问题
Based on the following definition found here
Returns an iterator pointing to the first element in the sorted range [first,last) which does not compare less than value. The comparison is done using either operator< for the first version, or comp for the second.
What would be the C equivalent implementation of lower_bound(). I understand that it would be a modification of binary search, but can't seem to quite pinpoint to exact implementation.
int lower_bound(int a[], int lowIndex, int upperIndex, int e);
Sample Case:
int a[]= {2,2, 2, 7 };
lower_bound(a, 0, 1,2) would return 0 --> upperIndex is one beyond the last inclusive index as is the case with C++ signature.
lower_bound(a, 0, 2,1) would return 0.
lower_bound(a, 0, 3,6) would return 3;
lower_bound(a, 0, 4,6) would return 3;
My attempted code is given below:
int low_bound(int low, int high, int e)
{
if ( low < 0) return 0;
if (low>=high )
{
if ( e <= a[low] ) return low;
return low+1;
}
int mid=(low+high)/2;
if ( e> a[mid])
return low_bound(mid+1,high,e);
return low_bound(low,mid,e);
}
回答1:
lower_bound is almost like doing a usual binary search, except:
- If the element isn't found, you return your current place in the search, rather than returning some null value.
- If the element is found, you search leftward until you find a non-matching element. Then you return a pointer/iterator to the first matching element.
Yes, it's really that simple. :-)
回答2:
Here are the equivalent implementations of upper_bound and lower_bound. This algorithm is O(log(n)) in the worst case, unlike the accepted answer which gets to O(n) in the worst case.
Note that here high index is set to n instead of n - 1. These functions can return an index which is one beyond the bounds of the array. I.e., it will return the size of the array if the search key is not found and it is greater than all the array elements.
int bs_upper_bound(int a[], int n, int x) {
int l = 0;
int h = n; // Not n - 1
while (l < h) {
int mid = (l + h) / 2;
if (x >= a[mid]) {
l = mid + 1;
} else {
h = mid;
}
}
return l;
}
int bs_lower_bound(int a[], int n, int x) {
int l = 0;
int h = n; // Not n - 1
while (l < h) {
int mid = (l + h) / 2;
if (x <= a[mid]) {
h = mid;
} else {
l = mid + 1;
}
}
return l;
}
The actual C++ implementation works for all containers. You can find it here.
回答3:
The lower_bound and upper_bound functions in python would be implemented as follows:
def binLowerBound(a, lo, hi, x):
if (lo > hi):
return hi
mid = (lo + hi) / 2;
if (a[mid] == x):
return binLowerBound(a, lo, mid-1, x)
elif (a[mid] > x):
return binLowerBound(a, lo, mid-1, x)
else:
return binLowerBound(a, mid+1, hi, x)
def binHigherBound(a, lo, hi, x):
if (lo > hi):
return lo
mid = (lo + hi) / 2;
if (a[mid] == x):
return binHigherBound(a, mid+1, hi, x)
elif (a[mid] > x):
return binHigherBound(a, lo, mid-1, x)
else:
return binHigherBound(a, mid+1, hi, x)
回答4:
I know that this is a very old post. However, I was working on a problem and I came across this post. I would like to add my iterative version for the problem which is an extension of the last answer. I checked this with the test cases I could think of. I've attached my code in C#.
This code was working for all ranges. However, the range should be within the first index to the last index+1. If the array is of size N and considering range as [0,N] the search space will be within [0,N). I know that's pretty obvious but it helped me checking some edge cases.
static int lower_bound(int[] a, int lo,int hi, int x)
{
while (lo < hi)
{
int mid = lo + (hi-lo) / 2;
if(a[mid]==x)
{
/*when there is a match, we should keep on searching
for the next same element. If the same element is not
found, mid is considered as the answer and added to 'hi'
Finally 'hi' is returned*/
if(a[mid-1]!=x)
{
hi=mid;
break;
}
else
hi=mid-1;
}
else if(a[mid]>x)
hi=mid-1;
else
lo=mid+1;
}
//if element is not found, -1 will be returned
if(a[hi]!=x)
return -1;
return hi;
}
static int upper_bound(int[] a, int lo,int hi, int x)
{
int temp=hi;
while (lo < hi)
{
int mid = lo + (hi-lo) / 2;
if(a[mid]==x)
{
/*this section make sure that program runs within
range [start,end)*/
if(mid+1==hi)
{
lo=mid;
break;
}
/*when there is a match, we should keep on searching
for the next same element. If the same element is not
found, mid is considered as the answer and added to
'lo'. Finally 'lo' is returned*/
if(a[mid+1]!=x)
{
lo=mid;
break;
}
else
lo=mid+1;
}
else if(a[mid]>x)
hi=mid-1;
else
lo=mid+1;
}
//if element is not found, -1 will be returned
if(a[lo]!=x)
return -1;
return lo;
}
Here is a test case that I used:
Array(a) : 1 2 2 2 2 5 5 5 5
size of the array(a) : 9
Considering search element as 2:
upper_bound(a,0,9,2)=4, lower_bound(a,0,9,2)=1
Considering search element as 5:
upper_bound(a,0,9,2)=8, lower_bound(a,0,9,2)=5
Considering search element as 1:
upper_bound(a,0,9,2)=0, lower_bound(a,0,9,2)=0
Considering search element as 5:
upper_bound(a,5,9,2)=8, lower_bound(a,5,9,2)=5
回答5:
int lowerBound (int *a, int size, int val) {
int lo = 0, hi = size - 1;
while (lo < hi) {
int mid = lo + (hi - lo)/2;
if (a[mid] < val)
lo = mid + 1;
else
hi = mid;
}
return lo;
}
回答6:
C++ Implementation
int binary_search_lower_bound(vector<int>& array, int target) {
int lo = 0, hi = (int)array.size();
int mid;
while(lo < hi) {
mid = lo + ((hi - lo) >> 1);
int val = array[mid];
if (target <= val)//array[mid])
hi = mid;
else
lo = mid + 1;
}
return lo;
}
Edit: Fixed bug for non-existing value.
回答7:
Example if this is the given array
1 2 3 3 4
and different values of x is
3 then firstOccurance will be 2 and lastOccurance will be 3
2 then firstOccurance will be 1 and lastOccurance will be 1
10 then firstOccurance will be -1 and lastOccurance will be -1
int firstOccurance(vector<int>& arr, int x){
int low = 0;
int high = arr.size();
int ans=-1;
while(low<=high){
int mid = (low+high)/2;
if(arr[mid]==x) ans=mid;
if(arr[mid]>=x) high=mid-1;
else low = mid+1;
}
return ans;
}
int lastOccurance(vector<int>& arr, int x){
int low = 0;
int high = arr.size();
int ans=-1;
while(low<=high){
int mid = (low+high)/2;
if(arr[mid]==x) ans=mid;
if(arr[mid]<=x) low=mid+1;
else high = mid-1;
}
return ans;
}
来源：https://stackoverflow.com/questions/6443569/implementation-of-c-lower-bound