Question

16.07. Maximum

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Description

Write a method that finds the maximum of two numbers. You should not use if-else or any other comparison operator.

Example:

Input:  a = 1, b = 2

Output:  2

Solutions

Solution 1: Bitwise Operation

We can extract the sign bit $k$ of $a-b$. If the sign bit is $1$, it means $a \lt b$; if the sign bit is $0$, it means $a \ge b$.

Then the final result is $a \times (k \oplus 1) + b \times k$.

The time complexity is $O(1)$, and the space complexity is $O(1)$.

class Solution:
  def maximum(self, a: int, b: int) -> int:
    k = (int(((a - b) & 0xFFFFFFFFFFFFFFFF) >> 63)) & 1
    return a * (k ^ 1) + b * k

class Solution {
  public int maximum(int a, int b) {
    int k = (int) (((long) a - (long) b) >> 63) & 1;
    return a * (k ^ 1) + b * k;
  }
}

class Solution {
public:
  int maximum(int a, int b) {
    int k = ((static_cast<long long>(a) - static_cast<long long>(b)) >> 63) & 1;
    return a * (k ^ 1) + b * k;
  }
};

func maximum(a int, b int) int {
  k := (a - b) >> 63 & 1
  return a*(k^1) + b*k
}

function maximum(a: number, b: number): number {
  const k: number = Number(((BigInt(a) - BigInt(b)) >> BigInt(63)) & BigInt(1));
  return a * (k ^ 1) + b * k;
}