note of introduction of Algorithms(Lecture 3 - Part1)

Lecture 3（part 1）

Divide and conquer

1. the general paradim of algrithm as bellow:

1. divide the problem into subproblems;

2. conqure each subproblems recrusively;

3. combine solution

2. Some typical problem (part 1)

the matrix mutiplication(strassen's algorithm) and the vlsi layout problem will be in the note leceture part 2.

• binary search

/*-

* MIT introduction of algrithm

* Lecture 3: binary search

* Fredric  : 2013-11-18

*/

#include<stdio.h>

#include<stdlib.h>



typedef unsigned int uint;



#define    MAX  11

uint g_array[MAX] = {1,2,3,5,7,12,16,34,67,89,100};

uint target = 100; //target number

int binarysearch(uint start, uint end);



void main(void)

{    

    int n = 0;

    printf("start to find the num:%d..\t\n", target);

    if(-1 != (n = binarysearch(0, MAX-1))){

        printf("the target %d has been found in num:%d", g_array[n],n);

    }

    system("pause");

    return;

}



/*-

* binary search recursive

*/

int binarysearch(uint start, uint end){

    uint n   = (start + end)/2;

    uint tmp = g_array[n];



    if(target == tmp){

        return n;

    }else{

        if(tmp > target){

            return binarysearch(start, n);

        }else{

            return binarysearch(n+1,end);

        }

    }

    return -1;

}

View Code

• powering a number

/*-

* MIT introduction of algrithm

* Lecture 3: powering a number

* Fredric  : 2013-11-17

*/

#include<stdio.h>

#include<stdlib.h>



typedef unsigned int uint;



//calculate the result of n^m, like n = 2, m = 3, result = 8

uint n = 10;

uint m = 7;// m > 1



double power_number(uint n, uint m); 



/*

* main function

*/

void main(void)

{    

    double result    = 0.0;

    result            = power_number(n,m);

    printf("the result of %d^%d is %lf /t/n", n,m,result);

    system("pause");

    return;

}



/*-

* powering a number

* result = 

* n^(m/2) * n^(m/2)           if m is even

* n^((m-1)/2) * n^((m-1)/2)*n if m is odd

*/

double power_number(uint n, uint m){

    if(0 == m){

        return 1;

    }



    if(0 == m%2){

        return power_number(n,m/2)*power_number(n,m/2);

    }else{

        return power_number(n,(m-1)/2)*power_number(n,(m-1)/2)*n;

    }

}

View Code

• Fibonacci number（using matrix mutiplication）

/*-

* MIT introduction of algrithm

* Lecture 3: Fibonnaci,using the matrix method

* Fredric  : 2013-11-17

*/

#include<stdio.h>

#include<stdlib.h>



typedef unsigned int uint;



/*-

* Input:

* pa00/01/10/11 according to the element of the Array Aij

* n: the number of the fibonacci

*/

void fibonacci_number(uint *pa00, uint *pa01, uint *pa10,uint *pa11, uint n);



void main(void)

{

    uint a00 = 1;

    uint a01 = 1;

    uint a10 = 1;

    uint a11 = 0;



    uint num = 9;//num > 0

    fibonacci_number(&a00,&a01,&a10,&a11, num);

    printf("The num %d fibonacci number is:%d\t\n", num, a10);



    system("pause");

    return;

}



/*-

* calculate the fibonacci number

* f(n) = 

* 0 if n = 0;

* 1 if n = 1;

* f(n-1) + f(n-1) if n > 1

* the divide and conquer algrithm is:

*  fn+1 fn      1   1  

*(        )  = (     )^n 

*  fn   fn-1    1   0

*/

void fibonacci_number(uint *pa00, uint *pa01, uint *pa10,uint *pa11, uint n){

    uint tmp00 = *pa00;

    uint tmp01 = *pa01;

    uint tmp10 = *pa10;

    uint tmp11 = *pa11;



    if(1 == n){

        return;

    }else{

        //Matrix mutiplication

        *pa00 = tmp00 * tmp00 + tmp01 * tmp10;

        *pa01 = tmp00 * tmp01 + tmp01 * tmp11;

        *pa10 = tmp10 * tmp00 + tmp11 * tmp10;

        *pa11 = tmp10 * tmp01 + tmp11 * tmp11;

        if(0 == n%2){

            fibonacci_number(pa00,pa01,pa10,pa11,n/2);

        }else{



            fibonacci_number(pa00,pa01,pa10,pa11,(n-1)/2);

            uint tmp00 = *pa00;

            uint tmp01 = *pa01;

            uint tmp10 = *pa10;

            uint tmp11 = *pa11;



            *pa00 = tmp00 + tmp01;

            *pa01 = tmp00;

            *pa10 = tmp10 + tmp11;

            *pa11 = tmp10;

        }

    }

}

View Code