(a) Prove the following loop invariant by induction on the number of loop iterations: Loop Invariant: After the kth iteration of the for loop, total = a1 + a2 + · · · + ak and L contains all elements from a1 , a2 , . . . , ak that are greater than the sum of all previous terms of the sequence.
(b) Use the loop invariant to prove that the algorithm is correct, i.e., that it returns a list
of all terms in the sequence that are greater than the sum of all previous terms of the sequence.
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(a) Prove the following loop invariant by induction on the number of loop iterations: Loop Invariant:...
a. Use pseudocode to specify a brute-force algorithm that takes as input a list of n positive integers and determines whether there are two distinct elements of the list that have as their sum a third element of the list. That is, whether there exists i, j.k such that iヂj, i关k,j关k and ai + aj = ak. The algorithm should loop through all triples of elements of the list checking whether the sum of the first two is the third...
Use a loop invariant to prove that the following algorithm correctly identifies the location of the minimum value in the array data. Input: data: array of integers Input: n: size of data Output: index min such that data[min] <= data[i] for any i from 1 to n Algorithm: FindMin min = 1; for i = 2 to n do if data[i] < data[min] then min = i; end end return min
The input consists of n numbers a1, a2, . . . , an and a target value t. The goal is to determine in how many possible ways can we add up two of these numbers to get t. Formally, your program needs to find the number of pairs of indices i, j, i < j such that ai+aj = t. For example, for 2, 7, 3, 1, 5, 6 and t = 7, we can get t in two...
in c++ language 1.Re-write the following for loop statement by using a while loop statement: int sum = 0; for(int i=0;i<=1000;i++){ sum+=i; } 1 (b). Following is the main () function of a program. The program asks a user to enter 150 integers and print the largest integer user entered. int main() { int score, highest; //missing portion of the program return 0; } 1(c). Find the missing portion of the following code, so the...
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PLEASE READ AND CODE IN BASIC C++ CODE. ALSO, PLEASE CODE USING THIS DO WHILE LOOP AND FORMAT: #include <iostream> using namespace std; int main() { //variables here do { // program here }while (true); } Objectives To learn to code, compile and run a program containing SELECTION structures Assignment Write an interactive C++.program to have a user input the length of three sides of a triangle. Allow the user to enter the sides...
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x G Answer The Following Muli m Belgium 3-1 Russia: Eden x ■ CBU I Cape Breton Univers resource%2Fcontent%2F1%2Fassig6,MATH 1203-W201 9pdf Due date: Thurs., Mar. 28 Please get an early start on this assignmext. If you have problens then come and see me to get help. Also remember, there are far more marks for procedure than for final answers. Write your solutions neatly and in a then come and see me to get help well organized fashion. Show all work....
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This C++ Program consists of: operator overloading, as well as experience with managing dynamic memory allocation inside a class. Task One common limitation of programming languages is that the built-in types are limited to smaller finite ranges of storage. For instance, the built-in int type in C++ is 4 bytes in most systems today, allowing for about 4 billion different numbers. The regular int splits this range between positive and negative numbers, but even an unsigned int (assuming 4 bytes)...