Calculation after the for loop is incorrect (C++) - c++

Question

The code I am currently working on is a random walker. The code represents a person taking a step in any random direction (up,down,left,right), then the new location is printed out respectively. In the beginning the user is prompted to enter any amount of steps or how many times the loop should be iterated. The goal of the code is to calculate the squared distance between (0,0)initial and (x,y)final. The distance should be equal to (xx)+(yy) because the initial position that would normally be subtracted is (0,0). The issue or semantic issue I am running into is with the distance calculation. The calculation is not always using the correct x or y value. For example if the final location was (0,-4), somehow x = -1, therefore the distance equals 17 instead of 16. This first example is in image 1. Image 2 is another run for the code. Any help or tips would be greatly appreciated, here is the code:
#include <iostream>
#include <stdlib.h>
#include <ctime>
#include <cmath>
using namespace std;
int main(){
int N;
cout << "Please enter N amount of steps, and for NetBeans users press
'enter' twice." << endl;
cin >> N;
cout << "% RandomWalker " << N << endl;;
int r;
srand( time(0));
int x = 0;
int y = 0;
for(int i = 0; i <= N; i++) {
cout << "(" << x << ", " << y << ")" << endl;
r=rand()%4;
if (r == 0 )
x++;
else if (r == 1 )
x--;
else if (r == 2 )
y++;
else if (r == 3 )
y--;
}
int d = (x*x)+(y*y);
cout << "the distance equals: " << d << endl;
cout << endl;
cout << "x equals before: "<< x << endl;
x = (pow(x,2));
cout << "x equals after squaring: "<< x << endl;
cout << endl;
cout <<"y equals before: " << y << endl;
y = (pow(y,2));
int sum = x + y;
cout <<"y equals after squaring: " << y << endl;
cout << endl;
cout << "x+y after squaring equals: " << sum << endl;
}

Answer 1

for(int i = 0; i <= N; i++)
Since you are starting from 0, the condition should be i < N.
Next issue, is int d = (x*x)+(y*y); The distance formula is
So the initialization should be
int d = sqrt((x * x) + (y * y));
Also what is the point of squaring the x and y values at the end?

Answer 2

You are printing the position BEFORE it is changed based on the value of r. So the last value that's printed out is not the actual final value of x and y, but the one of one step earlier. That's why you're getting unexpected distance.

Answer 3

Sorry for the delayed response, I figured out what I had to do. The object of the assignment was to print out each location and find the squared distance at the end of the loop. Here was the solution for anyone interested.
#include <iostream>
#include <stdlib.h>
#include <ctime>
#include <cmath>
using namespace std;
int main(){
int N;
cout << "Please enter N amount of steps, and for NetBeans users press
'enter' twice." << endl;
cin >> N;
cout << "% RandomWalker " << N << endl;;
int r;
srand( time(0));
int x = 0;
int y = 0;
cout << "(" << x << ", " << y << ")" << endl;
for(int i = 1; i <= N; i++) {
r=rand()%4;
if (r == 0 )
x++;
else if (r == 1 )
x--;
else if (r == 2 )
y++;
else if (r == 3 )
y--;
cout << "(" << x << ", " << y << ")" << endl;
}
x = (pow(x,2));
y = (pow(y,2));
int squaredDistance = x + y;
cout << "The squared distance is " << squaredDistance << endl;
}