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Consider the following program, where a and n are positive integers. Input: a, n x = a; m = n; y = 1; while (m
Consider the following program, where a and n are positive integers.
Input: a, n x = a;
m = n; y = 1;
while (m > 1) {
if m is even x = x*x;
m = m/2;
else if m is odd y = x*y;
x = x*x;
m = (m-1)/2;
}
Output x*y
Let xi , yi , and mi denote the value of the variables x, y, and m at the start of the ith iteration. Using induction show the following
i an = x mi i yi
Your proof must use induction. Otherwise you will not receive any credit.
3. Consider the following program, where a and n are positive integers. Input: a, n x = a; m=n; y = 1; while (m >1) if m is even x*x; x = else if m is odd y x m x*y; x*x ; (m-1)/2; = = = Output x*y Let ri, yi, and mi denote the value of the variables x, y, and m at the start of the ith iteration Using induction show the following mi Your proof must use induction. Otherwise you will not receive any creditStep by Step Solution
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