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Problem solution · Python

Pascals Triangle II

Pascals Triangle II: a Python solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Direct simulation
Source
Kamyu LeetCode Solutions
Length
56 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Direct simulation

For Pascals Triangle II, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 56 lines of Python from the credited upstream file pascals-triangle-ii.py.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from Kamyu LeetCode Solutions by kamyu104 and is used under the MIT licence.

Open problem ↗Original source ↗
Full codePascals Triangle II · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(n^2)# Space: O(1) class Solution(object):    # @return a list of integers    def getRow(self, rowIndex):        result = [0] * (rowIndex + 1)        for i in xrange(rowIndex + 1):            old = result[0] = 1            for j in xrange(1, i + 1):                old, result[j] = result[j], old + result[j]        return result     def getRow2(self, rowIndex):        """        :type rowIndex: int        :rtype: List[int]        """        row = [1]        for _ in range(rowIndex):            row = [x + y for x, y in zip([0] + row, row + [0])]        return row     def getRow3(self, rowIndex):        """        :type rowIndex: int        :rtype: List[int]        """        if rowIndex == 0: return [1]        res = [1, 1]         def add(nums):            res = nums[:1]            for i, j in enumerate(nums):                if i < len(nums) - 1:                    res += [nums[i] + nums[i + 1]]            res += nums[:1]            return res         while res[1] < rowIndex:            res = add(res)        return res  # Time:  O(n^2)# Space: O(n)class Solution2(object):    # @return a list of integers    def getRow(self, rowIndex):        result = [1]        for i in range(1, rowIndex + 1):            result = [1] + [result[j - 1] + result[j] for j in xrange(1, i)] + [1]        return result

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