给定一个数字数组,求出该数组的递增子序列的数字乘以该乘积所形成的最大乘积。
注意:单个数字应该是大小为1的递增子序列。
例子:
Input : arr[] = { 3, 100, 4, 5, 150, 6 }
Output : 45000
Maximum product is 45000 formed by the
increasing subsequence 3, 100, 150. Note
that the longest increasing subsequence
is different {3, 4, 5, 6}
Input : arr[] = { 10, 22, 9, 33, 21, 50, 41, 60 }
Output : 21780000
Maximum product is 21780000 formed by the
increasing subsequence 10, 22, 33, 50, 60.
先决条件:最长递增子序列
方法:使用动态方法来维护表mpis []。 mpis [i]的值存储以arr [i]结尾的乘积最大乘积。最初,所有递增子序列表的值都初始化为arr [i]。我们使用类似于LIS问题的递归方法来找到结果。
C++
/* Dynamic programming C++ implementation of maximum
product of an increasing subsequence */
#include
#define ll long long int
using namespace std;
// Returns product of maximum product increasing
// subsequence.
ll lis(ll arr[], ll n)
{
ll mpis[n];
/* Initialize MPIS values */
for (int i = 0; i < n; i++)
mpis[i] = arr[i];
/* Compute optimized MPIS values considering
every element as ending element of sequence */
for (int i = 1; i < n; i++)
for (int j = 0; j < i; j++)
if (arr[i] > arr[j] && mpis[i] < (mpis[j] * arr[i]))
mpis[i] = mpis[j] * arr[i];
/* Pick maximum of all product values */
return *max_element(mpis, mpis + n);
}
/* Driver program to test above function */
int main()
{
ll arr[] = { 3, 100, 4, 5, 150, 6 };
ll n = sizeof(arr) / sizeof(arr[0]);
printf("%lld", lis(arr, n));
return 0;
}
Java
/* Dynamic programming Java implementation
of maximum product of an increasing
subsequence */
import java.util.Arrays;
import java.util.Collections;
class GFG {
// Returns product of maximum product
// increasing subsequence.
static int lis(int[] arr, int n)
{
int[] mpis = new int[n];
int max = Integer.MIN_VALUE;
/* Initialize MPIS values */
for (int i = 0; i < n; i++)
mpis[i] = arr[i];
/* Compute optimized MPIS values
considering every element as ending
element of sequence */
for (int i = 1; i < n; i++)
for (int j = 0; j < i; j++)
if (arr[i] > arr[j] && mpis[i]
< (mpis[j] * arr[i]))
mpis[i] = mpis[j] * arr[i];
/* Pick maximum of all product values
using for loop*/
for (int k = 0; k < mpis.length; k++)
{
if (mpis[k] > max) {
max = mpis[k];
}
}
return max;
}
// Driver program to test above function
static public void main(String[] args)
{
int[] arr = { 3, 100, 4, 5, 150, 6 };
int n = arr.length;
System.out.println(lis(arr, n));
}
}
// This code is contributed by parashar.
Python3 highlight=# Dynamic programming Python3 implementation
# of maximum product of an increasing
# subsequence
# Returns product of maximum product
# increasing subsequence.
def lis (arr, n ):
mpis =[0] * (n)
# Initialize MPIS values
for i in range(n):
mpis[i] = arr[i]
# Compute optimized MPIS values
# considering every element as
# ending element of sequence
for i in range(1, n):
for j in range(i):
if (arr[i] > arr[j] and
mpis[i] < (mpis[j] * arr[i])):
mpis[i] = mpis[j] * arr[i]
# Pick maximum of all product values
return max(mpis)
# Driver code to test above function
arr = [3, 100, 4, 5, 150, 6]
n = len(arr)
print( lis(arr, n))
# This code is contributed by "Sharad_Bhardwaj".
C#
/* Dynamic programming C# implementation
of maximum product of an increasing
subsequence */
using System;
using System.Linq;
public class GFG {
// Returns product of maximum product
// increasing subsequence.
static long lis(long[] arr, long n)
{
long[] mpis = new long[n];
/* Initialize MPIS values */
for (int i = 0; i < n; i++)
mpis[i] = arr[i];
/* Compute optimized MPIS values considering
every element as ending element of sequence */
for (int i = 1; i < n; i++)
for (int j = 0; j < i; j++)
if (arr[i] > arr[j] && mpis[i] < (mpis[j] * arr[i]))
mpis[i] = mpis[j] * arr[i];
/* Pick maximum of all product values */
return mpis.Max();
}
/* Driver program to test above function */
static public void Main()
{
long[] arr = { 3, 100, 4, 5, 150, 6 };
long n = arr.Length;
Console.WriteLine(lis(arr, n));
}
}
// This code is contributed by vt_m.
PHP
$arr[$j] && $mpis[$i] < ($mpis[$j] * $arr[$i]))
$mpis[$i] = $mpis[$j] * $arr[$i];
/* Pick maximum of all product values */
return max($mpis);
}
/* Driver program to test above function */
$arr = array ( 3, 100, 4, 5, 150, 6 );
$n = sizeof($arr) / sizeof($arr[0]);
echo lis($arr, $n);
return 0;
?>
Javascript
输出:
45000
时间复杂度: O(n ^ 2)
辅助空间: O(n)