How do you solve Number of Ways to Split a String on LeetCode?

Number of Ways to Split a String (LeetCode #1573) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The optimal approach leverages the fact that if the total number of '1's in the string is not divisible by 3, we can immediately return 0. Otherwise, we can count the occurrences of '1's and determine valid split points using prefix sums and combinations.

What is the brute force solution for Number of Ways to Split a String?

The brute force approach for Number of Ways to Split a String is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible way to split the string into three parts and counting the valid splits where each part has the same number of '1's. This method is straightforward but inefficient for larger strings. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Number of Ways to Split a String?

Number of Ways to Split a String uses the following concepts: Math, String. The recommended patterns to study are: .

#1573

Number of Ways to Split a String

Medium

MathString

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

The optimal approach leverages the fact that if the total number of '1's in the string is not divisible by 3, we can immediately return 0. Otherwise, we can count the occurrences of '1's and determine valid split points using prefix sums and combinations.

⚙️

Algorithm

4 steps

1Step 1: Count the total number of '1's in the string. If it's not divisible by 3, return 0.
2Step 2: Calculate the target number of '1's per part (total_ones / 3).
3Step 3: Traverse the string and keep track of the number of '1's seen so far. Count how many times we reach the target number of '1's.
4Step 4: Use the counts of valid split points to calculate the number of ways to split the string.

solution.py19 lines

1# Full working Python code
2
3def countWays(s):
4    MOD = 10**9 + 7
5    total_ones = s.count('1')
6    if total_ones % 3 != 0:
7        return 0
8    target = total_ones // 3
9    count = 0
10    prefix_count = 0
11    ways = 0
12    for i in range(len(s)):
13        if s[i] == '1':
14            prefix_count += 1
15        if prefix_count == target:
16            count += 1
17        elif prefix_count == 2 * target:
18            ways += count
19    return ways % MOD

ℹ

Complexity note: This complexity is linear because we only traverse the string a few times without using additional data structures that scale with input size.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.