Sort Transformed Array in C++

Suppose we have a sorted array of integer nums and integer values a, b and c. We have to apply a quadratic function of the form f(x) = ax^2 + bx + c to each element x in the array. And the final array must be in sorted order.

So, if the input is like nums = [-4,-2,2,4], a = 1, b = 3, c = 5, then the output will be [3,9,15,33]

To solve this, we will follow these steps −

Define function f(), that takes x, a, b, c −
return ax^2 + bx + c
From the main method do the following −
n := size of nums
start := 0, end := n - 1
Define an array ret of size n
if a >= 0, then −
- for initialize i := n - 1, when i >= 0, update (decrease i by 1), do −
  - x := f(nums[start], a, b, c)
  - y := f(nums[end], a, b, c)
  - if x > y, then −
    - (increase start by 1)
    - ret[i] := x
  - Otherwise
    - ret[i] := y
    - (decrease end by 1)
Otherwise
- for initialize i := 0, when i < n, update (increase i by 1), do −
  - x := f(nums[start], a, b, c)
  - y := f(nums[end], a, b, c)
  - if x < y, then −
    - (increase start by 1)
    - ret[i] := x
  - Otherwise
    - ret[i] := y
    - (decrease end by 1)
return ret

Example

Let us see the following implementation to get better understanding −

Live Demo

#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:
   int f(int x, int a, int b, int c){
      return a * x * x + b * x + c;
   }
   vector<int< sortTransformedArray(vector<int<& nums, int a, int b, int c) {
      int n = nums.size();
      int start = 0;
      int end = n - 1;
      vector<int< ret(n);
      if (a >= 0) {
         for (int i = n - 1; i >= 0; i--) {
            int x = f(nums[start], a, b, c);
            int y = f(nums[end], a, b, c);
            if (x > y) {
               start++;
               ret[i] = x;
            }
            else {
               ret[i] = y;
               end--;
            }
         }
      }
      else {
         for (int i = 0; i < n; i++) {
            int x = f(nums[start], a, b, c);
            int y = f(nums[end], a, b, c);
            if (x < y) {
               start++;
               ret[i] = x;
            }
            else {
               ret[i] = y;
               end--;
            }
         }
      }
      return ret;
   }
};
main(){
   Solution ob;
   vector<int< v = {-4,-2,2,4};
   print_vector(ob.sortTransformedArray(v, 1, 3, 5));
}