nCr and nPr Calculator - Problem

You need to create a calculator that computes combinations (nCr) and permutations (nPr) for given values of n and r.

Given two integers n and r, calculate:

nCr (combinations): The number of ways to choose r items from n items where order doesn't matter
nPr (permutations): The number of ways to arrange r items from n items where order matters

The formulas are:

nCr = n! / (r! × (n-r)!)
nPr = n! / (n-r)!

You must implement a factorial helper function to compute factorials, then use it to calculate both nCr and nPr.

Return an array [nCr, nPr] containing both results.

Input & Output

Example 1 — Basic Case

$ Input: n = 5, r = 3

› Output: [10, 60]

💡 Note: nCr = 5!/(3!×2!) = 120/(6×2) = 10, nPr = 5!/2! = 120/2 = 60

Example 2 — Small Values

$ Input: n = 4, r = 2

› Output: [6, 12]

💡 Note: nCr = 4!/(2!×2!) = 24/(2×2) = 6, nPr = 4!/2! = 24/2 = 12

Example 3 — Edge Case r=1

$ Input: n = 6, r = 1

› Output: [6, 6]

💡 Note: nCr = 6!/(1!×5!) = 720/(1×120) = 6, nPr = 6!/5! = 720/120 = 6

Constraints

0 ≤ r ≤ n ≤ 20
n and r are non-negative integers

Visualization

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Asked in

a Amazon 15 M Microsoft 12 G Google 8

The key insight is to implement a reusable factorial helper function that eliminates code duplication. The optimal approach uses this helper to cleanly calculate nCr = n!/(r!×(n-r)!) and nPr = n!/(n-r)!. Time: O(n), Space: O(1)

Common Approaches

✓ Direct Multiplication

⏱️ Time: O(n) Space: O(1)

Compute n!, r!, and (n-r)! separately by multiplying all numbers from 1 to the target. Then apply the mathematical formulas directly.

Factorial Helper Function

⏱️ Time: O(n) Space: O(1)

Implement a single factorial helper function that can compute any factorial. Use this function to calculate n!, r!, and (n-r)! efficiently, then apply the mathematical formulas.

Direct Multiplication — Algorithm Steps

Step 1: Calculate n! by multiplying 1×2×3×...×n
Step 2: Calculate r! by multiplying 1×2×3×...×r
Step 3: Calculate (n-r)! by multiplying 1×2×3×...×(n-r)
Step 4: Apply formulas nCr = n!/(r!×(n-r)!) and nPr = n!/(n-r)!

Visualization

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Step-by-Step Walkthrough

Calculate n!

Multiply 1×2×3×...×n

Calculate r! and (n-r)!

Multiply for each factorial needed

Apply Formulas

Use factorials in nCr and nPr formulas

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>

void solution(int n, int r, int* result) {
    // Calculate n!
    long long nFactorial = 1;
    for (int i = 1; i <= n; i++) {
        nFactorial *= i;
    }
    
    // Calculate r!
    long long rFactorial = 1;
    for (int i = 1; i <= r; i++) {
        rFactorial *= i;
    }
    
    // Calculate (n-r)!
    long long nrFactorial = 1;
    for (int i = 1; i <= n - r; i++) {
        nrFactorial *= i;
    }
    
    // Calculate nCr and nPr
    result[0] = nFactorial / (rFactorial * nrFactorial);
    result[1] = nFactorial / nrFactorial;
}

int main() {
    int n, r;
    scanf("%d", &n);
    scanf("%d", &r);
    
    int result[2];
    solution(n, r, result);
    
    printf("[%d,%d]\n", result[0], result[1]);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Calculate three factorials, each taking O(n) time

✓ Linear Growth

Space Complexity

O(1)

Only uses variables to store intermediate results

✓ Linear Space

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nCr and nPr Calculator - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Direct Multiplication — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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