Probability Pi= (No. of Favourable Outcomes) / (Total no. of Outcomes).Given is a number N which is the number of containers present. And we have N copies of two numbers X and Y. The task is to divide copies of one number X into N containers such that the probability of drawing a copy of X is maximum. From above it can be seen that to maximize Pi, we can either maximize the numerator ( No. of favourable outcomes) or minimize the denominator(Total no. of Outcomes). This can be done in a manner that only one container has a copy ... Read More

We are given with a sum of sides of a cuboid. A cuboid has three sides length, breadth and height. The volume of cuboid is calculated as a product of all three sides.Volume of Cuboid = Length X Breadth X HeightThe maximum volume can be achieved if all three sides are as close as possible.Let’s now understand what we have to do using an example −For Example The problem given here provides us with the sum of sides, say S. And let sides be L, B, H. In order to maximize the volume we have to find the sides as close ... Read More

The task is to maximize the value of number A by replacing some of its digits with digits present in another number B. No digits will be replaced if A’s value cannot be maximized.Note − a digit from B can be used only once.Let’s now understand what we have to do using an example −Input A = “1221” B = “1211”Output Maximum value of A possible 2221Explanation − We here select 2 from B and replace it with the first 1 of A. Here it is the only choice as replacing any other digit of A with either 2 or 1 will ... Read More

For the given two arrays each of size N, the task is to find the maximum sum by choosing X elements from array 1 and Y elements from array 2.Let’s now understand what we have to do using an example −Input arr1 = {1, 2, 3, 4, 5} ; X=2 arr2 = {1, 3, 5, 2, 7}; Y=3Output Maximum sum here is : 24Explanation − We are selecting 2 number(s) from arr1 and 3 from arr2. Largest 2 of arr1 are 4, 5 and largest 3 of arr2 are 3, 5, 7. Total sum of these 5 elements is 24 which is ... Read More

We are given with a matrix of size n x n and a condition that a[i][j] = 0 and the task is to calculate the maximum difference of indices having a[i][j] = 0. So, we can clearly state that there must be at least one zero in a matrix.Input int matrix[][] = {    {0, 1, 1},    {0, 0, 0},    {4, 5, 1}}Output −Maximum difference of indices (i, j) such that A[i][j] = 0 in the given matrix is −Explanation − we have element 0 at matrix[0][0], matrix[1][0], matrix[1][1] and matrix[1][2]. So the maximum difference of indices will be ... Read More

Given the task is to divide an array arr[] into K consecutive sub-arrays and find the maximum possible value of maximum among the minimum of the K consecutive sub-srrays.Input arr[]={2, 8, 4, 3, 9, 1, 5}, K=3Output 9Explanation − The 3 consecutive sub arrays that can made are: {2, 8, 4, 3}, {9}, and {1, 5}The minimum values out of all these arrays are: (2, 9, 1)The maximum value out of these three is 9.Input arr[] = { 8, 4, 1, 9, 11}, K=1Output 11Approach used in the below program as followsIf we look at the task, it can be divided into 3 cases ... Read More

Given the task is to calculate the maximum number of pairs arr[i] + arr[j] that are divisible by K where arr[] is an array containing N integers.Given the condition that a particular index number cannot be used in more than one pair.Inputarr[]={1, 2 ,5 ,8 ,3 }, K=2Output 2Explanation − The desired pairs are: (0, 2), (1, 3) as 1+5=6 and 2+8=10 . Both 6 and 10 are divisible by 2.Alternative answers could be the pairs: (0, 4), (1, 3) or (2, 4), (1, 3) but the answer remains the same, that is, 2.Input arr[]={1 ,3 ,5 ,2 ,3 ,4 }, K=3Output 3Approach ... Read More

Given the task is to calculate the maximum product that can be obtained from four factors A, B, C, D of a given number N, given the condition −The sum of the four factors should be equal to the number N, that is, N=A+B+C+D.Input − N=10Output − 20Explanation − The factors of 10 are: 1, 2, 5, 10.Maximum product can be obtained by multiplying 5*2*2*1=20 and also it satisfies the given condition, that is, 5+2+2+1=10.Input − N=16Output − 256Explanation − The factors of 16 are: 1, 2, 4, 8, 16.Maximum product can be obtained by multiplying 4*4*4*4=256 and also it ... Read More

Given the task is to maximize a given number with ‘N’ number of digits by replacing its digit using another array that contains 10 digits as an alternative for all single-digit numbers 0 to 9, The given condition is that only a consecutive segment of numbers can be replaced and only once.Input N=1234, arr[]={3 ,0 ,1 ,5 ,7 ,7 ,8 ,2 ,9 ,4}Output 1257Explanation The number 3 can be replaced with its alternative 5= arr[3]The number 4 can be replaced with its alternative 7= arr[4]Input N=5183, arr[]={3 ,0 ,1 ,5 ,7 ,7 ,8 ,2 ,9 ,4}Output 7183Approach used in the below program as followsIn function ... Read More

Given the task is to calculate the maximum profit that can be made by selling at-most ‘M’ products.The total number of products are ‘N’ and the cost price and the selling price of each product is given in the lists CP[] and SP[] respectively.Input N=6, M=4 CP[]={1, 9, 5, 8, 2, 11} SP[]={1, 15, 10, 16, 5, 20}Output 28Explanation − The profit obtained from selling all the products are 0, 6, 5, 8, 3, 9 respectively.So, in order to make maximum profit by selling only 4 products, the products with the highest profit need to be chosen, that is, product number 2, ... Read More