result, val);
}
//check if it is zero
if (result[0]=='0') return "0";
return result;
}