Time Complexity

title: Time Complexity description: Big O notation aur algorithm analysis

Algorithm kitna time leta hai — input size ke saath kaise grow karta hai.

Big O Notation

Notation	Name	Example
O(1)	Constant	Array index access
O(log n)	Logarithmic	Binary search
O(n)	Linear	Linear search
O(n log n)	Linearithmic	Merge sort
O(n²)	Quadratic	Bubble sort
O(2ⁿ)	Exponential	Fibonacci recursive
O(n!)	Factorial	Permutations

Best → Worst: O(1) < O(log n) < O(n) < O(n log n) < O(n²) < O(2ⁿ) < O(n!)

Examples

O(1) — Constant

int getFirst(int[] arr) { return arr[0]; }

O(n) — Linear

java exampleWoHoTech

int sum(int[] arr) {
    int s = 0;
    for (int n : arr) s += n; // n iterations
    return s;
}

O(n²) — Quadratic

void bubbleSort(int[] arr) { for (int i = 0; i < arr.length; i++) // n for (int j = 0; j < arr.length-i-1; j++) // n if (arr[j] > arr[j+1]) { /* swap */ } // Total: n × n = n² }

O(log n) — Logarithmic

int binarySearch(int[] arr, int target) { int lo = 0, hi = arr.length - 1; while (lo <= hi) { int mid = lo + (hi - lo) / 2; if (arr[mid] == target) return mid; else if (arr[mid] < target) lo = mid + 1; else hi = mid - 1; } return -1; // Each iteration halves the search space }

Space Complexity

Algorithm kitna extra memory use karta hai.

O(1): Constant extra space (in-place)
O(n): Input size ke proportional extra space
O(log n): Recursive call stack (binary search recursion)

title: Time Complexity description: Big O notation aur algorithm analysis

Algorithm kitna time leta hai — input size ke saath kaise grow karta hai.

Big O Notation

Notation	Name	Example
O(1)	Constant	Array index access
O(log n)	Logarithmic	Binary search
O(n)	Linear	Linear search
O(n log n)	Linearithmic	Merge sort
O(n²)	Quadratic	Bubble sort
O(2ⁿ)	Exponential	Fibonacci recursive
O(n!)	Factorial	Permutations

Best → Worst: O(1) < O(log n) < O(n) < O(n log n) < O(n²) < O(2ⁿ) < O(n!)

Examples

O(1) — Constant

int getFirst(int[] arr) { return arr[0]; }

O(n) — Linear

java exampleWoHoTech

int sum(int[] arr) {
    int s = 0;
    for (int n : arr) s += n; // n iterations
    return s;
}

O(n²) — Quadratic

void bubbleSort(int[] arr) { for (int i = 0; i < arr.length; i++) // n for (int j = 0; j < arr.length-i-1; j++) // n if (arr[j] > arr[j+1]) { /* swap */ } // Total: n × n = n² }

O(log n) — Logarithmic

Space Complexity

Algorithm kitna extra memory use karta hai.

O(1): Constant extra space (in-place)
O(n): Input size ke proportional extra space
O(log n): Recursive call stack (binary search recursion)

Time Complexity

Big O Notation

Best → Worst: O(1) < O(log n) < O(n) < O(n log n) < O(n²) < O(2ⁿ) < O(n!)

Examples

O(1) — Constant

O(n) — Linear

O(n²) — Quadratic

O(log n) — Logarithmic

Space Complexity

Continue learning this concept

Time Complexity

Big O Notation

Best → Worst: O(1) < O(log n) < O(n) < O(n log n) < O(n²) < O(2ⁿ) < O(n!)

Examples

O(1) — Constant

O(n) — Linear

O(n²) — Quadratic

O(log n) — Logarithmic

Space Complexity

Continue learning this concept