Number Theory LeetCode Problems: 54 Python Solutions

1 pattern

How Number Theory problems are solved

A tag names the subject, not the method. These pattern hubs cover the techniques that actually solve Number Theory 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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When the Number Theory problem arrives live.

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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.

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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+

90%Subscription

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+

Number Theory problems by difficulty

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

Easy (8)

Easy problems
No.	Problem	Topics
0258	Add Digits	Math, Number Theory, Simulation
0914	X of a Kind in a Deck of Cards	Array, Hash Table, Math +2
1952	Three Divisors	Math, Enumeration, Number Theory
1979	Find Greatest Common Divisor of Array	Array, Math, Number Theory
2413	Smallest Even Multiple	Math, Number Theory
2427	Number of Common Factors	Math, Enumeration, Number Theory
2614	Prime In Diagonal	Array, Math, Matrix +1
2748	Number of Beautiful Pairs	Array, Hash Table, Math +2

Medium (24)

Medium problems
No.	Problem	Topics
0204	Count Primes	Array, Math, Enumeration +1
0858	Mirror Reflection	Geometry, Math, Number Theory
0866	Prime Palindrome	Math, Number Theory
1201	Ugly Number III	Math, Binary Search, Combinatorics +1
1447	Simplified Fractions	Math, String, Number Theory
1492	The kth Factor of n	Math, Number Theory
2001	Number of Pairs of Interchangeable Rectangles	Array, Hash Table, Math +2
2280	Minimum Lines to Represent a Line Chart	Geometry, Array, Math +2
2447	Number of Subarrays With GCD Equal to K	Array, Math, Number Theory
2470	Number of Subarrays With LCM Equal to K	Array, Math, Number Theory
2507	Smallest Value After Replacing With Sum of Prime Factors	Math, Number Theory, Simulation
2513	Minimize the Maximum of Two Arrays	Math, Binary Search, Number Theory
2521	Distinct Prime Factors of Product of Array	Array, Hash Table, Math +1
2523	Closest Prime Numbers in Range	Math, Number Theory
2601	Prime Subtraction Operation	Greedy, Array, Math +2
2607	Make K-Subarray Sums Equal	Greedy, Array, Math +2
2654	Minimum Number of Operations to Make All Array Elements Equal to 1	Array, Math, Number Theory
2761	Prime Pairs With Target Sum	Array, Math, Enumeration +1
2807	Insert Greatest Common Divisors in Linked List	Linked List, Math, Number Theory
2947	Count Beautiful Substrings I	Hash Table, Math, String +3
2436	Minimum Split Into Subarrays With GCD Greater Than OnePremium	Greedy, Array, Math +2
2464	Minimum Subarrays in a Valid SplitPremium	Array, Math, Dynamic Programming +1
2979	Most Expensive Item That Can Not Be BoughtPremium	Math, Dynamic Programming, Number Theory
2992	Number of Self-Divisible PermutationsPremium	Bit Manipulation, Array, Math +4

Hard (22)

Hard problems
No.	Problem	Topics
0952	Largest Component Size by Common Factor	Union Find, Array, Hash Table +2
1250	Check If It Is a Good Array	Array, Math, Number Theory
1627	Graph Connectivity With Threshold	Union Find, Array, Math +1
1735	Count Ways to Make Array With Product	Array, Math, Dynamic Programming +2
1766	Tree of Coprimes	Tree, Depth-First Search, Array +2
1799	Maximize Score After N Operations	Bit Manipulation, Array, Math +4
1808	Maximize Number of Nice Divisors	Recursion, Math, Number Theory
1819	Number of Different Subsequences GCDs	Array, Math, Counting +1
1994	The Number of Good Subsets	Bit Manipulation, Array, Hash Table +5
1998	GCD Sort of an Array	Union Find, Array, Math +2
2197	Replace Non-Coprime Numbers in Array	Stack, Array, Math +1
2338	Count the Number of Ideal Arrays	Math, Dynamic Programming, Combinatorics +1
2344	Minimum Deletions to Make Array Divisible	Array, Math, Number Theory +2
2543	Check if Point Is Reachable	Math, Number Theory
2584	Split the Array to Make Coprime Products	Array, Hash Table, Math +1
2709	Greatest Common Divisor Traversal	Union Find, Array, Math +1
2818	Apply Operations to Maximize Score	Stack, Greedy, Array +4
2862	Maximum Element-Sum of a Complete Subset of Indices	Array, Math, Number Theory
2867	Count Valid Paths in a Tree	Tree, Depth-First Search, Math +2
2183	Count Array Pairs Divisible by K	Array, Math, Number Theory
2941	Maximum GCD-Sum of a SubarrayPremium	Array, Math, Binary Search +1
2949	Count Beautiful Substrings II	Hash Table, Math, String +2

Number Theory LeetCode Problems: All 54,
With Python Solutions

How Number Theory problems are solved

When the Number Theory problem arrives live.

Approach

Approach

Approach

Number Theory problems by difficulty

Easy (8)

Medium (24)

Hard (22)

Keep exploring

How Number Theory problems are solved

When the Number Theory problem arrives live.

Approach

Approach

Approach

Number Theory problems by difficulty

Easy (8)8

Medium (24)24

Hard (22)22

Keep exploring

Easy (8)

Medium (24)

Hard (22)