Question

415. Add Strings

中文文档

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.

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])

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();
  }
}

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;
  }
};

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)
}

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('');
}

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()
  }
}

/**
 * @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('');
};