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In this article, we will learn about design and analysis of algorithm examples in Data Structures.

**What will be the Time Complexity of given program ?**

displayFunction() { int i,j;for(int i = 1; i<=n; i++){for(int j = 1; j<= n; j++){ printf("Analyse me"); } } } Answer:-Time Complexity of this program will be O(n2)

First **for loop** will execute 1 to n times. Right? For each value of i, j loop will execute n times.

So, i = 1 j will execute n times and prints Analyse me. i = 2, j will execute n times and prints Analyse me j = 3, j will execute n times and prints Analyse me . . . i = n, j will execute n times and prints Analyse me Answer:- Time complexity = n*n = n2

**What will be the Time Complexity of given program ?**

First **for** loop will execute n times. j loop is dependent on value of i. k is independent loop.

$$Note: 1+2+3+...+n = dfrac{n(n+1)}{2}$$

displayFunction() { int i,j,k,n;for(int i=1; i<=n; i++){for(int j=1; j<=i; j++){for(int k=1; k<=100; k++){ printf("Analyse me"); } } } } Answer:-Time Complexity of this program will be O(n2)

To solve these kind of problems analyse by placing values.

i=1 i=2 i=3 j=1 time j=2 times j=3 times k=1*100 times k=2*100 times k=3*100 times i=n j=n times k=n*100 times So, 100*1 + 2*100 + 3*100 +......+n*100 100(1 + 2 + 3 + ...... + n) 100((n(n+1))/2) 100* n2 Answer:-So time complexity will be O(n2)

**What will be the Time Complexity of given program ?**

First **for** loop will execute n times. j loop is dependent on value of i and executes i2 times. k is independent loop executes based on j loop and executes as many times as j loop satisfies the condition.

$$Note: 1^2+2^2+3^2+...+n^2 = dfrac{n(n+1)(2n+1)}{6}$$

displayFunction() { int i,j,k,n;for(int i=1; i<=n; i++){for(int j=1; j<=i2; j++){for(int k=1; k<=n/2; k++){ printf("Analyse me"); } } }

To solve these kind of problems analyse by placing values.

i=1 i=2 i=3 j=1 time j=4 times j=9 times k=1*(n/2) times k=4*(n/2) times k=9*(n/2) times i=n j=n2 times k=n2*(n/2) times So, (n/2)*1 + 4*(n/2) + 9*(n/2) +......+n2*(n/2) (n/2)(1 + 4 + 9 + ...... + n2) (n/2)(n(n+1)(2n+1))/6) Answer:- Time complexity will be O(n4)

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