pub fn add_binary(a: String, b: String) -> String {
  // Pad the strings with leading zeroes so they're the same length.
  let (a, b) = (
    format!("{:0>1$}", a, b.len()),
    format!("{:0>1$}", b, a.len()),
  );

  let mut carry = false;
  let mut sum = String::new();

  // Create reversed iterators for both binary strings.
  let (mut a, mut b) = (a.chars().rev(), b.chars().rev());

  while let Some(a) = a.next() {
    // Safe to unwrap since we know both iterators will be the same length.
    let b = b.next().unwrap();

    match (a, b) {
      ('1', '1') => {
        // For 1 + 1, if we need to carry it will be 01 + 01 -> 10 + 01 -> 11.
        // And otherwise it will be 01 + 01 -> 10, and carry next digit.
        if carry {
          sum.push('1');
        } else {
          sum.push('0');
          carry = true;
        }
      }

      // For 1 + 0 (and associatively 0 + 1), if we need to carry it's the same
      // as 01 + 01 -> 10. And keep the carry set.
      // And otherwise it will just be 01 + 00 -> 01.
      ('1', '0') | ('0', '1') => {
        if carry {
          sum.push('0');
        } else {
          sum.push('1');
        }
      }

      // For 0 + 0, if we need to carry it results in 1 and otherwise 0.
      ('0', '0') => {
        if carry {
          sum.push('1');
          carry = false;
        } else {
          sum.push('0');
        }
      }

      _ => unreachable!(),
    }
  }

  // And if the final digits required carrying, add the 1 here at the end.
  if carry {
    sum.push('1');
  }

  sum.chars().rev().collect()
}

#[test]
fn test_add_binary() {
  assert_eq!(add_binary("11".to_string(), "1".to_string()), "100");
  assert_eq!(add_binary("1010".to_string(), "1011".to_string()), "10101");
  assert_eq!(add_binary("1111".to_string(), "1111".to_string()), "11110");
  assert_eq!(
    add_binary(
      "10110101010001101011001011100011\
10100111101001010011000011000100\
11110111001001111010110000000010\
11100100110010110111101001100010\
10000101100010101010000111100100\
10100110010010100110111010011001\
11110111011101010000000110101001\
10000101110010101101011011011000"
        .to_string(),
      "11101111111010110101001000000110\
10010101100011001110011100101111\
10011111011100000010100111010100\
11101111111010111010011111001011\
00000001001010111100100000010010\
10110001010101011100001100000010\
11010000010010011101100000000111\
10000100111011110110000001110100"
        .to_string()
    ),
    "11010010100110010000001001110101\
00011110100110010000101111111010\
01001011010010111110101011101011\
11101010010110111001000100010110\
11000011010110110011010011111011\
10101011110100000001100011001110\
01100011110111110110110011011000\
10000101010111010001101110100110\
0"
  );
}