P1115 Maximum sub-segment sum
Topic link: https://www.luogu.com.cn/problem/P1115
Title description
Given a sequence a of length n, select a continuous and non-empty segment to maximize the sum.
Input format
The first line is an integer, indicating the length of the sequence n.
The second line has n integers, and the i-th integer represents the i-th number ai of the sequence.
Output format
Output an integer on a line to indicate the answer.
Sample input and output
Input #1
7
2 -4 3 -1 2 -4 3
Output #1
4
Explanation/Prompt
Example 1 Explanation
Select [3, 5] subsection {3,−1,2}, and the sum is 4.
Data scale and agreement
For 40% of the data, ensure that n≤ 2×10^3.
For 100% data, ensure that 1≤n≤2×10^5, −10^4 ≤ai ≤10^4.
Problem-solving ideas:
One-dimensional prefix sum: f[i] = max(w[i], w[i] + f[i-1])
code show as below:
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
long[] w = new long[200010];
long[] f = new long[200010];
int n = sc.nextInt();
long ans = -100000010;
for (int i = 1; i <= n; i++) {
w[i] = sc.nextLong();
f[i] = Math.max(w[i], w[i] + f[i - 1]);
ans = Math.max(ans, f[i]);
}
System.out.println(ans);
}
}