PHP algorithm analysis: efficient method to find missing numbers in an array

PHP algorithm analysis: an efficient method to find missing numbers in an array

In the process of developing PHP applications, we often encounter situations where we need to find missing numbers in an array. This situation is very common in data processing and algorithm design, so we need to master efficient search algorithms to solve this problem. This article will introduce an efficient method to find missing numbers in an array, and attach specific PHP code examples.

Problem Description

Suppose we have an array containing integers between 1 and 100, but one number is missing. We need to design an algorithm to find this missing number. In this example, the array should contain all integers between 1 and 100, but for some reason, one of the numbers is missing.

Solution

Method 1: Sum Difference Method

We can calculate the sum of all the numbers in the array, and then subtract all the numbers that the array should theoretically contain The sum of , the difference obtained is the missing number. The time complexity of this method is O(n), where n is the length of the array.

function findMissingNumber($arr)
{
    $n = count($arr);
    $sum = array_sum($arr);

    $expectedSum = ($n + 1) * ($n + 2) / 2;

    $missingNumber = $expectedSum - $sum;

    return $missingNumber;
}

$arr = [1, 2, 3, 4, 6, 7, 8, 9, 10]; //缺失数字为5
echo "缺失的数字是：" . findMissingNumber($arr);

Method 2: XOR operation method

We can also use the properties of XOR operation to solve this problem. XOR all the elements in the array and then XOR all the numbers between 1 and 100, and the final result is the missing number. The time complexity of this method is also O(n).

function findMissingNumber($arr)
{
    $n = count($arr);
    $missingNumber = 0;
    
    for($i = 0; $i < $n; $i++)
    {
        $missingNumber ^= $arr[$i];
        $missingNumber ^= ($i + 1);
    }

    $missingNumber ^= ($n + 1);

    return $missingNumber;
}

$arr = [1, 2, 3, 4, 6, 7, 8, 9, 10]; //缺失数字为5
echo "缺失的数字是：" . findMissingNumber($arr);

Summary

When dealing with the problem of finding missing numbers in an array, we can choose different methods to solve it. The two methods introduced above are relatively efficient algorithms and can quickly find missing numbers in the array. Depending on the specific application scenarios and requirements, choosing the appropriate algorithm can improve the efficiency and readability of the code.

I hope the methods introduced in this article will be helpful to you and can be applied in actual development. If you have any questions or suggestions, please leave a message below and we will be happy to answer you.

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