# 43. Multiply Strings - CPP - Solution

• ``````// 43. Multiply Strings
// https://leetcode.com/problems/multiply-strings/
// https://leetcode.com/discuss/26602/brief-c-solution-using-only-strings-and-without-reversal
// https://leetcode.com/discuss/71593/easiest-java-solution-with-graph-explanation
#include <iostream>
#include <string>
using namespace std;
class Solution {
public:
string multiply(const string& num1, const string& num2) {
size_t len1(num1.size());
size_t len2(num2.size());
//    num1 [len1] x num2 [len2]
// <= 99...9 [len1] x 99...9 [len2]
// =  (10 ^ len1 - 1) * (10 ^ len2 - 1)
// =  10 ^ (len1 + len2) - 10 ^ len1 - 10 ^ len2 + 1
// <= 10 ^ (len1 + len2) - 1
// =  99...9 [len1 + len2]
string result(len1 + len2, '0');
for (size_t i = len1; i >= 1; --i) {
int carry(0);
for (size_t j = len2; j >= 1; --j) {
int value = (num1[i - 1] - '0') * (num2[j - 1] - '0');
value += result[i + j - 1] - '0';
value += carry;
result[i + j - 1] = value % 10 + '0';
carry = value / 10;
}
result[i - 1] = carry + '0';
}
for (size_t i = 0; i < len1 + len2; ++i) {
if (result[i] != '0')
return result.substr(i, len1 + len2 - i);
}
return string(1, '0');
}
};
int main(void) {
Solution solution;
string num1("1234");
string num2("345");
cout << solution.multiply(num1, num2);
cout << "\nPassed\n";
return 0;
}``````

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