数字数组乘积中的第一个数字

给定一个数组“ n”个数字。我们需要找到这些“ n”个数字的乘积的第一位数
例子 ：

Input  : arr[] = {5, 8, 3, 7}
Output : 8
        Product of 5, 8, 3, 7 is 840
        and its first  digit is 8

Input  : arr[] = {6, 7, 9}
Output : 3

背景 ：
首先，我们从一个非常基本的问题开始，即如何找到任何数字x的第一个数字。要做到这一点，请将数字除以得到大于等于10的数字。完成后，我们将得到的数字将是x的第一个数字。

C++

// C++ implementation to find first digit of a
// single number
#include 
using namespace std;
 
int firstDigit(int x)
{
    // Keep dividing by 10 until it is
    // greater than equal to 10
    while (x >= 10)
        x = x / 10;
    return x;
}
 
// driver function
int main()
{
    cout << firstDigit(12345) << endl;
    cout << firstDigit(5432) << endl;
}

Java

// Java implementation to find first digit of a
// single number
 
class Test {
    static int firstDigit(int x)
    {
        // Keep dividing by 10 until it is
        // greater than equal to 10
        while (x >= 10)
            x = x / 10;
        return x;
    }
 
    // Driver method
    public static void main(String args[])
    {
        System.out.println(firstDigit(12345));
        System.out.println(firstDigit(5432));
    }
}

Python3

# Python implementation to
# find first digit of a
# single number
 
def firstDigit(x):
 
    # Keep dividing by 10 until it is
    # greater than equal to 10
    while(x >= 10):
        x = x//10
    return x
 
  
# driver function
 
print(firstDigit(12345))
print(firstDigit(5432))
 
# This code is contributed
# by Anant Agarwal.

C#

// C# implementation to find first
// digit of a single number
using System;
 
public class GFG {
     
    static int firstDigit(int x)
    {
         
        // Keep dividing by 10 until
        // it is greater than equal
        // to 10
        while (x >= 10)
            x = x / 10;
             
        return x;
    }
 
    // Driver method
    public static void Main()
    {
        Console.WriteLine(
                  firstDigit(12345));
                   
        Console.WriteLine(
                   firstDigit(5432));
    }
}
 
// This code is contributed by Sam007.

PHP

= 10)
        $x = $x / 10;
    return floor($x);
}
 
    // Driver Code
    echo firstDigit(12345),"\n" ;
    echo firstDigit(5432) ;
 
// This code is contributed by vishal tripathi.
?>

Javascript

 
// Javascript implementation to
// find first digit of a
// single number
 
function firstDigit(x)
{
     
    // Keep dividing by 10
    // until it is greater
    // than equal to 10
    while (x >= 10)
        x = x / 10;
    return Math.floor(x);
}
 
    // Driver Code
    document.write( firstDigit(12345)+"<br>" );
    document.write( firstDigit(5432)) ;
 
// This code is contributed by Bobby
 

输出：

1
5

解决方案 ：
对于数字数组，乘积可能很大，并且它们的乘法可能不适用于任何典型的数据类型。即使您使用Big int，该数字也将非常大，而直接除以10的方法查找第一个数字将非常慢。所以我们需要使用一些不同的东西
让数字成为$a_1$ ， $a_2$ ， $a_3$ …… $a_n$他们的乘积是P .P = $a_1$ * $a_2$ ….. * $a_n$ 。
令S = $log_{10}$ (P)= $log_{10}$ ( $a_1$ )+ $log_{10}$ ( $a_2$ ).. + $log_{10}$ ( $a_n$ )。
所以我们可以说P = $10^S$ 。
我们知道，任何数字都可以写为其底值和分数值的总和。
因此，P = $10^{floor(S) + fractional (S)}$这意味着P = $10^{floor(S)}$ * $10^{fractional(S)}$ 。
现在，我们可以应用上面讨论的方法来找到数字的第一个数字，因为在将P除以10直到大于10时，我们只剩下$10^{fractional(S)}$这将是我们的答案。分数(S)可以很容易地计算出分数(S)= S –下限(S)。

C++

// C++ implementation of finding first digit
// of product of n numbers
#include 
using namespace std;
 
// Teturns the first digit of product of elements of arr[]
int FirstDigit(int arr[], int n)
{
    // stores the logarithm of product of elements of arr[]
    double S = 0;
    for (int i = 0; i < n; i++)
        S = S + log10(arr[i] * 1.0);
 
    // fractional(s) = s - floor(s)
    double fract_S = S - floor(S);
 
    // ans = 10^fract_s
    int ans = pow(10, fract_S);
    return ans;
}
 
// Driver function
int main()
{
    int arr[] = { 5, 8, 3, 7 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << FirstDigit(arr, n) << endl;
    return 0;
}

Java

// Java implementation of finding first digit
// of product of n numbers
 
class Test {
    // Teturns the first digit of product of elements of arr[]
    static int FirstDigit(int arr[], int n)
    {
        // stores the logarithm of product of elements of arr[]
        double S = 0;
        for (int i = 0; i < n; i++)
            S = S + Math.log10(arr[i] * 1.0);
 
        // fractional(s) = s - floor(s)
        double fract_S = S - Math.floor(S);
 
        // ans = 10^fract_s
        int ans = (int)Math.pow(10, fract_S);
        return ans;
    }
 
    // Driver method
    public static void main(String args[])
    {
        int arr[] = { 5, 8, 3, 7 };
 
        System.out.println(FirstDigit(arr, arr.length));
    }
}

Python3

# Python implementation of
# finding first digit
# of product of n numbers
 
import math
 
# Returns the first digit of
# product of elements of arr[]
def FirstDigit (arr, n):
 
    # stores the logarithm of
    # product of elements of arr[]
    S = 0
    for i in range(n):
        S = S + math.log10(arr[i]*1.0)
  
    # fractional(s) = s - floor(s)
    fract_S = S - math.floor(S)
  
    # ans = 10 ^ fract_s
    ans = math.pow(10, fract_S)
    return ans
  
# Driver function
 
arr = [5, 8, 3, 7]
n = len(arr)
print((int)(FirstDigit(arr, n)))
     
# This code is contributed
# by Anant Agarwal.

C＃

// C# implementation of finding first
// digit of product of n numbers
using System;
 
public class GFG {
     
    // Teturns the first digit of product
    // of elements of arr[]
    static int FirstDigit(int[] arr, int n)
    {
         
        // stores the logarithm of product
        // of elements of arr[]
        double S = 0;
         
        for (int i = 0; i < n; i++)
            S = S + Math.Log10(arr[i] * 1.0);
 
        // fractional(s) = s - floor(s)
        double fract_S = S - Math.Floor(S);
 
        // ans = 10^fract_s
        int ans = (int)Math.Pow(10, fract_S);
         
        return ans;
    }
 
    // Driver method
    public static void Main()
    {
        int[] arr = { 5, 8, 3, 7 };
        int n = arr.Length;
         
        Console.WriteLine(FirstDigit(arr, n));
    }
}
 
// This code is contributed by Sam007.

输出 ：

8