Time Complexity of Loop with Powers Last Updated : 23 Aug, 2024 Comments Improve Suggest changes Like Article Like Report What is the time complexity of the below function? C++ void fun(int n, int k) { for (int i = 1; i <= n; i++) { int p = pow(i, k); for (int j = 1; j <= p; j++) { // Some O(1) work } } } // This code is contributed by Shubham Singh C void fun(int n, int k) { for (int i = 1; i <= n; i++) { int p = pow(i, k); for (int j = 1; j <= p; j++) { // Some O(1) work } } } Java static void fun(int n, int k) { for (int i = 1; i <= n; i++) { int p = Math.pow(i, k); for (int j = 1; j <= p; j++) { // Some O(1) work } } } // This code is contributed by umadevi9616 Python def fun(n, k): for i in range(1, n + 1): p = pow(i, k) for j in range(1, p + 1): # Some O(1) work # This code is contributed by Shubham Singh C# static void fun(int n, int k) { for (int i = 1; i <= n; i++) { int p = Math.Pow(i, k); for (int j = 1; j <= p; j++) { // Some O(1) work } } } // This code is contributed by umadevi9616 JavaScript <script> // JavaScript program for the above approach function fun(n, k) { for(let i = 1; i <= n; i++) { int p = Math.pow(i, k); for (let j = 1; j <= p; j++) { // Some O(1) work } } } // This code is contributed by Shubham Singh </script> Time complexity of above function can be written as 1k + 2k + 3k + ... n1k.Let us try few examples: k=1Sum = 1 + 2 + 3 ... n = n(n+1)/2 = n2/2 + n/2k=2Sum = 12 + 22 + 32 + ... n12. = n(n+1)(2n+1)/6 = n3/3 + n2/2 + n/6k=3Sum = 13 + 23 + 33 + ... n13. = n2(n+1)2/4 = n4/4 + n3/2 + n2/4 In general, asymptotic value can be written as (nk+1)/(k+1) + Θ(nk)If n>=k then the time complexity will be considered in O((nk+1)/(k+1)) and if n<k, then the time complexity will be considered as in the O(nk) Comment More infoAdvertise with us Next Article Time Complexity of Loop with Powers K kartik Follow Improve Article Tags : Analysis of Algorithms DSA time complexity Similar Reads Miscellaneous Problems of Time Complexity Prerequisite : Asymptotic Notations Time Complexity :Time complexity is the time needed by an algorithm expressed as a function of the size of a problem. It can also be defined as the amount of computer time it needs to run a program to completion. When we solve a problem of time complexity then thi 15 min read Multiplication with a power of 2 Given two numbers x and n, we need to multiply x with 2nExamples : Input : x = 25, n = 3 Output : 200 25 multiplied by 2 raised to power 3 is 200. Input : x = 70, n = 2 Output : 280 A simple solution is to compute n-th power of 2 and then multiply with x. C++ // Simple C/C++ program // to compute x 5 min read Compute power of power k times % m Given x, k and m. Compute (xxxx...k)%m, x is in power k times. Given x is always prime and m is greater than x. Examples: Input : 2 3 3 Output : 1 Explanation : ((2 ^ 2) ^ 2) % 3 = (4 ^ 2) % 3 = 1 Input : 3 2 3 Output : 0 Explanation : (3^3)%3 = 0 A naive approach is to compute the power of x k time 15+ min read A Time Complexity Question What is the time complexity of following function fun()? Assume that log(x) returns log value in base 2. C++ void fun() { int i, j; for (i = 1; i <= n; i++) for (j = 1; j <= log(i); j++) cout << "GeeksforGeeks"; } // This code is contributed by SHUBHAMSINGH10. C void fun() { in 2 min read Time Complexity of a Loop when Loop variable “Expands or Shrinks†exponentially For such cases, time complexity of the loop is O(log(log(n))).The following cases analyse different aspects of the problem. Case 1 : CPP for (int i = 2; i <=n; i = pow(i, k)) { // some O(1) expressions or statements } In this case, i takes values 2, 2k, (2k)k = 2k2, (2k2)k = 2k3, ..., 2klogk(log( 1 min read Like