Algorithm

Getting Started with AlgorithmWhat is an Algorithm?

Characteristics of Algorithm1 Topic

Analysis Framework

Performance Analysis3 Topics

Mathematical Analysis2 Topics

Sorting AlgorithmSorting Algorithm10 Topics

Searching Algorithm6 Topics

Fundamental of Data StructuresStacks

Queues

Graphs

Trees

Sets

Dictionaries

Divide and ConquerGeneral Method

Binary Search

Recurrence Equation for Divide and Conquer

Finding the Maximum and Minimum

Merge Sort

Quick Sort

Stassen’s Matrix Multiplication

Advantages and Disadvantages of Divide and Conquer

Decrease and ConquerInsertion Sort

Topological Sort

Greedy MethodGeneral Method

Coin Change Problem

Knapsack Problem

Job Sequencing with Deadlines

Minimum Cost Spanning Trees2 Topics

Single Source Shortest Paths1 Topic

Optimal Tree Problem1 Topic

Transform and Conquer Approach1 Topic

Dynamic ProgrammingGeneral Method with Examples

Multistage Graphs

Transitive Closure1 Topic

All Pairs Shortest Paths6 Topics

BacktrackingGeneral Method

NQueens Problem

Sum of Subsets problem

Graph Coloring

Hamiltonian Cycles

Branch and Bound2 Topics

0/1 Knapsack problem2 Topics

NPComplete and NPHard Problems1 Topic
Insertion Sort
Insertion sort works in the similar way as we sort cards in our hand in a card game.
We assume that the first card is already sorted then, we select an unsorted card. If the unsorted card is greater than the card in hand, it is placed on the right otherwise, to the left. In the same way, other unsorted cards are taken and put at their right place.
A similar approach is used by insertion sort.
Insertion sort is a sorting algorithm that places an unsorted element at its suitable place in each iteration.
How Insertion Sort Works?
Suppose we need to sort the following array.
 The first element in the array is assumed to be sorted. Take the second element and store it separately in
key
. Comparekey
with the first element. If the first element is greater thankey
, then key is placed in front of the first element.
2. Now, the first two elements are sorted.
Take the third element and compare it with the elements on the left of it. Placed it just behind the element smaller than it. If there is no element smaller than it, then place it at the beginning of the array.
3. In a similar way, place every unsorted element at its correct position.
Insertion Sort Algorithm
insertionSort(array)
mark first element as sorted
for each unsorted element X
'extract' the element X
for j < lastSortedIndex down to 0
if current element j > X
move sorted element to the right by 1
break loop and insert X here
end insertionSort
Insertion Sort Program in C
// Insertion sort in C
#include <stdio.h>
void printArray(int array[], int size)
{
for (int i = 0; i < size; i++)
{
printf("%d ", array[i]);
}
printf("\n");
}
void insertionSort(int array[], int size)
{
for (int step = 1; step < size; step++)
{
int key = array[step];
int j = step  1;
while (key < array[j] && j >= 0)
{
// For descending order, change key<array[j] to key>array[j].
array[j + 1] = array[j];
j;
}
array[j + 1] = key;
}
}
int main()
{
int data[] = {9, 5, 1, 4, 3};
int size = sizeof(data) / sizeof(data[0]);
insertionSort(data, size);
printf("Sorted array in ascending order:\n");
printArray(data, size);
}
Complexity
Time Complexities
 Worst Case Complexity:
O(n^{2})
Suppose, an array is in ascending order, and you want to sort it in descending order. In this case, worse case complexity occers.
Each element has to be compared with each of the other elements so, for every nth element,(n1)
number of comparisons are made.
Thus, the total number of comparisons =n*(n1) ~ n
^{2}
 Best Case Complexity:
O(n)
When the array is already sorted, the outer loop runs forn
number of times whereas the inner loop does not run at all. So, there is onlyn
number of comparison. Thus, complexity is linear.
 Average Case Complexity:
O(n^{2})
It occurs when the elements of a array are in jumbled order (neither ascending nor descending).
Space Complexity
Space complexity is O(1)
because an extra variable key
is used.
Insertion Sort Applications
The insertion sort is used when:
 the array is has a small number of elements
 there are only a few elements left to be sorted