43. Multiply Strings 大数

题目地址

把较大的数作为被乘数，与乘数的每一位相乘，然后加到最后的结果上。
使用数组存储最后的结果，注意相乘后的位数。

class Solution {
public:
    string multiply(string num1,string num2) {
        string ans;
        const int maxn = num1.size() + num2.size() + 5;
        int a[maxn] = {0};
        reverse(num1.begin(),num1.end());
        reverse(num2.begin(),num2.end());
        if (num2.size() > num1.size()) num1.swap(num2);
        for (int i = 0; i < num2.size(); ++i) {
            add(maxn,a,num1,num2,i);
        }
        int index = maxn - 1;
        while (index >= 0 && a[index] == 0) index--;
        for (int i = index; i >= 0; --i) {
            ans += a[i] + '0';
        }
        if (ans.size() == 0) ans += '0';
        return ans;
    }

    void add(const int maxn,int a[],const string &num1,const string &num2,int n) {
        int carry = 0,n1 = num2[n] - '0';
        int b[num1.size() + 5] = {0};
        for (int i = 0; i < num1.size(); ++i) {
            int n2 = num1[i] - '0';
            int now = (n1 * n2 + carry) % 10;
            carry = (n1 * n2 + carry) / 10;
            b[i] = now;
        }
        if (carry) b[num1.size()] = carry;
        carry = 0;
        for (int i = 0; i + n < maxn; ++i) {
            if (i < num1.size() + 1) {
                int now = (a[i + n] + b[i] + carry) % 10;
                carry = (a[i + n] + b[i] + carry) / 10;
                a[i + n] = now;
            } else {
                int now = (a[i + n] + carry) % 10;
                carry = (a[i] + carry) / 10;
                a[i + n] = now;
            }
        }

    }
};

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