Chapter II algorithms work test report

Experimental reporting requirements choose one topic for analysis. content include:

1. Practice topic
2. Problem Description
3. Algorithm Description
4. Time and space complexity algorithm analysis (analysis process have)
5. Feelings and experiences (for this practice of harvesting and doubts summarize)

The practice of a total of three questions, I chose to analyze the first question.

1. Practice questions asked:

7-1 binary search (20 points)

Value for n (1 <= n <= 1000), n non-descending order of an integer and the number of x to find, using the binary search algorithm to find the x, output x where the subscripts (0 ~ n-1) and the number of comparisons . If x does not exist, the output 1 and the number of comparisons.

Input formats:

The input common three lines: The first line is the value of n; n is an integer second line; the third line is the x value.

Output formats:

Where the subscript x output (0 ~ n-1) and the number of comparisons. If x does not exist, the output 1 and the number of comparisons.

2. Description of the problem:

It is simply in a non-descending order list to find the data you want to find, and compare the number of output index, using the methods specified dichotomy

Binary basic idea is to find the n elements is divided into two approximately equal portions, to take a [n / 2] x and compared, if x = a [n / 2], x is found, the algorithm is aborted. If x <a [n / 2], as long as the left half of the array a continuing search for x, if x> a [n / 2], the search for the right half of x as long as the array a. Such has been the search continues

3. Algorithm Description

　　3.1 Find interval counter initial value, left is 0, right to n-1

　　3.2 or less when left right, execute the following cycle of operations:

• 　　middle value is the middle value of the left and right;
• 　　Recording the number of cycles counter + 1.
• 　　The setting position of the recording intermediate key x are compared, if equal, the search is successful, return to the neutral position Middle;
• 　　If not equal, the recording sheet by the intermediate position into the former, the two sub-tables. If the key is smaller than the intermediate position of the recording of x, is taken as the left middle-1, otherwise it is taken right middle + 1.

　　3.3 cycle ends, the instructions to locate the interval is empty, then the lookup fails, returns 0.

Code Description:

int Binsearch(int array[], int n, int x){
    int left = 0;
    int right = n - 1;
    int counter = 0;
    while(left <= right){
        int middle = (left + right) / 2;
        counter++;
        if(x == array[middle]){
            cout << middle << endl;
            cout << counter;
            return middle;
        }
        if(x > array[middle]){
            left = middle + 1;
        }
        else right = middle - 1;
        
    }
        cout << "-1" << endl;
        cout <<counter; 
        return -1;
}

4. The time and complexity of the spatial analysis algorithm

Time complexity: a total of n elements, once for each section is the size of n, n / 2, n / 4, ..., n / 2 ^ k (Next, the operation of the remaining number of elements), where k is the cycle frequency. Since n / 2 ^ k after rounding> = 1, and even if n / 2 ^ k = 1, can be obtained k = log2n, (based on base 2, n for logarithmic), it may represent a time complexity O () = O (logn)

Space complexity: since in an array can be completed all the work, so that the space complexity of O (1)

5. feelings and experiences (for this practice of harvesting and doubts summarize)

Harvest is I am more familiar with the binary search algorithm

There are small details need to pay attention to some of the code:

• Functions can not return value of the function,
• Find the names of some variables such as the number of variable records should note, the best counter counts the class, boolean with flag