Maximum subarray sum in an array created after repeated concatenation
Last Updated :
02 Nov, 2024
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Given an array and a number k, find the largest sum of contiguous array in the modified array which is formed by repeating the given array k times.
Examples :
Input : arr[] = {-1, 10, 20}, k = 2
Output : 59
After concatenating array twice, we get {-1, 10, 20, -1, 10, 20} which has maximum subarray sum as 59.
Input : arr[] = {-1, -2, -3}, k = 3
Output : -1
Naive Approach – O(nk) Time and O(nk) Space
A simple solution is to create an array of size n*k, then run Kadane’s algorithm for the whole array.
Expected Approach – O(nk) Time and O(1) Space
An efficient solution is to run a loop on same array and use modular arithmetic to move back beginning after end of array.
Below is the implementation:
#include <bits/stdc++.h>
using namespace std;
// Returns sum of maximum sum subarray created
// after concatenating a[0..n-1] k times.
int maxSubArraySumRepeated(vector<int>& arr, int k) {
int n = arr.size();
int maxSoFar = INT_MIN, maxEndingHere = 0;
for (int i = 0; i < n * k; i++) {
// Use modular arithmetic to get the next element
maxEndingHere += arr[i % n];
maxSoFar = max(maxSoFar, maxEndingHere);
if (maxEndingHere < 0)
maxEndingHere = 0;
}
return maxSoFar;
}
/* Driver program to test maxSubArraySum */
int main() {
vector<int> arr = {10, 20, -30, -1};
int k = 3;
cout << "Maximum contiguous sum is "
<< maxSubArraySumRepeated(arr, k);
return 0;
}
// Returns sum of maximum sum subarray created
// after concatenating a[0..n-1] k times.
#include <stdio.h>
#include <limits.h>
int maxSubArraySumRepeated(int arr[], int n, int k) {
int maxSoFar = INT_MIN, maxEndingHere = 0;
for (int i = 0; i < n * k; i++) {
// Use modular arithmetic to get the next element
maxEndingHere += arr[i % n];
if (maxEndingHere > maxSoFar) {
maxSoFar = maxEndingHere;
}
if (maxEndingHere < 0) {
maxEndingHere = 0;
}
}
return maxSoFar;
}
// Driver program to test maxSubArraySumRepeated
int main() {
int arr[] = {10, 20, -30, -1};
int k = 3;
int n = sizeof(arr) / sizeof(arr[0]);
printf("Maximum contiguous sum is %d\n", maxSubArraySumRepeated(arr, n, k));
return 0;
}
// Returns sum of maximum sum subarray created
// after concatenating a[0..n-1] k times.
public class GfG {
public static int maxSubArraySumRepeated(int[] arr, int k) {
int n = arr.length;
int maxSoFar = Integer.MIN_VALUE, maxEndingHere = 0;
for (int i = 0; i < n * k; i++) {
// Use modular arithmetic to get the next element
maxEndingHere += arr[i % n];
maxSoFar = Math.max(maxSoFar, maxEndingHere);
if (maxEndingHere < 0)
maxEndingHere = 0;
}
return maxSoFar;
}
// Driver program to test maxSubArraySumRepeated
public static void main(String[] args) {
int[] arr = {10, 20, -30, -1};
int k = 3;
System.out.println("Maximum contiguous sum is " + maxSubArraySumRepeated(arr, k));
}
}
# Returns sum of maximum sum subarray created
# after concatenating a[0..n-1] k times.
def max_subarray_sum_repeated(arr, k):
n = len(arr)
max_so_far = float('-inf')
max_ending_here = 0
for i in range(n * k):
# Use modular arithmetic to get the next element
max_ending_here += arr[i % n]
max_so_far = max(max_so_far, max_ending_here)
if max_ending_here < 0:
max_ending_here = 0
return max_so_far
# Driver program to test max_subarray_sum_repeated
arr = [10, 20, -30, -1]
k = 3
print("Maximum contiguous sum is", max_subarray_sum_repeated(arr, k))
// Returns sum of maximum sum subarray created
// after concatenating a[0..n-1] k times.
using System;
using System.Linq;
class Program {
public static int MaxSubArraySumRepeated(int[] arr, int k) {
int n = arr.Length;
int maxSoFar = int.MinValue, maxEndingHere = 0;
for (int i = 0; i < n * k; i++) {
// Use modular arithmetic to get the next element
maxEndingHere += arr[i % n];
maxSoFar = Math.Max(maxSoFar, maxEndingHere);
if (maxEndingHere < 0)
maxEndingHere = 0;
}
return maxSoFar;
}
// Driver program to test MaxSubArraySumRepeated
static void Main() {
int[] arr = {10, 20, -30, -1};
int k = 3;
Console.WriteLine("Maximum contiguous sum is " + MaxSubArraySumRepeated(arr, k));
}
}
// Returns sum of maximum sum subarray created
// after concatenating a[0..n-1] k times.
function maxSubArraySumRepeated(arr, k) {
let n = arr.length;
let maxSoFar = Number.MIN_SAFE_INTEGER, maxEndingHere = 0;
for (let i = 0; i < n * k; i++) {
// Use modular arithmetic to get the next element
maxEndingHere += arr[i % n];
maxSoFar = Math.max(maxSoFar, maxEndingHere);
if (maxEndingHere < 0)
maxEndingHere = 0;
}
return maxSoFar;
}
// Driver program to test maxSubArraySumRepeated
let arr = [10, 20, -30, -1];
let k = 3;
console.log("Maximum contiguous sum is " + maxSubArraySumRepeated(arr, k));
Output
Maximum contiguous sum is 30
