Container With Most Water
Problem
The array gives the heights of vertical lines at the positions 0, 1, 2, .... Choose two lines. Together with the x-axis they form a container. The water amount is min(height1, height2) * distance between the lines. Print the largest amount.
Constraints
- 2 <= n <= 10^5
Examples
Input
9 1 8 6 2 5 4 8 3 7
Output
49
Solutions
Checking all pairs costs O(n^2). Starting with the widest pair and moving the shorter line inward loses nothing: with the same short line and a smaller width, the water can only be less.
/*
* Problem : Process an array.
* Input : n, then n integers.
* Output : The largest amount.
* Approach: Two pointers from the ends.
* 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: Start with the widest container: the first and the last line.
int left = 0;
int right = a.length - 1;
long best = 0;
while (left < right) {
// Step 2: The water level is the shorter line. The width is the distance.
long water = (long) Math.min(a[left], a[right]) * (right - left);
best = Math.max(best, water);
// Step 3: Move the shorter line inward. Moving the taller line can never give a bigger container.
if (a[left] < a[right]) {
left++;
} else {
right--;
}
}
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)
- Why move the shorter line?