{"id":7062009,"date":"2026-09-20T11:01:47","date_gmt":"2026-09-20T11:01:47","guid":{"rendered":"https:\/\/peraltafinancing.com\/animation\/big-o-notation-practice-problems-with-solutions\/"},"modified":"2026-09-20T11:01:47","modified_gmt":"2026-09-20T11:01:47","slug":"big-o-notation-practice-problems-with-solutions","status":"publish","type":"post","link":"https:\/\/fivemor.com\/?p=7062009","title":{"rendered":"Big O Notation Practice Problems with Solutions"},"content":{"rendered":"


\n<\/p>\n

\n

\u00a0<\/p>\n

Big O notation describes how the running time or space requirements of an algorithm grow as the input size n increases. This guide contains Big O practice problems ranging from beginner to advanced, with step-by-step solutions and explanations.<\/p>\n

\u00a0<\/p>\n

Big O notation?<\/b>
\nBig O notation describes how the running time or space requirements of an algorithm grow as the input size n increases. This guide contains Big O practice problems ranging from beginner to advanced, with step-by-step solutions and explanations.\n<\/p>\n

<\/p>\n

\n\n\n\n\n\n\n\n\n\n\n
Complexity<\/th>\nCommon example<\/th>\n<\/tr>\n<\/thead>\n
O(1)<\/td>\nArray access<\/td>\n<\/tr>\n
O(log n)<\/td>\nBinary search<\/td>\n<\/tr>\n
O(n)<\/td>\nLinear search<\/td>\n<\/tr>\n
O(n log n)<\/td>\nMerge sort<\/td>\n<\/tr>\n
O(n\u00b2)<\/td>\nNested loops<\/td>\n<\/tr>\n
O(2\u207f)<\/td>\nSome recursive algorithms<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

<\/p>\n

\n
\n

<\/p>\n

\n O(1)<\/span>
\n O(log n)<\/span>
\n O(n)<\/span>
\n O(n log n)<\/span>
\n O(n\u00b2)<\/span>
\n O(2\u207f)<\/span>\n <\/p>\n

<\/p><\/div>\n

<\/p>\n

\n

\n n<\/span>
\n =<\/span>
\n 64<\/strong>
\n :<\/span><\/p>\n


\n (1, log\u2082n, n)
\n =
\n (1,
\n 6<\/span>,
\n 64<\/span>)
\n <\/span>\n <\/p>\n

\n (n log\u2082n, n\u00b2)
\n =
\n (384<\/span>,
\n 4,096<\/span>)\n <\/p>\n

\n 2n<\/sup>
\n =
\n 1.84 \u00d7 1019<\/sup><\/span>\n <\/p>\n<\/p><\/div>\n

<\/p>\n<\/div>\n<\/div>\n

Problem 1: Constant Time O(1)<\/h2>\n

<\/p>\n

Question: What is the time complexity?<\/b><\/p>\n

Solution: O(1)<\/b><\/p>\n

Explanation: \u201cInside the function, a constant number of operations is performed: the modulus operation (% 2) and a comparison (== 0). The number of operations does not depend on the size of the input numbum (n).<\/b><\/p>\n

Problem 2: Linear Time O(n)<\/h2>\n

<\/p>\n

Question: What is the time complexity?<\/b><\/p>\n

Solution: O(n)<\/b><\/p>\n

Explanation: The function loops through the list of n elements twice. This gives 2n steps. Big O notation drops constant coefficients, so 2n simplifies to O(n).<\/b><\/p>\n

Problem 3: Logarithmic Time (O(log n))<\/h2>\n

<\/p>\n

Question: What is the time complexity?<\/p>\n

<\/b><\/p>\n

Solution: \\(O(\\log n)\\)<\/b><\/p>\n

Explanation: The complexity is \\(O(\\log n)\\) because the variable i doubles in each iteration, scaling logarithmically relative to n.<\/b><\/p>\n

Problem 4: Quadratic Time O(n\u00b2)<\/h>
\n<\/p>\n<\/div>\n

Explanation: Featuring nested loops where each individual loop runs n times, the total operations scale to \\(n^{2}\\) while constant-time work occurs inside<\/p>\n\n","protected":false},"excerpt":{"rendered":"

\u00a0 Big O notation describes how the running time or space requirements of an algorithm grow as the input size n increases. This guide contains Big O practice problems ranging from beginner to advanced, with step-by-step solutions and explanations. \u00a0 Big O notation? 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