Ball Moves - Google Top Interview Questions


Problem Statement :


You are given a list of integers nums containing 0s and 1s where a 0 means the cell is empty and 1 means there's a ball there.

Return a new list of integers A of the same length where A[i] is set to the total distance required to move all the balls to A[i]. The distance to move a ball in index j to index i is defined to be abs(j - i).

Constraints

n ≤ 100,000 where n is the length of nums

Example 1

Input

nums = [1, 1, 0, 1]

Output

[4, 3, 4, 5]

Explanation

A[0] = abs(0 - 0) + abs(1 - 0) + abs(3 - 0)

A[1] = abs(0 - 1) + abs(1 - 1) + abs(3 - 1)

A[2] = abs(0 - 2) + abs(1 - 2) + abs(3 - 2)

A[3] = abs(0 - 3) + abs(1 - 3) + abs(3 - 3)

For example, to move all the balls to A[1] we need to move the ball at index 0 to 1 for distance of 1 and 
move the ball at index 3 to 1 for distance of 2.


Solution :



title-img 




                        Solution in C++ :

vector<int> solve(vector<int>& nums) {
    int totalDistance = 0;
    int n = nums.size();
    int ballsToTheRight = 0;
    for (int i = 0; i < n; i++) {
        if (nums[i] == 0) continue;
        totalDistance += i;
        ballsToTheRight++;
    }
    int ballsToTheLeft = 0;
    for (int i = 0; i < n; i++) {
        if (nums[i]) {
            ballsToTheLeft++;
            ballsToTheRight--;
        }
        nums[i] = totalDistance;
        totalDistance -= ballsToTheRight - ballsToTheLeft;
    }
    return nums;
}
                    


                        Solution in Java :

import java.util.*;

class Solution {
    public int[] solve(int[] nums) {
        int sum = 0, ct = 0;
        int[] pf = new int[nums.length];
        for (int i = 0; i < nums.length; i++) {
            sum += ct;
            ct += nums[i];
            pf[i] = sum;
        }
        sum = ct = 0;
        for (int i = nums.length - 1; i > -1; i--) {
            sum += ct;
            ct += nums[i];
            pf[i] += sum;
        }
        return pf;
    }
}
                    


                        Solution in Python : 
                            
class Solution:
    def solve(self, nums):

        suffixSum = [0 for _ in range(len(nums))]
        prefixSum = [0 for _ in range(len(nums))]

        prefixCount = 0
        for i in range(len(nums)):
            prefixSum[i] = prefixCount + (prefixSum[i - 1] if i - 1 >= 0 else 0)
            if nums[i] == 1:
                prefixCount += 1

        suffixCount = 0
        for i in range(len(nums) - 1, -1, -1):
            suffixSum[i] = suffixCount + (suffixSum[i + 1] if len(nums) > i + 1 else 0)
            if nums[i] == 1:
                suffixCount += 1

        res = [prefixSum[i] + suffixSum[i] for i in range(len(nums))]

        return res


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