给定一个整数
。该任务是查找N的所有因子并打印N的四个因子的乘积，以便：
- 四个因子的总和等于N。
- 这四个因素的乘积最大。
如果无法找到4个这样的因素，则打印“不可能” 。
注意：为了使乘积最大化，这四个因素可以彼此相等。
例子：
Input : N = 24
Output : Product -> 1296
All factors are -> 1 2 3 4 6 8 12 24
Choose the factor 6 four times,
Therefore, 6+6+6+6 = 24 and product is maximum.
Input : N = 100
Output : Product -> 390625
All the factors are -> 1 2 4 5 10 10 20 25 50 100
Choose the factor 25 four times.
在上一篇文章中已经讨论了一种方法，该方法的复杂度为O(M ^ 3)，其中M是N的因子数。
通过执行以下步骤，可以获得时间复杂度O(N ^ 2)的有效方法。
- 将给定数字的所有因子存储在容器中。
- 遍历所有对，并将其总和存储在不同的容器中。
- 用对(element1，element2)标记索引(element1 + element2)，以获得获得总和的元素。
- 遍历所有pair_sums，并检查n-pair_sum是否在同一容器中，然后两个对形成四元组。
- 使用对散列数组获取组成该对的元素。
- 存储所有这些四倍的最大值，并在末尾打印。
下面是上述方法的实现：
C++
// C++ program to find four factors of N
// with maximum product and sum equal to N
#include
using namespace std;
// Function to find factors
// and to print those four factors
void findfactors(int n)
{
unordered_map mpp;
vector v, v1;
// push all the factors in the container
for (int i = 1; i <= sqrt(n); i++) {
if (n % i == 0) {
v.push_back(i);
if (i != (n / i) && i != 1)
v.push_back(n / i);
}
}
// number of factors
int s = v.size();
// Initial maximum
int maxi = -1;
// hash-array to mark the
// pairs
pair mp1[n + 5];
for (int i = 0; i < s; i++) {
// form all the pair sums
for (int j = i; j < s; j++) {
// if the pair sum is less than n
if (v[i] + v[j] < n) {
// push in another container
v1.push_back(v[i] + v[j]);
// mark the sum with the elements
// formed
mp1[v[i] + v[j]] = { v[i], v[j] };
// mark in the map that v[i]+v[j]
// is present
mpp[v[i] + v[j]] = 1;
}
}
}
// new size of all the pair sums
s = v1.size();
// iterate for all pair sum
for (int i = 0; i < s; i++) {
// the required part
int el = n - (v1[i]);
// if the required part is also
// present in pair sum
if (mpp[el] == 1) {
// find the elements with
// which the first pair is formed
int a = mp1[v1[i]].first;
int b = mp1[v1[i]].second;
// find the elements with
// which the second pair is formed
int c = mp1[n - v1[i]].first;
int d = mp1[n - v1[i]].second;
// check for previous maximum
maxi = max(a * b * c * d, maxi);
}
}
if (maxi == -1)
cout << "Not Possible\n";
else {
cout << "The maximum product is " << maxi << endl;
}
}
// Driver code
int main()
{
int n = 50;
findfactors(n);
return 0;
} Java
// Java program to find four factors of N
// with maximum product and sum equal to N
import java.util.*;
import java.lang.*;
import java.io.*;
class GFG
{
// Function to find factors
// and to print those four factors
static void findfactors(int n)
{
HashMap mpp = new HashMap<>();
Vector v = new Vector(),
v1 = new Vector();
// push all the factors in the container
for (int i = 1; i <= (int)Math.sqrt(n); i++)
{
if (n % i == 0)
{
v.add(i);
if (i != (n / i) && i != 1)
v.add(n / i);
}
}
// number of factors
int s = v.size();
// Initial maximum
int maxi = -1;
// hash-array to mark the
// pairs
int mp1_first[] = new int[n + 5],
mp1_second[] = new int[n + 5];
for (int i = 0; i < s; i++)
{
// form all the pair sums
for (int j = i; j < s; j++)
{
// if the pair sum is less than n
if (v.get(i) + v.get(j) < n)
{
// push in another container
v1.add(v.get(i) + v.get(j));
// mark the sum with the elements
// formed
mp1_first[v.get(i) +
v.get(j)] = v.get(i);
mp1_second[v.get(i) +
v.get(j)] = v.get(j);
// mark in the map that
// v.get(i)+v.get(j) is present
mpp.put(v.get(i) + v.get(j), 1);
}
}
}
// new size of all the pair sums
s = v1.size();
// iterate for all pair sum
for (int i = 0; i < s; i++)
{
// the required part
int el = n - (v1.get(i));
// if the required part is also
// present in pair sum
if (mpp.get(el) != null)
{
// find the elements with
// which the first pair is formed
int a = mp1_first[v1.get(i)];
int b = mp1_second[v1.get(i)];
// find the elements with
// which the second pair is formed
int c = mp1_first[n - v1.get(i)];
int d = mp1_second[n - v1.get(i)];
// check for previous maximum
maxi = Math.max(a * b * c * d, maxi);
}
}
if (maxi == -1)
System.out.println("Not Possible");
else
{
System.out.println("The maximum product" +
" is " + maxi);
}
}
// Driver code
public static void main(String args[])
{
int n = 50;
findfactors(n);
}
}
// This code is contributed by Arnab Kundu Python3
# Python3 program to find four factors of N
# with maximum product and sum equal to N
from math import sqrt, ceil, floor
# Function to find factors
# and to prthose four factors
def findfactors(n):
mpp = dict()
v = []
v1 = []
# push all the factors in the container
for i in range(1,ceil(sqrt(n)) + 1):
if (n % i == 0):
v.append(i)
if (i != (n // i) and i != 1):
v.append(n // i)
# number of factors
s = len(v)
# Initial maximum
maxi = -1
# hash-array to mark the
# pairs
mp1 = [0]*(n + 5)
for i in range(s):
# form all the pair sums
for j in range(i, s):
# if the pair sum is less than n
if (v[i] + v[j] < n):
# push in another container
v1.append(v[i] + v[j])
# mark the sum with the elements
# formed
mp1[v[i] + v[j]] =[v[i], v[j]]
# mark in the map that v[i]+v[j]
# is present
mpp[v[i] + v[j]] = 1
# new size of all the pair sums
s = len(v1)
# iterate for all pair sum
for i in range(s):
# the required part
el = n - (v1[i])
# if the required part is also
# present in pair sum
if (el in mpp):
# find the elements with
# which the first pair is formed
a = mp1[v1[i]][0]
b = mp1[v1[i]][1]
# find the elements with
# which the second pair is formed
c = mp1[n - v1[i]][0]
d = mp1[n - v1[i]][1]
# check for previous maximum
maxi = max(a * b * c * d, maxi)
if (maxi == -1):
print("Not Possible")
else :
print("The maximum product is ", maxi)
# Driver code
n = 50
findfactors(n)
# This code is contributed by mohit kumar 29C#
// C# program to find four factors of N
// with maximum product and sum equal to N
using System;
using System.Collections.Generic;
class GFG
{
// Function to find factors
// and to print those four factors
static void findfactors(int n)
{
Dictionary mpp = new Dictionary();
List v = new List(),
v1 = new List();
// push all the factors in the container
for (int i = 1; i <= (int)Math.Sqrt(n); i++)
{
if (n % i == 0)
{
v.Add(i);
if (i != (n / i) && i != 1)
v.Add(n / i);
}
}
// number of factors
int s = v.Count;
// Initial maximum
int maxi = -1;
// hash-array to mark the
// pairs
int []mp1_first = new int[n + 5];
int []mp1_second = new int[n + 5];
for (int i = 0; i < s; i++)
{
// form all the pair sums
for (int j = i; j < s; j++)
{
// if the pair sum is less than n
if (v[i] + v[j] < n)
{
// push in another container
v1.Add(v[i] + v[j]);
// mark the sum with the elements
// formed
mp1_first[v[i] +
v[j]] = v[i];
mp1_second[v[i] +
v[j]] = v[j];
// mark in the map that
// v[i]+v[j] is present
mpp.Add(v[i] + v[j], 1);
}
}
}
// new size of all the pair sums
s = v1.Count;
// iterate for all pair sum
for (int i = 0; i < s; i++)
{
// the required part
int el = n - (v1[i]);
// if the required part is also
// present in pair sum
if (mpp.ContainsKey(el))
{
// find the elements with
// which the first pair is formed
int a = mp1_first[v1[i]];
int b = mp1_second[v1[i]];
// find the elements with
// which the second pair is formed
int c = mp1_first[n - v1[i]];
int d = mp1_second[n - v1[i]];
// check for previous maximum
maxi = Math.Max(a * b * c * d, maxi);
}
}
if (maxi == -1)
Console.WriteLine("Not Possible");
else
{
Console.WriteLine("The maximum product" +
" is " + maxi);
}
}
// Driver code
public static void Main(String []args)
{
int n = 50;
findfactors(n);
}
}
// This code is contributed by PrinciRaj1992 输出：
The maximum product is 12500