分析以下算法的T(n)x=0;y=0;for (k=1;k<=n;k++)x++;for (i=1;i<=n;i++)for (j=1;j<=n;j++)y++;
Question
分析以下算法的T(n)
x=0;
y=0;
for (k=1;k<=n;k++)
x++;
for (i=1;i<=n;i++)
for (j=1;j<=n;j++)
y++;
Solution
The given algorithm consists of two main parts.
-
The first loop:
for (k=1;k<=n;k++)x++;This loop runs 'n' times. Therefore, the time complexity of this loop is O(n). -
The second part:
for (i=1;i<=n;i++)for (j=1;j<=n;j++)y++;This is a nested loop where both the outer loop and the inner loop run 'n' times. Therefore, the time complexity of this part is O(n^2).
When we consider the entire algorithm, we take the highest order of the time complexities of all parts. Therefore, the time complexity T(n) of the given algorithm is O(n^2).
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