Understand Minimum Number of Operations to Move All Balls to Each Box Problem

Problem Name: Minimum Number of Operations to Move All Balls to Each Box
Problem Description:

Problem: Minimum Number of Operations to Move All Balls to Each Box

You have n boxes represented as a binary string boxes, where:

  • '0' means the box is empty.
  • '1' means the box contains one ball.

You can move a ball from one box to an adjacent box in one operation. A box is adjacent if the difference in their indices is 1.

You need to calculate an array answer of size n where:

  • answer[i] is the minimum number of operations required to move all balls to the ith box, considering the initial positions of the balls.

Examples

Example 1:

Input:
boxes = "110"
Output:
[1, 1, 3]

Boxes

The number of operations required to move all balls to the 0th index box from the initial state = 1.

Boxes

The number of operations required to move all balls to the 1st index box from the initial state = 1.

Boxes

The number of operations required to move all balls to the 3rd index box from the initial state = 2.

Boxes

The total number of operations required to move all balls to each index box from the initial state is given by the array:

ans = [1, 1, 3]

Explanation:

  1. For the first box: Move one ball from the second box → 1 operation.
  2. For the second box: Move one ball from the first box → 1 operation.
  3. For the third box:
    • Move one ball from the first box → 2 operations.
    • Move one ball from the second box → 1 operation.
      Total = 3 operations.

Example 2:

Input:
boxes = "001011"
Output:
[11, 8, 5, 4, 3, 4]

Constraints

n=boxes.lengthn = \text{boxes.length} 1≤n≤20001 \leq n \leq 2000 boxes[i]∈{0,1}\text{boxes}[i] \in \{ 0 , 1 \}
Category:
  • Leetcode Problem of the Day
  • Arrays
  • Strings
Programming Language:
  • Java
Reference Link:

https://leetcode.com/problems/minimum-number-of-operations-to-move-all-balls-to-each-box/description/?envType=daily-question&envId=2025-01-06

Online IDE

Scroll down for output
Java
Output:
Loading component...
Loading component...
Tracking code (View only. In case you want to track the code, click this button):
Main Function:
Main Function is not defined.
Helper Function:
INPUT:  boxes = "110"
OUTPUT:  [1, 1, 3]
public static int[] minOperations(String boxes) {
int n = boxes.length();
int[] distances = new int[n];
int prefixCount = 0;
int prefixSum = 0;
for( int i = 0; i < n ; i++){
distances[i] = prefixCount * i - prefixSum;
if(boxes.charAt(i) == '1'){
++prefixCount;
prefixsum += i; 
}//If End
}//Loop End
int suffixCount = 0;
int suffixSum = 0;
for(int i = n-1; i >= 0; --i) {
distances[i] += suffixSum - suffixCount * i;
if ( boxes.charAt(i) == '1' ) {
++suffixCount;
suffixSum += i;
}//If End
}//Loop End
return distances;
}//function end
Utility Functions and Global variables:
Utility Function is not required.
Privacy Policy | About