Maximum Subarray Sum (Kadane)
Problem
Read an array. Print the largest sum of a non-empty continuous part (subarray).
Constraints
- 1 <= n <= 10^5
- -10^4 <= a[i] <= 10^4
Examples
Input
9 -2 1 -3 4 -1 2 1 -5 4
Output
6
Solutions
At each element we decide: continue the old subarray, or start fresh. A negative old sum is never worth keeping.
/*
* Problem : Process an array.
* Input : n, then n integers.
* Output : The best sum.
* Approach: One pass.
* Time : O(n)
* Space : O(1)
* Java : 8 or newer.
*/
import java.util.Scanner;
public class Main {
// This method solves the task. It receives the input and returns the answer.
static long solve(int[] a) {
// Step 1: current = best sum of a subarray that ends at this position.
long current = a[0];
long best = a[0];
for (int i = 1; i < a.length; i++) {
// Step 2: Either extend the previous subarray, or start a new one at this element.
current = Math.max(a[i], current + a[i]);
// Step 3: Keep the best value seen so far.
best = Math.max(best, current);
}
return best;
}
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
int size = scanner.nextInt();
int[] a = new int[size];
for (int i = 0; i < size; i++) {
a[i] = scanner.nextInt();
}
System.out.println(solve(a));
}
}
Hints (1)
- When is it better to start a new subarray?