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Maximize the sum of array by multiplying prefix of array with -1 in C++
We are given an integer array and the task is to firstly fetch the prefix of an array and then multiply it with -1, secondly calculate the prefix sum of an array and lastly find the maximum sum from the prefix array generated.
Prefix array is generated as −
First element of prefixArray[0] = first element of an array
Second element of prefixArray[1] = prefixArray[0] + arr[1]
Third element of prefixArray[2] = prefixArray[1] + arr[2]
Fourth element of prefixArray[3] = prefixArray[2] + arr[3] …..etc.
Let us see various input output scenarios for this -
In − int arr[] = {2, 4, 1, 5, 2}
Out − Prefix array is: -2 2 3 8 10 Maximize the sum of array by multiplying prefix of array with -1 are: 21
Explanation − we are given with an integer array. So we will firstly fetch the prefix of an array which is 2 and multiple it with -1. So, the new array will be {-2, 4, 1, 5, 2}. Now, we will form the prefix array which is {-2, 2, 3, 8, 10}. The last step is to maximize the sum as -2+2+3+8+`0 = 21 which is the final output.
In − int arr[] = {-1, 4, 2, 1, -9, 6};
Out − Prefix array is: 1 5 7 8 -1 5 Maximize the sum of array by multiplying prefix of array with -1 are: 19
Explanation − we are given with an integer array. So we will firstly fetch the prefix of an array which is -1 and multiple it with -1. So, the new array will be {1, 4, 2, 1, -9, 6}. Now, we will form the prefix array which is {1, 5, 7, 8, -1, 5}. The last step is to maximize the sum as 1+5+8+5 = 19 which is the final output.
Approach used in the below program is as follows −
Declare an integer array and a temporary variable as x to -1 then set arr[0] to arr[0] * x.
Calculate the size of an array. Declare a prefix array as prefix_arry[size]. Call a function create_prefix_arr(arr, size, prefix_array) to generate the prefix array from the given array. Print the prefix array
Call the function maximize_sum(prefix_array, size) that will store the maximum sum of the array.
Inside the function void create_prefix_arr(int arr[], int size, int prefix_array[])
Set prefix_array[0] to arr[0].
Start loop FOR from i to 0 till the size of an array. Inside the loop, set prefix_array[i] to prefix_array[i-1] + arr[i].
Inside the function int maximize_sum(int prefix_array[], int size)
Declare a temporary variable as temp and set it to -1.
Start loop FOR from i to 0 till the size of an array. Inside the loop, set temp as max(temp, prefix_array[i])
Declare an array as arr[temp +1] and initialise all the elements of an array with 0.
Start loop FOR from i to 0 till the size of an array. Inside the loop, set arr[prefix_array[i]]++
Declare a temporary variable as max_sum and set it to 0. Declare a variable as int i to temp
Start loop WHILE i>0. Check IF arr[i] > 0 then set max_sum to max_sum + i and decrement the arr[i-1]-- and decrement the arr[i]--. ELSE, decrement the i by 1.
Return max_sum.
Example
#include <bits/stdc++.h>
using namespace std;
#define Max_size 5
//create the prefix array
void create_prefix_arr(int arr[], int size, int prefix_array[]) {
prefix_array[0] = arr[0];
for(int i=0; i<size; i++) {
prefix_array[i] = prefix_array[i-1] + arr[i];
}
}
//find the maximum sum of prefix array
int maximize_sum(int prefix_array[], int size) {
int temp = -1;
for(int i = 0; i < size; i++) {
temp = max(temp, prefix_array[i]);
}
int arr[temp + 1];
memset(arr, 0, sizeof(arr));
for(int i = 0; i < size; i++) {
arr[prefix_array[i]]++;
}
int max_sum = 0;
int i = temp;
while(i>0) {
if(arr[i] > 0) {
max_sum = max_sum + i;
arr[i-1]--;
arr[i]--;
} else {
i--;
}
}
return max_sum;
}
int main() {
int arr[] = {2, 4, 1, 5, 2};
int x = -1;
arr[0] = arr[0] * x;
int size = sizeof(arr) / sizeof(arr[0]);
int prefix_array[size];
//call function to create a prefix array
create_prefix_arr(arr, size, prefix_array);
//print the prefix array
cout<<"Prefix array is: ";
for(int i = 0; i < size; i++) {
cout << prefix_array[i] << " ";
}
//print the maximum sum of prefix array
cout<<"\nMaximize the sum of array by multiplying prefix of array with -1 are:" <<maximize_sum(prefix_array, size);
return 0;
}Output
If we run the above code it will generate the following Output
Prefix array is: -2 2 3 8 10 Maximize the sum of array by multiplying prefix of array with -1 are: 21
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