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Count of Smaller Numbers After Self in C++
Suppose we have an array nums, we have to find another array called count, in this count array, the count[i] stores the number of smaller elements to the right of nums[i].
So if the input is like: [5,2,7,1], then the result will be [2,1,1,0].
To solve this, we will follow these steps −
Define one method called update(), this will take index, array bit and n
while index <= n, do −
increase bit[index]
index = index + (index) AND ( - index)
Define one array called query(), this will take index and bits array
ans := 0
while index > 0, do −
ans = ans + bit[index]
index = index – (index AND - index)
return ans
From the main method, do the following −
n := size of nums
Define an array res of size n
if (n is non-zero) is false, then, return res
maxx := 0, minn = nums [0]
for initializing i := 1, when i < n, increase i by 1 do −
minn := min of nums[i] and minn
for initializing i := 0, when i < n, increase i by 1 do −
nums[i] := nums[i] - minn + 1
maxx := max of nums[i] and maxx
Define an array bit of size maxx + 1
for initializing i := n - 1, when i >= 0, decrease i by 1 do −
num = nums[i] – 1
x := Call the function query(num,bit)
res[i] := x
Call the function update(num + 1, bit, maxx)
return res
Example
Let us see the following implementation to get better understanding −
#include <bits/stdc++.h>
using namespace std;
void print_vector(vector<auto> v){
cout << "[";
for(int i = 0; i<v.size(); i++){
cout << v[i] << ", ";
}
cout << "]"<<endl;
}
class Solution {
public:
void update(int index,vector <int>& bit, int n){
while(index<=n){
bit[index]++;
index += (index)&(-index);
}
}
int query(int index, vector <int> bit){
int ans = 0;
while(index>0){
ans+=bit[index];
index -= index&(-index);
}
return ans;
}
vector<int> countSmaller(vector<int>& nums) {
int n = nums.size();
vector <int> res(n);
if(!n)return res;
int maxx = 0;
int minn = nums[0];
for(int i =1;i<n;i++)minn = min(nums[i],minn);
for(int i =0;i<n;i++){
nums[i] = nums[i]-minn+1;
maxx = max(nums[i],maxx);
}
vector <int> bit(maxx+1);
for(int i =n-1;i>=0;i--){
int num = nums[i]-1;
int x = query(num,bit);
res[i] = x;
update(num+1,bit,maxx);
}
return res;
}
};
main(){
Solution ob;
vector<int> v = {5,2,7,1};
print_vector(ob.countSmaller(v));
}Input
[5,2,7,1]
Output
[2, 1, 1, 0, ]
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