One algorithm per day (finding the smallest k elements (arrays ))

Question:

Input n integers and output k smallest numbers.

For example:

For example, if you enter the 8 numbers 1, 2, 3, 5, 6, 7, and 8, the minimum four digits are 1, 2, 3, and 4.
Solution:
Of course, the simplest method is to sort all the n integers, but the time complexity of this method is particularly high.
Therefore, I used another k space in exchange for time. Each time a number is read from the input n integers. If the number of inserted elements in the array is less than k, the read integer is directly put into the array. Otherwise, the array with the length of k is full and cannot be inserted into the array. It can only be replaced.
If the integer to be read is smaller than the maximum value of k integers in the array, replace the maximum value with the integer to be read; if the integer to be read is larger than the maximum value of k integers in the array, the integer to be read cannot be one of the smallest k integers. This approach is equivalent to sorting k integers, so time complexity can be reduced to O (n + nlogk ). Generally, k is much smaller than n, so this method is better than the previous idea.

Run the following program in VS2010: The program in the example is correct. If there is any error, you may wish to specify it ..
[Cpp]
<Span style = "font-size: 18px;" >#include <iostream>
# Include <limits. h>
Using namespace std;
# Define N 100
# Define K 5
 
Void bubble_sort_k (int array [], int num)
{
Int I = 0;
Int j = 0;
// Int flag = 0;
Int temp = 0;
For (I = 0; I <num; I ++)
{
// Flag = 1;
For (j = I + 1; j <num; j ++)
{
If (array [I]> array [j])
{
Temp = array [j];
Array [j] = array [I];
Array [I] = temp;
// Flag = 0;
}
}
// If (flag = 1)
// Break;
}
Return;
}
 
Int main ()
{
Int array_n [N] = {INT_MAX };
// Int array_n [N] = {9, 8, 7, 6, 5, 4, 3, 2, 1 };
Int array_k [K] = {INT_MAX };
Int I = 0;
Int j = 0;
Int m = 0;
Int number = 0;
While (cin> I)
{
 
Array_n [number] = I;
Number ++;
}
// Number = 9;
For (j = 0; j <K; j ++)
{
Array_k [j] = array_n [j];
}

Bubble_sort_k (array_k, K );
 
For (I = K; I <number; I ++)
{
For (j = 0; j <K; j ++) // compare from the smallest element of the array
{
If (array_n [I] <array_k [j])
{
For (int n = K-1; n> j; n --) // After finding which element is smaller than this number, move the subsequent part to remove the largest element from the array.
{
Array_k [n] = array_k [n-1];
}
Array_k [j] = array_n [I];
Break;
}
}
}
For (m = 0; m <K; m ++)
{
Cout <array_k [m] <endl;
}
Return 0;
}
</Span>