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Merge Sort Tree in C++
We are given an integer array, a set of segment start and end pointers and a key value and the problem statement here is to find all the values in the given range which are smaller than or equal to the given key value.
Let us understand with example
Input − arr[] = {7, 8 , 1, 4 , 6 , 8 , 10 }
Segment 1: start = 2, end = 4, k = 2
Segment 2: start = 1, end = 6, k = 3
Output − Count of number which are smaller than or equal to key value in the given range are 2 6
Explanation − [8, 1, 4] represents the range from 2 to 4 and 2 is the 2nd smallest number in the range [7, 8 , 1, 4 , 6 , 8 ] represents the range from 1 to 6 and 6 is the 3rd smallest number in the range
Input − arr[] = {2, 7 , 9, 4 , 6 , 5 , 1 |
Segment 1: start = 3, end = 6, k = 4
Segment 2: start = 2, end = 5, k = 3
Output − Count of number which are smaller than or equal to key value in the given range are: 9 7
Explanation − [9, 4 , 6 , 5] represents the range from 3 to 6 and 9 is the 4th smallest number in the given range [7 , 9, 4 , 6 ] represents the range from 2 to 4 and 7 is the 3rd smallest number in the given segment range
Approach used in the below program is as follows −
Declare an integer type array. Calculate the size of an array. Declare a vector type variable forming the pair of integer types. Start FOR loop to push the data from array to vector.
Sort the given vector. Create a vector array of integer types with the MAX size.
Call the function as generateTree(1, 0, size - 1, vec, tree) and set getSmallestIndex to queryWrapper(2, 5, 2, size, vec, tree).
Print the input[getSmallestIndex].
Set getSmallestIndex to call the function as queryWrapper(1, 6, 4, size, vec, tree).
Inside the function as void generateTree(int treeIndex, int leftIndex, int rightIndex, vector<pair<int, int> > &a, vector<int> tree[])
Check IF leftIndex to rightIndex then set tree[treeIndex].push_back(a[leftIndex].second) and return
Set midValue to (leftIndex + rightIndex) / 2and call generateTree(2 * treeIndex, leftIndex, midValue, a, tree), generateTree(2 * treeIndex + 1, midValue + 1, rightIndex, a, tree) and merge(tree[2 * treeIndex].begin(), tree[2 * treeIndex].end(), tree[2 * treeIndex + 1].begin(). Set tree[2 * treeIndex + 1].end(),back_inserter(tree[treeIndex]))
Inside the function as int calculateKSmallest(int startIndex, int endIndex, int queryStart, int queryEnd, int treeIndex, int key, vector tree[])
Check IF startIndex to endIndex then return tree[treeIndex][0]
Set mid to (startIndex + endIndex) / 2, last_in_query_range to (upper_bound(tree[2 * treeIndex].begin(),tree[2 * treeIndex].end(), queryEnd) - tree[2 * treeIndex].begin())
set first_in_query_range to (lower_bound(tree[2 * treeIndex].begin(),tree[2 * treeIndex].end(), queryStart) - tree[2 * treeIndex].begin()) and M to last_in_query_range - first_in_query_range
Check IF M greater than equals to key then return calculateKSmallest(startIndex, mid, queryStart,queryEnd, 2 * treeIndex, key, tree)
ELSE, then return calculateKSmallest(mid + 1, endIndex, queryStart, queryEnd, 2 * treeIndex + 1, key - M, tree).
Inside the function int queryWrapper(int queryStart, int queryEnd, int key, int n, vector<pair<int, int> > &a, vector<int>tree[])
return call to the function calculateKSmallest(0, n - 1, queryStart - 1, queryEnd - 1, 1, key, tree)
Example
#include <bits/stdc++.h>
using namespace std;
const int MAX = 1000;
void generateTree(int treeIndex, int leftIndex, int rightIndex, vector<pair<int, int> > &a, vector<int> tree[]){
if (leftIndex == rightIndex){
tree[treeIndex].push_back(a[leftIndex].second);
return;
}
int midValue = (leftIndex + rightIndex) / 2;
generateTree(2 * treeIndex, leftIndex, midValue, a, tree);
generateTree(2 * treeIndex + 1, midValue + 1, rightIndex, a, tree);
merge(tree[2 * treeIndex].begin(), tree[2 * treeIndex].end(), tree[2 * treeIndex + 1].begin(),
tree[2 * treeIndex + 1].end(), back_inserter(tree[treeIndex]));
}
int calculateKSmallest(int startIndex, int endIndex, int queryStart, int queryEnd, int treeIndex, int key, vector<int> tree[]){
if (startIndex == endIndex){
return tree[treeIndex][0];
}
int mid = (startIndex + endIndex) / 2;
int last_in_query_range = (upper_bound(tree[2 * treeIndex].begin(), tree[2 * treeIndex].end(), queryEnd) - tree[2 * treeIndex].begin());
int first_in_query_range = (lower_bound(tree[2 * treeIndex].begin(), tree[2 * treeIndex].end(),queryStart) - tree[2 * treeIndex].begin());
int M = last_in_query_range - first_in_query_range;
if (M >= key){
return calculateKSmallest(startIndex, mid, queryStart, queryEnd, 2 * treeIndex, key, tree);
}
else {
return calculateKSmallest(mid + 1, endIndex, queryStart,queryEnd, 2 * treeIndex + 1, key - M, tree);
}
}
int queryWrapper(int queryStart, int queryEnd, int key, int n,
vector<pair<int, int> > &a, vector<int> tree[]){
return calculateKSmallest(0, n - 1, queryStart - 1, queryEnd - 1, 1, key, tree);
}
int main(){
int input[] = { 7, 8 , 1, 4 , 6 , 8 , 10 };
int size = sizeof(input)/sizeof(input[0]);
vector<pair<int, int> > vec;
for (int i = 0; i < size; i++) {
vec.push_back(make_pair(input[i], i));
}
sort(vec.begin(), vec.end());
vector<int> tree[MAX];
generateTree(1, 0, size - 1, vec, tree);
cout<<"Count of number which are smaller than or equal to key value in the given range are:"<<endl;
int getSmallestIndex = queryWrapper(2, 4, 2, size, vec, tree);
cout << input[getSmallestIndex] << endl;
getSmallestIndex = queryWrapper(1, 6, 3, size, vec, tree);
cout << input[getSmallestIndex] << endl;
return 0;
}Output
If we run the above code it will generate the following Output
Count of number which are smaller than or equal to key value in the given range are: 4 6
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