Use php to optimize the number of daffodils

The narcissus number refers to an n-digit number (n>=3). The sum of the n-th power of the numbers in each digit is equal to itself, and n is its number of digits. (For example: 1^3 5^3 3^3 = 153)

The Narcissus number is also called Armstrong’s number.

There are 4 narcissus numbers with three digits: 153, 370, 371, 407

There are 3 narcissus numbers with four digits : 1634, 8208, 9474

There are three five-digit narcissus numbers: 54748, 92727, 93084

Six-digit narcissus numbers There is one number: 548834

The seven-digit daffodil number has four: 1741725, 4210818, 9800817, 9926315

The eight-digit number There are three daffodil numbers: 24678050, 24678051, 88593477

....

The largest daffodil number has 39 digits ( 115132219018763992565095597973971522401), there are 88 daffodil numbers in the decimal natural numbers.

php Find the number of daffodils

1. Find the number of daffodils by exhaustive method, find 3 ~7-digit narcissus number

<?php
// 穷举求水仙花数
function narcissistic($n){
    if($n<3 || $n>39){
        return false;
    }
    // 保存执行结果
    $result = array();
    $start = pow(10,$n-1);
    $end = pow(10, $n);
    for($i=$start; $i<$end; $i++){
        $total = 0;
        $nums = str_split($i, 1);
        foreach($nums as $num){
            $total += pow($num, $n);
        }
        if($total==$i){
            array_push($result, $i);
        }
    }
    return $result;
}
// 获取当前microtime
function getMicrotime(){
    list($usec, $sec) = explode(&#39; &#39;, microtime());
    return (float)$usec + (float)$sec;
}
// 设定超时时间为3600秒
set_time_limit(3600);
// 记录开始运行时间
$start = getMicrotime();
// 执行求出3~7位的水仙花数
for($i=3; $i<=7; $i++){
    $result[$i] = implode(&#39;,&#39;, narcissistic($i));
}
// 记录运行结束时间
$end = getMicrotime();
// 输出运行时间
echo &#39;run time:&#39;.(float)($end - $start);
// 打印结果
echo &#39;<pre class="brush:php;toolbar:false">&#39;;
print_r($result);
echo &#39;

Execution result:

run time:82.230147838593
Array
(
    [3] => 153,370,371,407
    [4] => 1634,8208,9474
    [5] => 54748,92727,93084
    [6] => 548834
    [7] => 1741725,4210818,9800817,9926315
)

2. Optimization algorithm Narcissus number, find the narcissus number between 3 and 7 digits

Optimization method: Create a 0-9 N-order correspondence table for pow to reduce the number of calculations

<?php
// 优化求水仙花数
function narcissistic($n){
    if($n<3 || $n>39){
        return false;
    }
    // 保存执行结果
    $result = array();
    // n阶pow对应表
    $powlist = getPow($n);
    $start = pow(10,$n-1);
    $end = pow(10, $n);
    for($i=$start; $i<$end; $i++){
        $total = 0;
        $nums = str_split($i, 1);
        foreach($nums as $num){
            $total += $powlist[$num];
        }
        if($total==$i){
            array_push($result, $i);
        }
    }
    return $result;
}
// 获取当前microtime
function getMicrotime(){
    list($usec, $sec) = explode(&#39; &#39;, microtime());
    return (float)$usec + (float)$sec;
}
// 获取n阶pow对应表
function getPow($n){
    $powlist = array();
    for($i=0; $i<=9; $i++){
        array_push($powlist, pow($i,$n));
    }
    return $powlist;
}
// 设定超时时间为3600秒
set_time_limit(3600);
// 记录开始运行时间
$start = getMicrotime();
// 执行求出3~7位的水仙花数
for($i=3; $i<=7; $i++){
    $result[$i] = implode(&#39;,&#39;, narcissistic($i));
}
// 记录运行结束时间
$end = getMicrotime();
// 输出运行时间
echo &#39;run time:&#39;.(float)($end - $start);
// 打印结果
echo &#39;<pre class="brush:php;toolbar:false">&#39;;
print_r($result);
echo &#39;

Execution results:

run time:47.354328155518
Array
(
    [3] => 153,370,371,407
    [4] => 1634,8208,9474
    [5] => 54748,92727,93084
    [6] => 548834
    [7] => 1741725,4210818,9800817,9926315
)

Comparing the results, the optimized algorithm reduced the execution time by 42%.

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