Analyze the following algorithm, and determine it's computational complexity. Find the number of times each step is executed.

Algorithm M: Given n elements X[1], X[2],..., X[n], we will find m and j such that $$m = X[j] = max_{1 \leq i \leq n}X[i]$$ where j is the largest index that satisfies this relation.

M1 [Initialization] j := n, k := n-1, m := X[n];
M2 [All tested?] IF k = 0 THEN TERMINATE;
M3 [Compare.] IF $$X[k] \leq m$$ THEN GOTO M5;
M4 [Change m.] j := k, m := X[k];
M5 [Decrease k] k := k - 1; GOTO M2

Question

Analyze the following algorithm, and determine it's computational complexity. Find the number of times each step is executed.

Algorithm M: Given n elements X[1], X[2],..., X[n], we will find m and j such that $$m = X[j] = max_{1 \leq i \leq n}X[i]$$ where j is the largest index that satisfies this relation.

M1 [Initialization] j := n, k := n-1, m := X[n];
M2 [All tested?] IF k = 0 THEN TERMINATE;
M3 [Compare.] IF $$X[k] \leq m$$ THEN GOTO M5;
M4 [Change m.] j := k, m := X[k];
M5 [Decrease k] k := k - 1; GOTO M2