Range Addition with a Difference Array
Problem
An array of n zeros is given. Then k updates come, each is l r v: add v to every element from index l to index r (0-based, both included). Print the final array after all updates. Input: the first line is n, and then one update per line.
Constraints
- 1 <= n <= 10^5
- 1 <= k <= 10^5
Examples
Input
5 1 3 2 2 4 3 0 2 -2
Output
-2 0 3 5 3
Solutions
Each update touches only two cells of the difference array: +v at l and -v after r. At the end, one running sum rebuilds the array. The cost is O(n + k) instead of O(n k).
/*
* Problem : Apply the updates.
* Input : n and the updates.
* Output : The final array.
* Approach: Difference array
* Time : O(n + k)
* Space : O(n)
* Java : 8 or newer.
*/
import java.util.Scanner;
import java.util.Arrays;
import java.util.stream.Collectors;
public class Main {
// This method solves the task. It receives the input and returns the answer.
static int[] solve(String[] lines) {
int n = Integer.parseInt(lines[0]);
// Step 1: diff[i] says how much the value changes when we go from index i - 1 to index i.
int[] diff = new int[n + 1];
for (int i = 1; i < lines.length; i++) {
String[] part = lines[i].split(" ");
int left = Integer.parseInt(part[0]);
int right = Integer.parseInt(part[1]);
int value = Integer.parseInt(part[2]);
// Step 2: An update changes only two places: it starts at left and stops after right.
diff[left] += value;
diff[right + 1] -= value;
}
// Step 3: A running sum of diff gives the real array.
int[] result = new int[n];
int running = 0;
for (int i = 0; i < n; i++) {
running += diff[i];
result[i] = running;
}
return result;
}
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
java.util.List<String> all = new java.util.ArrayList<>();
while (scanner.hasNextLine()) {
String line = scanner.nextLine().trim();
if (!line.isEmpty()) {
all.add(line);
}
}
String[] lines = all.toArray(new String[0]);
System.out.println(Arrays.stream(solve(lines)).mapToObj(String::valueOf).collect(Collectors.joining(" ")));
}
}
Hints (1)
- Why does -v after r stop the update?