问题
// Find a maximum element in the array.
findMax(A)
findMaxHelper(A, 0, A.length)
findMaxHelper(A, left, right)
if (left == right - 1)
return A[left]
else
max1 = findMaxHelper(A, left, (right + left) / 2)
max2 = findMaxHelper(A, (right + left) / 2, right)
if (max1 > max2)
return max1
else
return max2
I am having a hard time understanding what is happening in this pseudo-code.
Can someone help explain what is happening at each line. I need to understand this code before I can answer the questions.
I know that the function findMax calls the helper function findMaxHelper, then findMaxHelper uses recursion. Other than that, I really don't understand it.
回答1:
You are using Divide and Conquer algorithm for finding the maximum element from the array. First, you are dividing the array into individual elements (divide), then you are comparing the elements (conquer). You are dividing the array using calling findMaxHelper recursively.
The general idea of Divide and conquer is shown in the figure:
Example:
Here max is same as your findMaxHelper function with two arguments i.e. left and right.
Check this example for more in depth understanding of the concept.
回答2:
Jaguar has put the concept quite nicely and Paul has provided correct and detailed explanation. To add to this , I would like to share a simple C code that gives you an idea how the code gets executed. Here's the code with the same input Jaguar used :
#include<stdio.h>
int findMaxHelper(int A[], int left, int right){
int max1,max2;
int static tabcount;
int loop;
for(loop = 0 ; loop <tabcount;loop++) printf("\t");
tabcount++;
printf(" Entering: findMaxHelper(A, left = %d ,right = %d)\n\n",left,right);
if (left == right - 1){
for(loop = 0 ; loop <tabcount;loop++) printf("\t");
printf("\b\b\b\b\b\b\bLeaving: findMaxHelper(A, left = %d ,right = %d)| returning %d\n\n",left,right , A[left]);
tabcount--;
return A[left];
}
else
{
max1 = findMaxHelper(A, left, (right + left) / 2);
max2 = findMaxHelper(A, (right + left) / 2, right);
if (max1 > max2){
for(loop = 0 ; loop <tabcount;loop++) printf("\t");
printf("\b\b\b\b\b\b\bLeaving: findMaxHelper(A, left = %d ,right = %d) | returning max1=%d\n\n",left,right,max1);
tabcount--;
return max1;
}
else {
for(loop = 0 ; loop <tabcount;loop++) printf("\t");
printf("\b\b\b\b\b\b\bLeaving: findMaxHelper(A, left = %d ,right = %d)| returning max2=%d\n\n",left,right,max2);
tabcount--;
return max2;
}
}
}
int main (){
int A[] = { 34,3,47,91,32,0 };
int Ans =findMaxHelper(A,0,7);
printf( "And The Answer Is = %d \n",Ans);
}
U can copy paste the code on ur linux machine ...Maybe put sleep(5) after every printf and see how recursion ACTUALLY works !... Hope this helps... I will also share the output from my system here :
Entering: findMaxHelper(A, left = 0 ,right = 7)
Entering: findMaxHelper(A, left = 0 ,right = 3)
Entering: findMaxHelper(A, left = 0 ,right = 1)
Leaving: findMaxHelper(A, left = 0 ,right = 1)| returning 34
Entering: findMaxHelper(A, left = 1 ,right = 3)
Entering: findMaxHelper(A, left = 1 ,right = 2)
Leaving: findMaxHelper(A, left = 1 ,right = 2)| returning 3
Entering: findMaxHelper(A, left = 2 ,right = 3)
Leaving: findMaxHelper(A, left = 2 ,right = 3)| returning 47
Leaving: findMaxHelper(A, left = 1 ,right = 3)| returning max2=47
Leaving: findMaxHelper(A, left = 0 ,right = 3)| returning max2=47
Entering: findMaxHelper(A, left = 3 ,right = 7)
Entering: findMaxHelper(A, left = 3 ,right = 5)
Entering: findMaxHelper(A, left = 3 ,right = 4)
Leaving: findMaxHelper(A, left = 3 ,right = 4)| returning 91
Entering: findMaxHelper(A, left = 4 ,right = 5)
Leaving: findMaxHelper(A, left = 4 ,right = 5)| returning 32
Leaving: findMaxHelper(A, left = 3 ,right = 5) | returning max1=91
Entering: findMaxHelper(A, left = 5 ,right = 7)
Entering: findMaxHelper(A, left = 5 ,right = 6)
Leaving: findMaxHelper(A, left = 5 ,right = 6)| returning 0
Entering: findMaxHelper(A, left = 6 ,right = 7)
Leaving: findMaxHelper(A, left = 6 ,right = 7)| returning 0
Leaving: findMaxHelper(A, left = 5 ,right = 7)| returning max2=0
Leaving: findMaxHelper(A, left = 3 ,right = 7) | returning max1=91
Leaving: findMaxHelper(A, left = 0 ,right = 7)| returning max2=91
And The Answer Is = 91
回答3:
findMaxHelper divides the array into half each time, and find the max in left,right:
eg you have array A = [1, 3, 5, 8], call findMax(A) -> findMaxHelper(A, 0, A.length):
max1 | max2
1 3 | 5 8
max1|max2 | max1|max2
1 |3 | 5 |8
回答4:
#include<stdio.h>
#include<stdlib.h>
int high,*a,i=0,n,h;
int max(int *);
int main()
{
printf("Size of array: ");
scanf("%d",&n);
a=(int *)malloc(n*sizeof(int)); //dynamic allocation
for(i=0;i<n;i++)
{
scanf("%d",(a+i));
}
i=0;
high=*a;
h=max(a);
printf("The highest element is %d\n",h);
}
int max(int *a)
{
if(i<n)
{
if(*(a+i)>high)
{high=*(a+i);}
i++;
max(a); //recursive call
}
return high;
}
回答5:
Basically finding max in array is not recommended by recursion as it is not required. Divide and conquer algorithms(recursive) are more time costly. But even though if you want to use it, you can use my below algorithm. Basically, it brings the largest element of array at first position and has almost linear running time.(This algo is just a recursive-illusion though!):
int getRecursiveMax(int arr[], int size){
if(size==1){
return arr[0];
}else{
if(arr[0]< arr[size-1]){
arr[0]=arr[size-1];
}
return(getRecursiveMax(arr,size-1));
}
}
来源：https://stackoverflow.com/questions/13117159/find-maximum-value-in-an-array-by-recursion