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Generate an array of maximum sum such that each element exceeds all elements present either on its left or right

  • Last Updated : 06 Sep, 2021
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Given an array A[] consisting of N positive integers, the task is to construct an array B[] of size N having maximum possible sum of array elements satisfying the following criteria for every index i:

  • The array element B[i] must be less than or equal to A[i].
  • For every index i, B[i] must be greater than all elements present either on its left or its right.

Examples:

Input: A[] = {10, 6, 8}
Output: 10 6 6
Explanation:
Consider the array B[] as {10, 6, 6} that satisfy the given criteria as shown below having the maximum sum of elements:

  1. For array element B[0](= 10): The maximum element to the left and the right of the index 0 in the array B[] is -1 and 6 respectively and B[0](= 10) is less than or equal to -1.
  2. For array element B[1](= 6): The maximum element to the left and the right of the index 1 in the array B[] is 10 and 6 respectively and B[1](= 6) is less than or equal to 6.
  3. For array element B[2](= 6): The maximum element to the left and the right of the index 2 in the array B[] is 10 and -1 respectively and B[2](= 6) is less than or equal to -1.

Input: A[ ] = {1, 2, 3, 1}
Output: 1 2 3 1

Approach: The given problem can be solved by observing the fact that there is always a maximum element in the array which is first increasing and then monotonically decreasing. Therefore, the idea is to make every array element of the new array B[] maximum one by one and then check for the maximum sum. Follow the steps below to solve the given problem:



  • Initialize the arrays, say arrA[] and ans[] that stores the array elements A[] and the resultant array respectively.
  • Initialize a variable, say maxSum as 0 that stores the maximum sum of array elements.
  • Iterate over the range [0, N] and perform the following steps:
    • Initialize an array, say arrB[] that can stores the resultant array.
    • Assign all the array element arrB[i] in the monotonically increasing order till every index i.
    • Assign all the array element arrB[i] in the monotonically decreasing order over then range [i, N].
    • Now, find the sum of array arrB[] and if the sum is greater than maxSum then update the maxSum and the array ans[] to the current sum and current array arrB[] constructed.
  • After completing the above steps, print the array arrB[] as the resultant array.

Below is the implementation of the above approach:

C++




// C++ code for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to construct the array
// having maximum sum satisfying the
// given criteria
void maximumSumArray(int arr[], int N)
{
    // Declaration of the array arrA[]
    // and ans[]
    vector<int> arrA(N), ans(N);
 
    // Stores the maximum sum of the
    // resultant array
    int maxSum = 0;
 
    // Initialize the array arrA[]
    for (int i = 0; i < N; i++)
        arrA[i] = arr[i];
 
    // Traversing the array arrA[]
    for (int i = 0; i < N; i++) {
 
        // Initialize the array arrB[]
        vector<int> arrB(N);
        int maximum = arrA[i];
 
        // Assign the maximum element
        // to the current element
        arrB[i] = maximum;
 
        // Form the first increasing
        // till every index i
        for (int j = i - 1; j >= 0; j--) {
            arrB[j] = min(maximum, arrA[j]);
            maximum = arrB[j];
        }
 
        // Make the current element
        // as the maximum element
        maximum = arrA[i];
 
        // Forming decreasing from the
        // index i + 1 to the index N
        for (int j = i + 1; j < N; j++) {
            arrB[j] = min(maximum, arrA[j]);
            maximum = arrB[j];
        }
 
        // Initialize the sum
        int sum = 0;
 
        // Find the total sum
        for (int j = 0; j < N; j++)
            sum += arrB[j];
 
        // Check if the total sum is
        // at least the sum found
        // then make ans as ansB
        if (sum > maxSum) {
            maxSum = sum;
            ans = arrB;
        }
    }
 
    // Print the final array formed
    for (int val : ans) {
        cout << val << " ";
    }
}
 
// Driver Code
int main()
{
    int A[] = { 10, 6, 8 };
    int N = sizeof(A) / sizeof(A[0]);
    maximumSumArray(A, N);
 
    return 0;
}

Java




// Java program for the above approach
import java.io.*;
 
class GFG {
 
// Function to construct the array
// having maximum sum satisfying the
// given criteria
static void maximumSumArray(int arr[], int N)
{
    // Declaration of the array arrA[]
    // and ans[]
    int[] arrA  = new int[(N)];
    int[] ans  = new int[(N)];
 
    // Stores the maximum sum of the
    // resultant array
    int maxSum = 0;
 
    // Initialize the array arrA[]
    for (int i = 0; i < N; i++)
        arrA[i] = arr[i];
 
    // Traversing the array arrA[]
    for (int i = 0; i < N; i++) {
 
        // Initialize the array arrB[]
        int[] arrB = new int[(N)];
        int maximum = arrA[i];
 
        // Assign the maximum element
        // to the current element
        arrB[i] = maximum;
 
        // Form the first increasing
        // till every index i
        for (int j = i - 1; j >= 0; j--) {
            arrB[j] = Math.min(maximum, arrA[j]);
            maximum = arrB[j];
        }
 
        // Make the current element
        // as the maximum element
        maximum = arrA[i];
 
        // Forming decreasing from the
        // index i + 1 to the index N
        for (int j = i + 1; j < N; j++) {
            arrB[j] = Math.min(maximum, arrA[j]);
            maximum = arrB[j];
        }
 
        // Initialize the sum
        int sum = 0;
 
        // Find the total sum
        for (int j = 0; j < N; j++)
            sum += arrB[j];
 
        // Check if the total sum is
        // at least the sum found
        // then make ans as ansB
        if (sum > maxSum) {
            maxSum = sum;
            ans = arrB;
        }
    }
 
    // Print the final array formed
    for (int val : ans) {
        System.out.print(val + " ");
    }
}
 
// Driver Code
public static void main(String[] args)
{
    int A[] = { 10, 6, 8 };
    int N = A.length;
    maximumSumArray(A, N);
}
}
 
// This code is contributed by splevel62.

Python3




# Python program for the above approach;
 
# Function to construct the array
# having maximum sum satisfying the
# given criteria
def maximumSumArray(arr, N):
     
    # Declaration of the array arrA[]
    # and ans[]
    arrA = [0] * N
    ans = [0] * N
 
    # Stores the maximum sum of the
    # resultant array
    maxSum = 0;
 
    # Initialize the array arrA[]
    for i in range(N):
        arrA[i] = arr[i];
 
    # Traversing the array arrA[]
    for i in range(N):
         
        # Initialize the array arrB[]
        arrB = [0] * N
        maximum = arrA[i];
 
        # Assign the maximum element
        # to the current element
        arrB[i] = maximum;
 
        temp = 0
         
        # Form the first increasing
        # till every index i
        for j in range(i - 1, -1, -1):
            arrB[j] = min(maximum, arrA[j]);
            maximum = arrB[j];
            temp = j
         
 
        # Make the current element
        # as the maximum element
        maximum = arrA[i];
 
        # Forming decreasing from the
        # index i + 1 to the index N
        for j in range(i + 1, N):
            arrB[j] = min(maximum, arrA[j]);
            maximum = arrB[j];
         
 
        # Initialize the sum
        sum = 0;
 
        # Find the total sum
        for j in range(N):
            sum += arrB[j];
 
        # Check if the total sum is
        # at least the sum found
        # then make ans as ansB
        if (sum > maxSum):
            maxSum = sum;
            ans = arrB;
         
    # Print the final array formed
    for val in ans:
        print(val);
     
# Driver Code
A = [ 10, 6, 8 ];
N = len(A)
 
maximumSumArray(A, N);
 
# This code is contributed by _Saurabh_Jaiswal

C#




// C# code for the above approach
using System;
using System.Collections.Generic;
 
class GFG{
 
// Function to construct the array
// having maximum sum satisfying the
// given criteria
static void maximumSumArray(int []arr, int N)
{
    // Declaration of the array arrA[]
    // and ans[]
    int []arrA = new int[N];
    int []ans = new int[N];
 
    // Stores the maximum sum of the
    // resultant array
    int maxSum = 0;
 
    // Initialize the array arrA[]
    for (int i = 0; i < N; i++)
        arrA[i] = arr[i];
 
    // Traversing the array arrA[]
    for (int i = 0; i < N; i++) {
 
        // Initialize the array arrB[]
        int []arrB = new int[N];
        int maximum = arrA[i];
 
        // Assign the maximum element
        // to the current element
        arrB[i] = maximum;
 
        // Form the first increasing
        // till every index i
        for (int j = i - 1; j >= 0; j--) {
            arrB[j] = Math.Min(maximum, arrA[j]);
            maximum = arrB[j];
        }
 
        // Make the current element
        // as the maximum element
        maximum = arrA[i];
 
        // Forming decreasing from the
        // index i + 1 to the index N
        for (int j = i + 1; j < N; j++) {
            arrB[j] = Math.Min(maximum, arrA[j]);
            maximum = arrB[j];
        }
 
        // Initialize the sum
        int sum = 0;
 
        // Find the total sum
        for (int j = 0; j < N; j++)
            sum += arrB[j];
 
        // Check if the total sum is
        // at least the sum found
        // then make ans as ansB
        if (sum > maxSum) {
            maxSum = sum;
            ans = arrB;
        }
    }
 
    // Print the final array formed
    foreach (int val in ans) {
        Console.Write(val + " ");
    }
}
 
// Driver Code
public static void Main()
{
    int []A = { 10, 6, 8 };
    int N = A.Length;
    maximumSumArray(A, N);
}
}
 
// This code is contributed by SURENDRA_GANGWAR.

Javascript




<script>
 
// JavaScript program for the above approach;
 
// Function to construct the array
// having maximum sum satisfying the
// given criteria
function maximumSumArray(arr, N)
{
     
    // Declaration of the array arrA[]
    // and ans[]
    let arrA = new Array(N);
    let ans = new Array(N);
 
    // Stores the maximum sum of the
    // resultant array
    let maxSum = 0;
 
    // Initialize the array arrA[]
    for(let i = 0; i < N; i++)
        arrA[i] = arr[i];
 
    // Traversing the array arrA[]
    for(let i = 0; i < N; i++)
    {
         
        // Initialize the array arrB[]
        let arrB = new Array(N);
        let maximum = arrA[i];
 
        // Assign the maximum element
        // to the current element
        arrB[i] = maximum;
 
        // Form the first increasing
        // till every index i
        for(let j = i - 1; j >= 0; j--)
        {
            arrB[j] = Math.min(maximum, arrA[j]);
            maximum = arrB[j];
        }
 
        // Make the current element
        // as the maximum element
        maximum = arrA[i];
 
        // Forming decreasing from the
        // index i + 1 to the index N
        for(let j = i + 1; j < N; j++)
        {
            arrB[j] = Math.min(maximum, arrA[j]);
            maximum = arrB[j];
        }
 
        // Initialize the sum
        let sum = 0;
 
        // Find the total sum
        for(let j = 0; j < N; j++)
            sum += arrB[j];
 
        // Check if the total sum is
        // at least the sum found
        // then make ans as ansB
        if (sum > maxSum)
        {
            maxSum = sum;
            ans = arrB;
        }
    }
 
    // Print the final array formed
    for(let val of ans)
    {
        document.write(val + " ");
    }
}
 
// Driver Code
let A = [ 10, 6, 8 ];
let N = A.length;
 
maximumSumArray(A, N);
 
// This code is contributed by Potta Lokesh
 
</script>
Output: 
10 6 6

 

Time Complexity: O(N2)
Auxiliary Space: O(N)

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