给定长度为N的两个数组arr []和arr2 [] ，任务是在重新排列第二个数组后，找到由两个数组的相同索引元素的乘积组成的所有子数组的最小和。
注意：由于答案可能非常大，请以10 9 + 7模输出答案。
例子：
Input: arr[] = {1, 2}, arr2[] = {2, 3}
Output: 14
Explanation:
Rearrange the arr2[] to {3, 2}
Therefore, the product of same indexed elements of two arrays becomes {3, 4}.
Possible subarrays are {3}, {4}, {3, 4}
Sum of the subarrays = 3 + 4 + 7 = 14.
Input: arr[] = {1, 2, 3}, arr2[] = {2, 3, 2}
Output: 43
Explanation:
Rearrange arr2[] to {3, 2, 2}
Therefore, the product of thesame indexed elements of two arrays becomes {3, 4, 6}.
Therefore, sum of all the subarrays = 3 + 4 + 6 + 7 + 10 + 13 = 43
方法：
可以观察到，第i个元素出现在(i + 1)*(n – i)子数组中。因此，任务是使(i +1)*(n – i)* a [i] * b [i]之和最大。请按照以下步骤解决问题：
- 由于arr2 []的元素只能重新排列，因此(i +1)*(n – i)* a [i]的值对于每个第i个元素都是恒定的。
- 因此，为所有指标计算(i +1)*(n – i)* a [i]的值，然后对乘积进行排序。
- 排序的阵列ARR2 []降序排列。
- 对于每个第i个索引，以降序计算(i +1)*(n – i)* a [i]和升序为arr2 [i]的乘积之和。
下面是上述方法的实现：
C++
// C++ Program to implement
// the above approach
#include
#define ll long long
using namespace std;
const int mod = (int)1e9 + 7;
// Returns the greater of
// the two values
bool comp(ll a, ll b)
{
if (a > b)
return true;
else
return false;
}
// Function to rearrange the second array such
// that the sum of its product of same indexed
// elements from both the arrays is minimized
ll findMinValue(vector& a, vector& b)
{
int n = a.size();
// Stores (i - 1) * (n - i) * a[i]
// for every i-th element
vector pro(n);
for (int i = 0; i < n; ++i) {
// Updating the value of pro
// according to the function
pro[i] = ((ll)(i + 1) * (ll)(n - i));
pro[i] *= (1LL * a[i]);
;
}
// Sort the array in revese order
sort(b.begin(), b.end(), comp);
// Sort the products
sort(pro.begin(), pro.end());
ll ans = 0;
for (int i = 0; i < n; ++i) {
// Updating the ans
ans += (pro[i] % mod * b[i]) % mod;
ans %= mod;
}
// Return the ans
return ans;
}
// Driver code
int main()
{
vector a = { 1, 2, 3 };
vector b = { 2, 3, 2 };
// Function call
cout << findMinValue(a, b) << endl;
} Java
// Java program to implement
// the above approach
import java.util.*;
class GFG{
static int mod = (int)1e9 + 7;
// Function to rearrange the second array such
// that the sum of its product of same indexed
// elements from both the arrays is minimized
static int findMinValue(int [] a, int []b)
{
int n = a.length;
// Stores (i - 1) * (n - i) * a[i]
// for every i-th element
int [] pro = new int[n];
for(int i = 0; i < n; ++i)
{
// Updating the value of pro
// according to the function
pro[i] = ((i + 1) * (n - i));
pro[i] *= (1L * a[i]);
;
}
// Sort the array in revese order
Integer[] input = Arrays.stream(b).boxed(
).toArray(Integer[]::new);
Arrays.sort(input, (x, y) -> y - x);
b = Arrays.stream(input).mapToInt(
Integer::intValue).toArray();
// Sort the products
Arrays.sort(pro);
int ans = 0;
for(int i = 0; i < n; ++i)
{
// Updating the ans
ans += (pro[i] % mod * b[i]) % mod;
ans %= mod;
}
// Return the ans
return ans;
}
// Driver code
public static void main(String[] args)
{
int []a = { 1, 2, 3 };
int []b = { 2, 3, 2 };
// Function call
System.out.print(findMinValue(a, b) + "\n");
}
}
// This code is contributed by 29AjayKumarPython3
# Python3 Program to implement
# the above approach
mod = 1e9 +7
# Function to rearrange
# the second array such
# that the sum of its
# product of same indexed
# elements from both
# the arrays is minimized
def findMinValue(a, b):
n = len(a)
# Stores (i - 1) * (n - i) * a[i]
# for every i-th element
pro = [0] * (n)
for i in range (n):
# Updating the value of pro
# according to the function
pro[i] = ((i + 1) * (n - i))
pro[i] *= (a[i])
# Sort the array in revese order
b.sort(reverse = True)
# Sort the products
pro.sort()
ans = 0
for i in range (n):
# Updating the ans
ans += (pro[i] % mod * b[i]) % mod
ans %= mod
# Return the ans
return ans
# Driver code
if __name__ == "__main__":
a = [1, 2, 3]
b = [2, 3, 2]
# Function call
print (int(findMinValue(a, b)))
# This code is contributed by Chitranayal输出：
43
时间复杂度： O(N log N)
辅助空间： O(N)