Bit Manipulation

Bit manipulation treats an integer as a row of switches. Many problems get simple once you look at one bit at a time: XOR cancels pairs, AND can only lose bits, and OR can only gain them.

The nine chapters start with the basics, cover XOR and AND/OR properties, splitting a problem bit by bit, trial filling from the highest bit down, bitwise identities and linear basis, then end with constructive and mixed problems. It suits anyone who tends to skip bit problems and wants a set of them in a sensible order.

95 problemsRating 1181–29189 Chapters

Open the study room

Want company while you work through this list? Sign in, open the study room, and your heroine will bring you the problems one at a time.

I. Fundamentals

Problem	Rating
3370. Smallest Number with All Set Bits	1199
3226. Number of Bit Changes to Make Two Integers Equal	1247
1356. Sort Integers by the Number of 1 Bits	1258
461. Hamming Distance	1282
2220. Minimum Bit Flips to Convert Number	1282
1342. Number of Steps to Reduce a Number to Zero	Unrated
476. Number Complement	Unrated
1009. Complement of Base 10 Integer	Unrated
868. Binary Gap	1307
2917. Find the K OR of an Array	1389
693. Binary Number with Alternating Bits	Unrated
2657. Find the Prefix Common Array of Two Arrays	Unrated
231. Power of Two	Unrated
342. Power of Four	Unrated
191. Number of 1 Bits	Unrated
338. Counting Bits	Unrated
2595. Number of Even AND Odd Bits	Unrated
2154. Keep Multiplying Found Values by Two	Unrated
3211. Generate Binary Strings Without Adjacent Zeros	Unrated
3690. Split AND Merge Array Transformation	Unrated

II. XOR Properties

Problem	Rating
1486. XOR Operation in an Array	1181
1720. Decode Xored Array	1284
2433. Find the Original Array of Prefix XOR	1367
1310. XOR Queries of a Subarray	1460
2683. Neighboring Bitwise XOR	1518
1829. Maximum XOR for Each Query	1523
2997. Minimum Number of Operations to Make Array XOR Equal to K	1525
1442. Count Triplets That Can Form Two Arrays of Equal XOR	1525
2429. Minimize XOR	1532
2527. Find XOR Beauty of Array	1550
2317. Maximum XOR After Operations	1679
2588. Count the Number of Beautiful Subarrays	1697
2564. Substring XOR Queries	1959
1734. Decode Xored Permutation	2024
2857. Count Pairs of Points with Distance K	2082
1803. Count Pairs with XOR in a Range	2479

III. AND / OR Properties

Problem	Rating
2980. Check If Bitwise OR Has Trailing Zeros	1234
1318. Minimum Flips to Make a OR B Equal to C	1383
2419. Longest Subarray with Maximum Bitwise AND	1496
2871. Split Array Into Maximum Number of Subarrays	1750
2401. Longest Nice Subarray	1750
2680. Maximum OR	1912
3133. Minimum Array End	1935
3108. Minimum Cost Walk in Weighted Graph	2109
3117. Minimum Sum of Values by Dividing Array	2735
3171. Find Subarray with Bitwise OR Closest to K	Unrated
1521. Find a Value of a Mysterious Function Closest to Target	Unrated
3097. Shortest Subarray with OR at Least K II	1891
2411. Smallest Subarrays with Maximum Bitwise OR	1938
3209. Number of Subarrays with AND Value of K	2050
898. Bitwise Ors of Subarrays	Unrated

IV. Bit Contribution & Splitting

Problem	Rating
477. Total Hamming Distance	Unrated
1863. Sum of All Subset XOR Totals	Unrated
2425. Bitwise XOR of All Pairings	1622
2275. Largest Combination with Bitwise AND Greater Than Zero	1642
1835. Find XOR Sum of All Pairs Bitwise AND	1825
3688. Bitwise OR of Even Numbers in an Array	Unrated
3153. Sum of Digit Differences of All Pairs	1645

V. Trial Filling Technique

Problem	Rating
421. Maximum XOR of Two Numbers in an Array	Unrated
2935. Maximum Strong Pair XOR II	2349
3145. Find Products of Elements of Big Array	2859
3022. Minimize OR of Remaining Elements Using Operations	2918
3287. Find the Maximum Sequence Value of Array	Unrated

VI. Bitwise Identities

Problem	Rating
1835. Find XOR Sum of All Pairs Bitwise AND	1825
2354. Number of Excellent Pairs	2076

VII. Linear Basis

Problem	Rating
3681. Maximum XOR of Subsequences	Unrated
3630. Partition Array for Maximum XOR AND AND	2744

VIII. Constructive Bit Problems

Problem	Rating
2546. Apply Bitwise Operations to Make Strings Equal	1605
1558. Minimum Numbers of Function Calls to Make Target Array	1637
2571. Minimum Operations to Reduce an Integer to 0	1649
3315. Construct the Minimum Bitwise Array II	1715
2568. Minimum Impossible OR	1754
3644. Maximum K to Sort a Permutation	1775
2509. Cycle Length Queries in a Tree	1948
2939. Maximum XOR Product	2128
2749. Minimum Operations to Make the Integer Zero	2132
2835. Minimum Operations to Form Subsequence with Target Sum	2207
2897. Apply Operations on Array to Maximize Sum of Squares	2301
810. Chalkboard XOR Game	2341

IX. Miscellaneous

Problem	Rating
136. Single Number	Unrated
260. Single Number III	Unrated
2965. Find Missing AND Repeated Values	Unrated
137. Single Number II	Unrated
645. Set Mismatch	Unrated
190. Reverse Bits	Unrated
371. Sum of Two Integers	Unrated
201. Bitwise AND of Numbers Range	Unrated
2438. Range Product Queries of Powers	1610
1680. Concatenation of Consecutive Binary Numbers	1630
1261. Find Elements in a Contaminated Binary Tree	Unrated
89. Gray Code	Unrated
1238. Circular Permutation in Binary Representation	1775
982. Triples with Bitwise AND Equal to Zero	2085
3307. Find the K Th Character in String Game II	2232
1611. Minimum One Bit Operations to Make Integers Zero	2345
3514. Number of Unique XOR Triplets II	Unrated

It comes fifth on Track 1, after Data Structures, but the order is only a suggestion, so you can open it from the full catalog whenever you like.

Ratings come from zerotrac's LeetCode contest ratings. Some problems have no zerotrac rating and are marked Unrated.

Open the study room