MIT 算法导论 （四） Divide and Conquer

Steps:

• Divide the problem (instance) into subproblems.
• Conquer the subproblems by solving them recursively.
• Combine subproblem solutions.

A typical algorithm solved by D&V is merge sort. Frist we partitions the array into two sorted array recursivly, that is the Dvide part.Then we combine the two sorted array into one sorted array(the subroutine), that is the conquer part. At last we combine these steps , that is the combine part (almost do nothing, that's why the name got no "combine").

 

A example of D&C solution. compute xⁿ  .  T(n) = lgn (write by myself don't judge pl)

function ntox(x,n)
{
    if(n == 1) return x;
    if(n%2 == 0)
    {//even
        var res = ntox(x,n/2);
        var result = res * res;
    }
    else
    {//odd
        var res = ntox(x,(n-1)/2) ;
        var result = res * res * x;
    }
    return result;
}