Episode 7 — DSA with JavaScript / 7.7 — Math Problems and Algorithms

7.7.a — Math Operations & Algorithms

<< 7.7 Overview

Mathematical operations in programming

Math operations are fundamental building blocks for DSA problems. Understanding how to work with numbers efficiently is essential.

Power (Exponentiation)

Naive: O(n)

function power(base, exp) {
    let result = 1;
    for (let i = 0; i < exp; i++) result *= base;
    return result;
}

Fast exponentiation: O(log n)

2^10 = (2^5)^2
2^5  = 2 * (2^2)^2
2^2  = (2^1)^2
2^1  = 2 * (2^0)^2
2^0  = 1

Only 4 multiplications instead of 10!

function fastPow(base, exp) {
    if (exp === 0) return 1;
    if (exp % 2 === 0) {
        const half = fastPow(base, exp / 2);
        return half * half;
    }
    return base * fastPow(base, exp - 1);
}

long long fastPow(long long base, int exp) {
    if (exp == 0) return 1;
    if (exp % 2 == 0) {
        long long half = fastPow(base, exp / 2);
        return half * half;
    }
    return base * fastPow(base, exp - 1);
}

Square root

Newton's method (Babylonian)

function sqrt(n) {
    if (n < 0) return NaN;
    if (n === 0) return 0;
    let guess = n;
    while (Math.abs(guess * guess - n) > 0.0001) {
        guess = (guess + n / guess) / 2;
    }
    return guess;
}

Integer square root (binary search)

function intSqrt(n) {
    if (n < 2) return n;
    let lo = 1, hi = Math.floor(n / 2);
    while (lo <= hi) {
        const mid = Math.floor((lo + hi) / 2);
        if (mid * mid === n) return mid;
        if (mid * mid < n) { lo = mid + 1; }
        else { hi = mid - 1; }
    }
    return hi;
}

int intSqrt(int n) {
    if (n < 2) return n;
    int lo = 1, hi = n / 2, ans = 0;
    while (lo <= hi) {
        long long mid = lo + (hi - lo) / 2;
        if (mid * mid == n) return mid;
        if (mid * mid < n) { ans = mid; lo = mid + 1; }
        else hi = mid - 1;
    }
    return ans;
}

GCD — Euclidean algorithm

GCD(48, 18):
  48 % 18 = 12
  18 % 12 = 6
  12 % 6  = 0
  → GCD = 6

Visualization:
  gcd(48, 18)
  → gcd(18, 12)
  → gcd(12, 6)
  → gcd(6, 0) → return 6

function gcd(a, b) {
    while (b !== 0) {
        [a, b] = [b, a % b];
    }
    return a;
}

int gcd(int a, int b) {
    while (b) { int t = b; b = a % b; a = t; }
    return a;
}

Time: O(log(min(a,b)))

LCM

function lcm(a, b) {
    return (a * b) / gcd(a, b);
}

Prime checking

Is 29 prime?
  √29 ≈ 5.38 → check divisors 2, 3, 5
  29 % 2 = 1 ✓
  29 % 3 = 2 ✓
  29 % 5 = 4 ✓
  → 29 is prime!

function isPrime(n) {
    if (n < 2) return false;
    if (n === 2) return true;
    if (n % 2 === 0) return false;
    for (let i = 3; i * i <= n; i += 2) {
        if (n % i === 0) return false;
    }
    return true;
}

bool isPrime(int n) {
    if (n < 2) return false;
    if (n == 2) return true;
    if (n % 2 == 0) return false;
    for (int i = 3; (long long)i * i <= n; i += 2)
        if (n % i == 0) return false;
    return true;
}

Time: O(√n)

Sieve of Eratosthenes

Find all primes up to N.

Mark composites:
  2: mark 4,6,8,10,...
  3: mark 9,12,15,...
  5: mark 25,30,...
  ...

Sieve for N=20:
  [_, _, 2, 3, _, 5, _, 7, _, _, _, 11, _, 13, _, _, _, 17, _, 19, _]

function sieve(n) {
    const isPrime = new Array(n + 1).fill(true);
    isPrime[0] = isPrime[1] = false;
    for (let i = 2; i * i <= n; i++) {
        if (isPrime[i]) {
            for (let j = i * i; j <= n; j += i) {
                isPrime[j] = false;
            }
        }
    }
    return isPrime.reduce((acc, v, i) => v ? [...acc, i] : acc, []);
}

console.log(sieve(30));
// [2,3,5,7,11,13,17,19,23,29]

vector<int> sieve(int n) {
    vector<bool> is_prime(n + 1, true);
    is_prime[0] = is_prime[1] = false;
    for (int i = 2; i * i <= n; i++)
        if (is_prime[i])
            for (int j = i * i; j <= n; j += i)
                is_prime[j] = false;
    vector<int> primes;
    for (int i = 2; i <= n; i++)
        if (is_prime[i]) primes.push_back(i);
    return primes;
}

Time: O(n log log n) | Space: O(n)

Factorial, permutations, combinations

function factorial(n) {
    let r = 1;
    for (let i = 2; i <= n; i++) r *= i;
    return r;
}

function nPr(n, r) { return factorial(n) / factorial(n - r); }
function nCr(n, r) { return factorial(n) / (factorial(r) * factorial(n - r)); }

Efficient nCr (avoid overflow)

function nCr(n, r) {
    if (r > n - r) r = n - r;
    let result = 1;
    for (let i = 0; i < r; i++) {
        result *= (n - i);
        result /= (i + 1);
    }
    return result;
}

Armstrong numbers

A number where the sum of its digits raised to the power of the digit count equals the number itself.

153 → 1³ + 5³ + 3³ = 1 + 125 + 27 = 153 ✓

function isArmstrong(n) {
    const digits = String(n).split("").map(Number);
    const power = digits.length;
    const sum = digits.reduce((s, d) => s + Math.pow(d, power), 0);
    return sum === n;
}

Palindrome number

function isPalindromeNum(n) {
    if (n < 0) return false;
    let rev = 0, orig = n;
    while (n > 0) {
        rev = rev * 10 + n % 10;
        n = Math.floor(n / 10);
    }
    return rev === orig;
}

Digit manipulation

function sumOfDigits(n) {
    let sum = 0;
    n = Math.abs(n);
    while (n > 0) { sum += n % 10; n = Math.floor(n / 10); }
    return sum;
}

function countDigits(n) {
    if (n === 0) return 1;
    return Math.floor(Math.log10(Math.abs(n))) + 1;
}

function reverseNumber(n) {
    let rev = 0, neg = n < 0;
    n = Math.abs(n);
    while (n > 0) { rev = rev * 10 + n % 10; n = Math.floor(n / 10); }
    return neg ? -rev : rev;
}

Modular arithmetic

// (a + b) % m = ((a % m) + (b % m)) % m
// (a * b) % m = ((a % m) * (b % m)) % m

function modPow(base, exp, mod) {
    let result = 1;
    base %= mod;
    while (exp > 0) {
        if (exp % 2 === 1) result = (result * base) % mod;
        exp = Math.floor(exp / 2);
        base = (base * base) % mod;
    }
    return result;
}

long long modPow(long long base, long long exp, long long mod) {
    long long result = 1;
    base %= mod;
    while (exp > 0) {
        if (exp & 1) result = result * base % mod;
        exp >>= 1;
        base = base * base % mod;
    }
    return result;
}

Scenario bank (math)

7.7a-001 — GCD of multiple numbers (v1)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-002 — Prime factorization (v2)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-003 — Count trailing zeros in factorial (v3)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-004 — Check perfect number (v4)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-005 — Find nth Fibonacci using matrix exponentiation (v5)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-006 — Compute nCr mod p (v6)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-007 — Check if number is power of 2 (v7)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-008 — Find all divisors of N (v8)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-009 — Convert decimal to any base (v9)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-010 — Euler's totient function (v10)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-011 — Check Harshad number (v11)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-012 — Compute modular inverse (v12)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-013 — Count primes in a range (v13)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-014 — Digital root computation (v14)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-015 — Find GCD of array (v15)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-016 — Happy number check (v16)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-017 — Josephus problem (v17)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-018 — Catalan number computation (v18)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-019 — Count set bits (v19)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-020 — Find next prime after N (v20)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-021 — GCD of multiple numbers (v21)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-022 — Prime factorization (v22)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-023 — Count trailing zeros in factorial (v23)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-024 — Check perfect number (v24)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-025 — Find nth Fibonacci using matrix exponentiation (v25)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-026 — Compute nCr mod p (v26)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-027 — Check if number is power of 2 (v27)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-028 — Find all divisors of N (v28)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-029 — Convert decimal to any base (v29)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-030 — Euler's totient function (v30)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-031 — Check Harshad number (v31)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-032 — Compute modular inverse (v32)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-033 — Count primes in a range (v33)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-034 — Digital root computation (v34)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-035 — Find GCD of array (v35)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-036 — Happy number check (v36)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-037 — Josephus problem (v37)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-038 — Catalan number computation (v38)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-039 — Count set bits (v39)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-040 — Find next prime after N (v40)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-041 — GCD of multiple numbers (v41)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-042 — Prime factorization (v42)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-043 — Count trailing zeros in factorial (v43)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-044 — Check perfect number (v44)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-045 — Find nth Fibonacci using matrix exponentiation (v45)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-046 — Compute nCr mod p (v46)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-047 — Check if number is power of 2 (v47)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-048 — Find all divisors of N (v48)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-049 — Convert decimal to any base (v49)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-050 — Euler's totient function (v50)

  • Level: Beginner
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-051 — Check Harshad number (v51)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-052 — Compute modular inverse (v52)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-053 — Count primes in a range (v53)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-054 — Digital root computation (v54)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-055 — Find GCD of array (v55)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-056 — Happy number check (v56)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-057 — Josephus problem (v57)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-058 — Catalan number computation (v58)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-059 — Count set bits (v59)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-060 — Find next prime after N (v60)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-061 — GCD of multiple numbers (v61)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-062 — Prime factorization (v62)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-063 — Count trailing zeros in factorial (v63)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-064 — Check perfect number (v64)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-065 — Find nth Fibonacci using matrix exponentiation (v65)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-066 — Compute nCr mod p (v66)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-067 — Check if number is power of 2 (v67)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-068 — Find all divisors of N (v68)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-069 — Convert decimal to any base (v69)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-070 — Euler's totient function (v70)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-071 — Check Harshad number (v71)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-072 — Compute modular inverse (v72)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-073 — Count primes in a range (v73)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-074 — Digital root computation (v74)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-075 — Find GCD of array (v75)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-076 — Happy number check (v76)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-077 — Josephus problem (v77)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-078 — Catalan number computation (v78)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-079 — Count set bits (v79)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-080 — Find next prime after N (v80)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-081 — GCD of multiple numbers (v81)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-082 — Prime factorization (v82)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-083 — Count trailing zeros in factorial (v83)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-084 — Check perfect number (v84)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-085 — Find nth Fibonacci using matrix exponentiation (v85)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-086 — Compute nCr mod p (v86)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-087 — Check if number is power of 2 (v87)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-088 — Find all divisors of N (v88)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-089 — Convert decimal to any base (v89)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-090 — Euler's totient function (v90)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-091 — Check Harshad number (v91)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-092 — Compute modular inverse (v92)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-093 — Count primes in a range (v93)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-094 — Digital root computation (v94)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-095 — Find GCD of array (v95)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-096 — Happy number check (v96)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-097 — Josephus problem (v97)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-098 — Catalan number computation (v98)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-099 — Count set bits (v99)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-100 — Find next prime after N (v100)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-101 — GCD of multiple numbers (v101)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-102 — Prime factorization (v102)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-103 — Count trailing zeros in factorial (v103)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-104 — Check perfect number (v104)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-105 — Find nth Fibonacci using matrix exponentiation (v105)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-106 — Compute nCr mod p (v106)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-107 — Check if number is power of 2 (v107)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-108 — Find all divisors of N (v108)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-109 — Convert decimal to any base (v109)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-110 — Euler's totient function (v110)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-111 — Check Harshad number (v111)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-112 — Compute modular inverse (v112)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-113 — Count primes in a range (v113)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-114 — Digital root computation (v114)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-115 — Find GCD of array (v115)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-116 — Happy number check (v116)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-117 — Josephus problem (v117)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-118 — Catalan number computation (v118)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-119 — Count set bits (v119)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-120 — Find next prime after N (v120)

  • Level: Intermediate
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-121 — GCD of multiple numbers (v121)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-122 — Prime factorization (v122)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-123 — Count trailing zeros in factorial (v123)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-124 — Check perfect number (v124)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-125 — Find nth Fibonacci using matrix exponentiation (v125)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-126 — Compute nCr mod p (v126)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-127 — Check if number is power of 2 (v127)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-128 — Find all divisors of N (v128)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-129 — Convert decimal to any base (v129)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-130 — Euler's totient function (v130)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-131 — Check Harshad number (v131)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-132 — Compute modular inverse (v132)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-133 — Count primes in a range (v133)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-134 — Digital root computation (v134)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-135 — Find GCD of array (v135)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-136 — Happy number check (v136)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-137 — Josephus problem (v137)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-138 — Catalan number computation (v138)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-139 — Count set bits (v139)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-140 — Find next prime after N (v140)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-141 — GCD of multiple numbers (v141)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-142 — Prime factorization (v142)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-143 — Count trailing zeros in factorial (v143)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-144 — Check perfect number (v144)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-145 — Find nth Fibonacci using matrix exponentiation (v145)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-146 — Compute nCr mod p (v146)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-147 — Check if number is power of 2 (v147)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-148 — Find all divisors of N (v148)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-149 — Convert decimal to any base (v149)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-150 — Euler's totient function (v150)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-151 — Check Harshad number (v151)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-152 — Compute modular inverse (v152)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-153 — Count primes in a range (v153)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-154 — Digital root computation (v154)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-155 — Find GCD of array (v155)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-156 — Happy number check (v156)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-157 — Josephus problem (v157)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-158 — Catalan number computation (v158)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-159 — Count set bits (v159)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-160 — Find next prime after N (v160)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-161 — GCD of multiple numbers (v161)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-162 — Prime factorization (v162)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-163 — Count trailing zeros in factorial (v163)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-164 — Check perfect number (v164)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-165 — Find nth Fibonacci using matrix exponentiation (v165)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-166 — Compute nCr mod p (v166)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-167 — Check if number is power of 2 (v167)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-168 — Find all divisors of N (v168)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-169 — Convert decimal to any base (v169)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.

7.7a-170 — Euler's totient function (v170)

  • Level: Advanced
  • Approach: Apply appropriate technique.
  • Time: Analyze.
  • Space: Identify.
  • Edge cases: empty, single, boundary.
  • JS & C++: Both.