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- Construct a DFA A so that L(A) = L(N) where N is the following NFA:coin change problem in dynamic programming approach Pseudocode is below: DPChange(M, c, d): bestNumCoins[0] = 0 for m = 1 to M bestNumCoins[m] = inf for i = 1 to d if m >= c[i] if bestNumCoins[m-c[i]] + 1 < bestNumCoins[m] bestNumCoins[m] = bestNumCoins[m-c[i]] + 1 return bestNumCoins[M] Convert this pseudocode to Python. What is the runtime? Change the function to return the best number of coins and combination of denominations as a vector by creating a new function DPC_t that is similar as DPChange but declares an array coinsUsed that keeps track of the coins in the best “path” to a given entry M. DPC_t should return both bestNumCoins and coinsUsed. Create a function pCoins that prints the sequence of coins used to get to M. Has the runtime changed with this backtrace?coin change problem in dynamic programming approach Pseudocode is below: DPChange(M, c, d): bestNumCoins[0] = 0 for m = 1 to M bestNumCoins[m] = inf for i = 1 to d if m >= c[i] if bestNumCoins[m-c[i]] + 1 < bestNumCoins[m] bestNumCoins[m] = bestNumCoins[m-c[i]] + 1 return bestNumCoins[M] Convert this pseudocode to Python. Change the function to return the best number of coins and combination of denominations as a vector by creating a new function DPC_t that is similar as DPChange but declares an array coinsUsed that keeps track of the coins in the best “path” to a given entry M. DPC_t should return both bestNumCoins and coinsUsed. Create a function pCoins that prints the sequence of coins used to get to M. Has the runtime changed with this backtrace?
- // Description: Write a program that outputs a root of a given function f(x) by using a bi-section method. // f(x) = x3 + 5x2 +7x +2Following C code computes the approximate roots and the absolute approximate error of f(x)=x³ -(1/sin(x)) function with both Regula-Falsi and Bisection methods for ten iterations. If the user enters key "1" Regula-Falsi method, if the user enters key "2" Bisection method, will run in the program. In this context, fill in the blanks of the given C code. double function(double x) { return int main(int argc, char *argv[]) { double a,b,x[10],error,FA,FB,FX; int option,i; printf(" ENTER 1 FOR Regula Falsi, ITER Bisection \n"); scanf("%d",&option); printf("Enter base of definition invterval\n"); scanf("%lf",&a); printf("Enter top of definition interval\n"); scanf("%lf",&b); FA= function (a); FB= function (b); if(FA*FB<0){ for(i=0;i< ;i++){ switch(option){ case 1: break;Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents and 5 cents. Write a dynamicprogramming based recursive algorithm, which returns the smallest (optimal) number of coins needed to solve this problem. For example, if your algorithm is called A, and N = 13, then A(N) = A(13) returns 4, since 5+5+2+1 = 13 used the smallest (optimal) number of coins. In contrast, 5+5+1+1+1 is not an optimal answer.
- In C programming Mathematically, given a function f, we recursively define fk(n) as follows: if k = 1, f1(n) = f(n). Otherwise, for k > 1, fk(n) = f(fk-1(n)). Assume that there is an existing function f, which takes in a single integer and returns an integer. Write a recursive function fcomp, which takes in both n and k (k > 0), and returns fk(n). int f(int n);int fcomp(int n, int k){Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents and 5 cents. Write a dynamic programming-based recursive algorithm, which returns the smallest (optimal) number of coins needed to solve this problem. For example, if your algorithm is called A, and N = 13, then A(N) = A(13) returns 4, since 5+5+2+1 = 13 used the smallest (optimal) number of coins. In contrast, 5+5+1+1+1 is not an optimal answer. Draw the recursion tree for the algorithm where N = 7. Derive the complexity bound of the algorithm. Do not need to prove the complexity bound formally, just derive it by analyzing each component in your algorithm.void deleteRange( int from, int to) { int i, j = 0; for (i = 0; i < counter; i++) { if (i <= from - 1 || i >= to + 1) { A[j] = A[i]; j++; } } for (int i = 0; i < j; i++) cout << A[i] << " "; } Above method deletes range of elements from an array. Please explain the logic of above code in simple english (algorithm and comments).
- void deleteRange( int from, int to) {int i, j = 0;for (i = 0; i < counter; i++) {if (i <= from - 1 || i >= to + 1) {A[j] = A[i];j++;}}for (int i = 0; i < j; i++)cout << A[i] << " ";} Above method deletes range of elements from an array. Consider array A[] globally declared and counter is its size. Please explain the logic of above code in simple english (algorithm and comments).Computer Science Write in the programming language Pythona pushdown automaton simulator (a program that simulates a pushdown automaton) where: V = {w | w ∈ {a, b}* and w starts and ends with the same symbol}.int functionC (int n) { int i, j, sumC = 0; for (i=n; i > 0; i=i-5) for (j=1; j 0) { if (functionC(n) % 2 == 0) { for (i=m; i > 0; i=i/3) sumE++; } else (10) Asymptotic runtime of functionE { for (i=m; i > 0; i=i-3) sumE--; } n--; } return sumE;