Counting Frog Paths

There is a frog initially placed at the origin of the coordinate plane. In exactly 

$1$ second, the frog can either move up $1$ the unit, move right $1$ unit, or stay still. In other words, from position $(x,y)$, the frog can spend $1$ second to move to:

• $(x+1,y)$
• $(x,y+1)$
• $(x,y)$

After $T$ seconds, a villager who sees the frog reports that the frog lies on or inside a square of side-length $s$ with coordinates $(X,Y)$, $(X+s,Y)$, $(X,Y+s)$, $(X+s,Y+s)$. Calculate how many points with integer coordinates on or inside this square could be the frog's position after exactly $T$ seconds

Example:

Input:  x = 2, y = 2, s = 3, t = 6
Output: 6

Approach

C++

#include <bits/stdc++.h>
using namespace std;

int countFrogPaths(int x, int y, int s, int t)
{
    int sum = 0;
    for (int i = x; i <= x + s; i++)
    {
        for (int j = y; j <= s + y; j++)
        {
            if (i + j <= t)
                sum++;
        }
    }
    return sum;
}
int main()
{

    int x = 2, y = 2, s = 3, t = 6;

    cout << countFrogPaths(x, y, s, t) << "\n";

    return 0;
}