Combinatorics LeetCode Problems: 32 Python Solutions

1 pattern

How Combinatorics problems are solved

A tag names the subject, not the method. These pattern hubs cover the techniques that actually solve Combinatorics problems — each one explains the approach, gives a Python template and states its complexity.

Math and Number TheoryFind the closed form, the invariant, or the modular identity — and skip the loop entirely.

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Technical interview · 45 minsolution.pyShared editor · Python 3Longest substring without repeatsMediumGiven a string s, return the length of the longest contiguous substring in which every character is unique.s = "abcabcbb"
→ 31def length_of_longest_substring(s: str) -> int:2 last_seen = {}3 left = best = 04 for right, ch in enumerate(s):5 if ch in last_seen and last_seen[ch] >= left:

python

def length_of_longest_substring(s: str) -> int:    last_seen = {}                    # char -> index    left = best = 0    for right, ch in enumerate(s):        if ch in last_seen and last_seen[ch] >= left:            left = last_seen[ch] + 1  # jump past it        last_seen[ch] = right        best = max(best, right - left + 1)    return best    last_seen = {}                    # char -> index

Approach

At each index r, the window's left edge is:

left r = max (left r -1, last[s r] + 1)

Time O(n): each character enters and leaves the window once.
Space O(min(n, k)): k is the size of the character set.

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python

Please analyze this context and help me answer the question or solve the problem.

Technical interview · 45 minsolution.pyShared editor · Python 3Longest substring without repeatsMediumGiven a string s, return the length of the longest contiguous substring in which every character is unique.s = "abcabcbb"
→ 31def length_of_longest_substring(s: str) -> int:2 last_seen = {}3 left = best = 04 for right, ch in enumerate(s):5 if ch in last_seen and last_seen[ch] >= left:

python

def length_of_longest_substring(s: str) -> int:    last_seen = {}                    # char -> index    left = best = 0    for right, ch in enumerate(s):        if ch in last_seen and last_seen[ch] >= left:            left = last_seen[ch] + 1  # jump past it        last_seen[ch] = right        best = max(best, right - left + 1)    return best    last_seen = {}                    # char -> index

Approach

At each index r, the window's left edge is:

left r = max (left r -1, last[s r] + 1)

Time O(n): each character enters and leaves the window once.
Space O(min(n, k)): k is the size of the character set.

Type your message...

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QuitEscHide+QCapture+PCrop+OSubmit+EnterPress to get answerLeft/Right+Up/Down+

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python

Please analyze this context and help me answer the question or solve the problem.

Technical interview · 45 minsolution.pyShared editor · Python 3Longest substring without repeatsMediumGiven a string s, return the length of the longest contiguous substring in which every character is unique.s = "abcabcbb"
→ 31def length_of_longest_substring(s: str) -> int:2 last_seen = {}3 left = best = 04 for right, ch in enumerate(s):5 if ch in last_seen and last_seen[ch] >= left:

python

def length_of_longest_substring(s: str) -> int:    last_seen = {}                    # char -> index    left = best = 0    for right, ch in enumerate(s):        if ch in last_seen and last_seen[ch] >= left:            left = last_seen[ch] + 1  # jump past it        last_seen[ch] = right        best = max(best, right - left + 1)    return best    last_seen = {}                    # char -> index

Approach

At each index r, the window's left edge is:

left r = max (left r -1, last[s r] + 1)

Time O(n): each character enters and leaves the window once.
Space O(min(n, k)): k is the size of the character set.

Type your message...

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QuitEscHide+QCapture+PCrop+OSubmit+EnterPress to get answerLeft/Right+Up/Down+

Combinatorics problems by difficulty

Problems with a complete Python solution are listed first, then by ascending problem number.

Easy (2)

Easy problems
No.	Problem	Topics
1863	Sum of All Subset XOR Totals	Bit Manipulation, Array, Math +3
2928	Distribute Candies Among Children I	Math, Combinatorics, Enumeration

Medium (13)

Medium problems
No.	Problem	Topics
0062	Unique Paths	Math, Dynamic Programming, Combinatorics
1201	Ugly Number III	Math, Binary Search, Combinatorics +1
1621	Number of Sets of K Non-Overlapping Line Segments	Math, Dynamic Programming, Combinatorics
1641	Count Sorted Vowel Strings	Math, Dynamic Programming, Combinatorics
2063	Vowels of All Substrings	Math, String, Dynamic Programming +1
2221	Find Triangular Sum of an Array	Array, Math, Combinatorics +1
2400	Number of Ways to Reach a Position After Exactly k Steps	Math, Dynamic Programming, Combinatorics
2597	The Number of Beautiful Subsets	Array, Hash Table, Math +4
2929	Distribute Candies Among Children II	Math, Combinatorics, Enumeration
2930	Number of Strings Which Can Be Rearranged to Contain Substring	Math, Dynamic Programming, Combinatorics
0634	Find the Derangement of An ArrayPremium	Math, Dynamic Programming, Combinatorics
2539	Count the Number of Good SubsequencesPremium	Hash Table, Math, String +2
2638	Count the Number of K-Free SubsetsPremium	Array, Math, Dynamic Programming +2

Hard (17)

Hard problems
No.	Problem	Topics
0458	Poor Pigs	Math, Dynamic Programming, Combinatorics
0920	Number of Music Playlists	Math, Dynamic Programming, Combinatorics
1359	Count All Valid Pickup and Delivery Options	Math, Dynamic Programming, Combinatorics
1467	Probability of a Two Boxes Having The Same Number of Distinct Balls	Array, Math, Dynamic Programming +3
1569	Number of Ways to Reorder Array to Get Same BST	Tree, Union Find, Binary Search Tree +7
1643	Kth Smallest Instructions	Array, Math, Dynamic Programming +1
1735	Count Ways to Make Array With Product	Array, Math, Dynamic Programming +2
1830	Minimum Number of Operations to Make String Sorted	Math, String, Combinatorics
1866	Number of Ways to Rearrange Sticks With K Sticks Visible	Math, Dynamic Programming, Combinatorics
1916	Count Ways to Build Rooms in an Ant Colony	Tree, Graph, Topological Sort +3
2338	Count the Number of Ideal Arrays	Math, Dynamic Programming, Combinatorics +1
2514	Count Anagrams	Hash Table, Math, String +2
2842	Count K-Subsequences of a String With Maximum Beauty	Greedy, Hash Table, Math +2
2954	Count the Number of Infection Sequences	Array, Math, Combinatorics
2963	Count the Number of Good Partitions	Array, Hash Table, Math +1
2912	Number of Ways to Reach Destination in the GridPremium	Math, Dynamic Programming, Combinatorics
2927	Distribute Candies Among Children IIIPremium	Math, Combinatorics

Combinatorics LeetCode Problems: All 32,
With Python Solutions

How Combinatorics problems are solved

When the Combinatorics problem arrives live.

Approach

Approach

Approach

Combinatorics problems by difficulty

Easy (2)

Medium (13)

Hard (17)

Keep exploring

How Combinatorics problems are solved

When the Combinatorics problem arrives live.

Approach

Approach

Approach

Combinatorics problems by difficulty

Easy (2)2

Medium (13)13

Hard (17)17

Keep exploring

Easy (2)

Medium (13)

Hard (17)