Minimum Swaps to Group All 1's Together
Given aĀ binary array data
, returnĀ the minimum number of swaps required to group all 1
ās present in the array together in any place in the array.
Example 1:
Input: data = [1,0,1,0,1]
Output: 1
Explanation: There are 3 ways to group all 1's together:
[1,1,1,0,0]
using 1 swap.
[0,1,1,1,0]
using 2 swaps.
[0,0,1,1,1]
using 1 swap.
The minimum is 1.
Example 2:
Input: data = [0,0,0,1,0]
Output: 0
Explanation: Since there is only one 1 in the array, no swaps are needed.
Example 3:
Input: data = [1,0,1,0,1,0,0,1,1,0,1]
Output: 3
Explanation: One possible solution that uses 3 swaps is [0,0,0,0,0,1,1,1,1,1,1].
Constraints:
1 <= data.length <= 105
data[i]
is either0
or1
.
Solution
This is a classic sliding window question that has a fixed size.
We wish to find a window to store all the 1's in the very end, thus we fix the size to the total number of 1's.
Since we want to use minimum number of swaps, it will be best if we can find a window with most 1's (or least 0's).
Let count1
be the number of 1's in the entire data
. We will initialize total
to be the number of 1's in the window from index 0 to the count1
(which is the sum of the window).
Then, as we slide the window to the right, we remove data[r-count1]
from the total
and add data[r]
to the total
so that total
is the sum of the new window.
Then for each window that has size of count1
, we compare for the minimum swaps. Here, we calcluate the swaps count1-total
, as the number of swaps is just the number of 0's in the window.
Implementation
def minSwaps(self, data):
count1 = data.count(1)
total = 0
for i in range(count1): total += data[i]
swaps = count1-total
for r in range(count1, len(data)):
total += data[r]
total -= data[r-count1]
swaps = min(swaps, count1-total)
return swaps
Ready to land your dream job?
Unlock your dream job with a 2-minute evaluator for a personalized learning plan!
Start EvaluatorHow many times is a tree node visited in a depth first search?
Recommended Readings
LeetCode Patterns Your Personal Dijkstra's Algorithm to Landing Your Dream Job The goal of AlgoMonster is to help you get a job in the shortest amount of time possible in a data driven way We compiled datasets of tech interview problems and broke them down by patterns This way we
Recursion Recursion is one of the most important concepts in computer science Simply speaking recursion is the process of a function calling itself Using a real life analogy imagine a scenario where you invite your friends to lunch https algomonster s3 us east 2 amazonaws com recursion jpg You first
Runtime Overview When learning about algorithms and data structures you'll frequently encounter the term time complexity This concept is fundamental in computer science and offers insights into how long an algorithm takes to complete given a certain input size What is Time Complexity Time complexity represents the amount of time
Want a Structured Path to Master System Design Too? Donāt Miss This!