Problem 3. Let n be an integer. Write dynamic programming algorithm which determines in how many ways, with repetitions, can n be written as the sum of 1,2,4 and prove its time complexity.

An algorithm A, has a runtime T1(n) defined (in seconds) by the following function:- T1(n) = n? +n +50 For n = 9, the runtime of algorithm A, is 140 seconds. Runtime of another algorithm A, is represented by the following equation:- T2(n) = 2n³ + 14n + 230 For n = 2, the runtime of algorithm Az is 274 seconds. Algorithm Az with runtime represented by the following equation. T3(n) = 3n? + 33n + 333 Identify all values of n (if such values exist) for which the runtime of Az exceeds the given runtime of 140 sec of A, but is less than the runtime of 274 seconds of A2. Type your answer here.

Please help me solve the problem step by step.

Identify the big-O time complexity of each of the following functions:void f1(int n) {for(int i=0; i<(3*n+n); ++i) {cout << i << endl;}for(int i=0; i<(10*n); ++i) {cout << i << endl;}}void f2(int n) {if(n==0) { return; }f2(n-1);f2(n-3);}void f3(int n) {for(int i=0; i<n; ++i) {for(int j=0; j<n; ++j) {for(int k=0; k<n; ++k) {cout << i << endl;}}}}