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Engineering
Data Structures and Algorithms
Problem 1: Given is the following algorithm to determine the maximal value of an array A of size N. MaxValue (A[1..N]): max = A[1] i = 2 for (i < N): { if A[i]> max: max = A[i] i=i+1 }| return max A loop invariant is stated as: Variable max holds the maximal value of all values in A[1..i-1] (that is: values at indices 1 to i-1). Using this loop invariant, prove the correct of algorithm MaxValue. Follow the standard three steps... Initialization: Prior to the first iteration, where i = 2, show that the invariant holds. Maintenance: Based on the initialization, the loop invariant is known to holds prior to the some i-th iteration. Show that the loop invariant will also hold prior to the i+1-the iteration. Termination: Show that after the Nth (last) iteration (prior to an imaginary N+1st iteration), the loop invariant still holds. Argue that this state means that the solution to the problem (the largest value in the array) has been found.

Problem 1: Given is the following algorithm to determine the maximal value of an array A of size N. MaxValue (A[1..N]): max = A[1] i = 2 for (i < N): { if A[i]> max: max = A[i] i=i+1 }| return max A loop invariant is stated as: Variable max holds the maximal value of all values in A[1..i-1] (that is: values at indices 1 to i-1). Using this loop invariant, prove the correct of algorithm MaxValue. Follow the standard three steps... Initialization: Prior to the first iteration, where i = 2, show that the invariant holds. Maintenance: Based on the initialization, the loop invariant is known to holds prior to the some i-th iteration. Show that the loop invariant will also hold prior to the i+1-the iteration. Termination: Show that after the Nth (last) iteration (prior to an imaginary N+1st iteration), the loop invariant still holds. Argue that this state means that the solution to the problem (the largest value in the array) has been found.

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Problem 1: Given is the following algorithm to determine the maximal value of an array A of size N. MaxValue (A[1..N]): max = A[1] i = 2 for (i < N) : { if A[i]> max: max = A[i] i=i+1 }| return max A loop invariant is stated as: Variable max holds the maximal value of all values in A[1..i-1] (that is: values at indices 1 to i-1). Using this loop invariant, prove the correct of algorithm MaxValue. Follow the standard three steps... Initialization: Prior to the first iteration, where i = 2, show that the invariant holds. Maintenance: Based on the initialization, the loop invariant is known to holds prior to the some i-th iteration. Show that the loop invariant will also hold prior to the i+1-the iteration. Termination: Show that after the Nth (last) iteration (prior to an imaginary N+1st iteration), the loop invariant still holds. Argue that this state means that the solution to the problem (the largest value in the array) has been found.
Transcribed Image Text:Problem 1: Given is the following algorithm to determine the maximal value of an array A of size N. MaxValue (A[1..N]): max = A[1] i = 2 for (i < N) : { if A[i]> max: max = A[i] i=i+1 }| return max A loop invariant is stated as: Variable max holds the maximal value of all values in A[1..i-1] (that is: values at indices 1 to i-1). Using this loop invariant, prove the correct of algorithm MaxValue. Follow the standard three steps... Initialization: Prior to the first iteration, where i = 2, show that the invariant holds. Maintenance: Based on the initialization, the loop invariant is known to holds prior to the some i-th iteration. Show that the loop invariant will also hold prior to the i+1-the iteration. Termination: Show that after the Nth (last) iteration (prior to an imaginary N+1st iteration), the loop invariant still holds. Argue that this state means that the solution to the problem (the largest value in the array) has been found.
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