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415. Add Strings

Description

Given two non-negative integers, num1 and num2 represented as string, return the sum of num1 and num2 as a string.

You must solve the problem without using any built-in library for handling large integers (such as BigInteger). You must also not convert the inputs to integers directly.

 

Example 1:

Input: num1 = "11", num2 = "123"
Output: "134"

Example 2:

Input: num1 = "456", num2 = "77"
Output: "533"

Example 3:

Input: num1 = "0", num2 = "0"
Output: "0"

 

Constraints:

  • 1 <= num1.length, num2.length <= 104
  • num1 and num2 consist of only digits.
  • num1 and num2 don't have any leading zeros except for the zero itself.

Solutions

Solution 1: Two Pointers

We use two pointers $i$ and $j$ to point to the end of the two strings respectively, and start adding bit by bit from the end. Each time we take out the corresponding digits $a$ and $b$, calculate their sum $a + b + c$, where $c$ represents the carry from the last addition. Finally, we append the units digit of $a + b + c$ to the end of the answer string, and then take the tens digit of $a + b + c$ as the value of the carry $c$, and loop this process until the pointers of both strings have pointed to the beginning of the string and the value of the carry $c$ is $0$.

Finally, reverse the answer string and return it.

The time complexity is $O(\max(m, n))$, where $m$ and $n$ are the lengths of the two strings respectively. Ignoring the space consumption of the answer string, the space complexity is $O(1)$.

The following code also implements string subtraction, refer to the subStrings(num1, num2) function.

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class Solution:
    def addStrings(self, num1: str, num2: str) -> str:
        i, j = len(num1) - 1, len(num2) - 1
        ans = []
        c = 0
        while i >= 0 or j >= 0 or c:
            a = 0 if i < 0 else int(num1[i])
            b = 0 if j < 0 else int(num2[j])
            c, v = divmod(a + b + c, 10)
            ans.append(str(v))
            i, j = i - 1, j - 1
        return "".join(ans[::-1])

    def subStrings(self, num1: str, num2: str) -> str:
        m, n = len(num1), len(num2)
        neg = m < n or (m == n and num1 < num2)
        if neg:
            num1, num2 = num2, num1
        i, j = len(num1) - 1, len(num2) - 1
        ans = []
        c = 0
        while i >= 0:
            c = int(num1[i]) - c - (0 if j < 0 else int(num2[j]))
            ans.append(str((c + 10) % 10))
            c = 1 if c < 0 else 0
            i, j = i - 1, j - 1
        while len(ans) > 1 and ans[-1] == '0':
            ans.pop()
        if neg:
            ans.append('-')
        return ''.join(ans[::-1])

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class Solution {
    public String addStrings(String num1, String num2) {
        int i = num1.length() - 1, j = num2.length() - 1;
        StringBuilder ans = new StringBuilder();
        for (int c = 0; i >= 0 || j >= 0 || c > 0; --i, --j) {
            int a = i < 0 ? 0 : num1.charAt(i) - '0';
            int b = j < 0 ? 0 : num2.charAt(j) - '0';
            c += a + b;
            ans.append(c % 10);
            c /= 10;
        }
        return ans.reverse().toString();
    }

    public String subStrings(String num1, String num2) {
        int m = num1.length(), n = num2.length();
        boolean neg = m < n || (m == n && num1.compareTo(num2) < 0);
        if (neg) {
            String t = num1;
            num1 = num2;
            num2 = t;
        }
        int i = num1.length() - 1, j = num2.length() - 1;
        StringBuilder ans = new StringBuilder();
        for (int c = 0; i >= 0; --i, --j) {
            c = (num1.charAt(i) - '0') - c - (j < 0 ? 0 : num2.charAt(j) - '0');
            ans.append((c + 10) % 10);
            c = c < 0 ? 1 : 0;
        }
        while (ans.length() > 1 && ans.charAt(ans.length() - 1) == '0') {
            ans.deleteCharAt(ans.length() - 1);
        }
        if (neg) {
            ans.append('-');
        }
        return ans.reverse().toString();
    }
}

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class Solution {
public:
    string addStrings(string num1, string num2) {
        int i = num1.size() - 1, j = num2.size() - 1;
        string ans;
        for (int c = 0; i >= 0 || j >= 0 || c; --i, --j) {
            int a = i < 0 ? 0 : num1[i] - '0';
            int b = j < 0 ? 0 : num2[j] - '0';
            c += a + b;
            ans += to_string(c % 10);
            c /= 10;
        }
        reverse(ans.begin(), ans.end());
        return ans;
    }

    string subStrings(string num1, string num2) {
        int m = num1.size(), n = num2.size();
        bool neg = m < n || (m == n && num1 < num2);
        if (neg) {
            swap(num1, num2);
        }
        int i = num1.size() - 1, j = num2.size() - 1;
        string ans;
        for (int c = 0; i >= 0; --i, --j) {
            c = (num1[i] - '0') - c - (j < 0 ? 0 : num2[j] - '0');
            ans += to_string((c + 10) % 10);
            c = c < 0 ? 1 : 0;
        }
        while (ans.size() > 1 && ans.back() == '0') {
            ans.pop_back();
        }
        if (neg) {
            ans.push_back('-');
        }
        reverse(ans.begin(), ans.end());
        return ans;
    }
};

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func addStrings(num1 string, num2 string) string {
    i, j := len(num1)-1, len(num2)-1
    ans := []byte{}
    for c := 0; i >= 0 || j >= 0 || c > 0; i, j = i-1, j-1 {
        if i >= 0 {
            c += int(num1[i] - '0')
        }
        if j >= 0 {
            c += int(num2[j] - '0')
        }
        ans = append(ans, byte(c%10+'0'))
        c /= 10
    }
    for i, j := 0, len(ans)-1; i < j; i, j = i+1, j-1 {
        ans[i], ans[j] = ans[j], ans[i]
    }
    return string(ans)
}

func subStrings(num1 string, num2 string) string {
    m, n := len(num1), len(num2)
    neg := m < n || (m == n && num1 < num2)
    if neg {
        num1, num2 = num2, num1
    }
    i, j := len(num1)-1, len(num2)-1
    ans := []byte{}
    for c := 0; i >= 0; i, j = i-1, j-1 {
        c = int(num1[i]-'0') - c
        if j >= 0 {
            c -= int(num2[j] - '0')
        }
        ans = append(ans, byte((c+10)%10+'0'))
        if c < 0 {
            c = 1
        } else {
            c = 0
        }
    }
    for len(ans) > 1 && ans[len(ans)-1] == '0' {
        ans = ans[:len(ans)-1]
    }
    if neg {
        ans = append(ans, '-')
    }
    for i, j := 0, len(ans)-1; i < j; i, j = i+1, j-1 {
        ans[i], ans[j] = ans[j], ans[i]
    }
    return string(ans)
}

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function addStrings(num1: string, num2: string): string {
    let i = num1.length - 1;
    let j = num2.length - 1;
    const ans: number[] = [];
    for (let c = 0; i >= 0 || j >= 0 || c; --i, --j) {
        c += i < 0 ? 0 : +num1[i];
        c += j < 0 ? 0 : +num2[j];
        ans.push(c % 10);
        c = Math.floor(c / 10);
    }
    return ans.reverse().join('');
}

function subStrings(num1: string, num2: string): string {
    const m = num1.length;
    const n = num2.length;
    const neg = m < n || (m == n && num1 < num2);
    if (neg) {
        const t = num1;
        num1 = num2;
        num2 = t;
    }
    let i = num1.length - 1;
    let j = num2.length - 1;
    const ans: number[] = [];
    for (let c = 0; i >= 0; --i, --j) {
        c = +num1[i] - c;
        if (j >= 0) {
            c -= +num2[j];
        }
        ans.push((c + 10) % 10);
        c = c < 0 ? 1 : 0;
    }
    while (ans.length > 1 && ans.at(-1) === 0) {
        ans.pop();
    }
    return (neg ? '-' : '') + ans.reverse().join('');
}

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impl Solution {
    pub fn add_strings(num1: String, num2: String) -> String {
        let mut res = vec![];
        let s1 = num1.as_bytes();
        let s2 = num2.as_bytes();
        let (mut i, mut j) = (s1.len(), s2.len());
        let mut is_over = false;
        while i != 0 || j != 0 || is_over {
            let mut sum = if is_over { 1 } else { 0 };
            if i != 0 {
                sum += (s1[i - 1] - b'0') as i32;
                i -= 1;
            }
            if j != 0 {
                sum += (s2[j - 1] - b'0') as i32;
                j -= 1;
            }
            is_over = sum >= 10;
            res.push((sum % 10).to_string());
        }
        res.into_iter().rev().collect()
    }
}

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/**
 * @param {string} num1
 * @param {string} num2
 * @return {string}
 */
var addStrings = function (num1, num2) {
    let i = num1.length - 1;
    let j = num2.length - 1;
    const ans = [];
    for (let c = 0; i >= 0 || j >= 0 || c; --i, --j) {
        c += i < 0 ? 0 : +num1[i];
        c += j < 0 ? 0 : +num2[j];
        ans.push(c % 10);
        c = Math.floor(c / 10);
    }
    return ans.reverse().join('');
};

/**
 * @param {string} num1
 * @param {string} num2
 * @return {string}
 */
var subStrings = function (num1, num2) {
    const m = num1.length;
    const n = num2.length;
    const neg = m < n || (m == n && num1 < num2);
    if (neg) {
        const t = num1;
        num1 = num2;
        num2 = t;
    }
    let i = num1.length - 1;
    let j = num2.length - 1;
    const ans = [];
    for (let c = 0; i >= 0; --i, --j) {
        c = +num1[i] - c;
        if (j >= 0) {
            c -= +num2[j];
        }
        ans.push((c + 10) % 10);
        c = c < 0 ? 1 : 0;
    }
    while (ans.length > 1 && ans.at(-1) === 0) {
        ans.pop();
    }
    return (neg ? '-' : '') + ans.reverse().join('');
};

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class Solution {
    fun addStrings(num1: String, num2: String): String {
        val result = mutableListOf<Int>()

        val chars_1 = num1.toCharArray()
        val chars_2 = num2.toCharArray()
        var over = 0
        var i = num1.length
        var j = num2.length

        while (i > 0 || j > 0 || over > 0) {
            val a = if (i > 0) chars_1[--i] - '0' else 0
            val b = if (j > 0) chars_2[--j] - '0' else 0
            val sum = a + b + over
            over = sum / 10
            result.add(sum % 10)
        }

        return result.reversed().joinToString("")
    }
}

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