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
A simple solution is to create an array of size n*k, then run Kadane’s algorithm. Time complexity would be O(nk) and auxiliary space would be O(n*k)
A better solution is to run a loop on same array and use modular arithmetic to move back beginning after end of array.
C++
// C++ program to print largest contiguous // array sum when array is created after // concatenating a small array k times. #include<bits/stdc++.h> using namespace std; // Returns sum of maximum sum subarray created // after concatenating a[0..n-1] k times. int maxSubArraySumRepeated(int a[], int n, int k) { int max_so_far = INT_MIN, max_ending_here = 0; for (int i = 0; i < n*k; i++) { // This is where it differs from Kadane's // algorithm. We use modular arithmetic to // find next element. max_ending_here = max_ending_here + a[i%n]; if (max_so_far < max_ending_here) max_so_far = max_ending_here; if (max_ending_here < 0) max_ending_here = 0; } return max_so_far; } /*Driver program to test maxSubArraySum*/int main() { int a[] = {10, 20, -30, -1}; int n = sizeof(a)/sizeof(a[0]); int k = 3; cout << "Maximum contiguous sum is " << maxSubArraySumRepeated(a, n, k); return 0; } |
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Java
// Java program to print largest contiguous // array sum when array is created after // concatenating a small array k times. import java.io.*; class GFG { // Returns sum of maximum sum // subarray created after // concatenating a[0..n-1] k times. static int maxSubArraySumRepeated(int a[], int n, int k) { int max_so_far = 0; int INT_MIN, max_ending_here=0; for (int i = 0; i < n*k; i++) { // This is where it differs from // Kadane's algorithm. We use modular // arithmetic to find next element. max_ending_here = max_ending_here + a[i % n]; if (max_so_far < max_ending_here) max_so_far = max_ending_here; if (max_ending_here < 0) max_ending_here = 0; } return max_so_far; } // Driver program to test maxSubArraySum public static void main (String[] args) { int a[] = {10, 20, -30, -1}; int n = a.length; int k = 3; System.out.println("Maximum contiguous sum is " + maxSubArraySumRepeated(a, n, k)); } } // This code is contributed by vt_m |
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Python3
# Python program to print # largest contiguous # array sum when array # is created after # concatenating a small # array k times. # Returns sum of maximum # sum subarray created # after concatenating # a[0..n-1] k times. def maxSubArraySumRepeated(a, n, k): max_so_far = -2147483648 max_ending_here = 0 for i in range(n*k): # This is where it # differs from Kadane's # algorithm. We use # modular arithmetic to # find next element. max_ending_here = max_ending_here + a[i%n] if (max_so_far < max_ending_here): max_so_far = max_ending_here if (max_ending_here < 0): max_ending_here = 0 return max_so_far # Driver program # to test maxSubArraySum a = [10, 20, -30, -1] n = len(a) k = 3 print("Maximum contiguous sum is ", maxSubArraySumRepeated(a, n, k)) # This code is contributed # by Anant Agarwal. |
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C#
// C# program to print largest contiguous // array sum when array is created after // concatenating a small array k times. using System; class GFG { // Returns sum of maximum sum // subarray created after // concatenating a[0..n-1] k times. static int maxSubArraySumRepeated(int []a, int n, int k) { int max_so_far = 0; int max_ending_here=0; for (int i = 0; i < n * k; i++) { // This is where it differs from // Kadane's algorithm. We use modular // arithmetic to find next element. max_ending_here = max_ending_here + a[i % n]; if (max_so_far < max_ending_here) max_so_far = max_ending_here; if (max_ending_here < 0) max_ending_here = 0; } return max_so_far; } // Driver Code public static void Main () { int []a = {10, 20, -30, -1}; int n = a.Length; int k = 3; Console.Write("Maximum contiguous sum is " + maxSubArraySumRepeated(a, n, k)); } } // This code is contributed by nitin mittal. |
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PHP
<?php // PHP program to print largest contiguous // array sum when array is created after // concatenating a small array k times. // Returns sum of maximum // sum subarray created // after concatenating // a[0..n-1] k times. function maxSubArraySumRepeated($a, $n, $k) { $INT_MIN=0; $max_so_far = $INT_MIN; $max_ending_here = 0; for ($i = 0; $i < $n*$k; $i++) { // This is where it differs // from Kadane's algorithm. // We use modular arithmetic // to find next element. $max_ending_here = $max_ending_here + $a[$i % $n]; if ($max_so_far < $max_ending_here) $max_so_far = $max_ending_here; if ($max_ending_here < 0) $max_ending_here = 0; } return $max_so_far; } // Driver Code $a = array(10, 20, -30, -1); $n = sizeof($a); $k = 3; echo "Maximum contiguous sum is " , maxSubArraySumRepeated($a, $n, $k); // This code is contributed by nitin mittal. ?> |
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Output :
Maximum contiguous sum is 30
Can we use the repeating property of array to get a better solution ?
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Improved By : nitin mittal
