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Articles by Narendra Kumar
Page 2 of 18
Maximum XOR using K numbers from 1 to n in C++
In this problem, we are given two positive integers n and k. Our task is to find maximum xor between 1 to n using maximum X numbersLet’s take an example to understand the problem, Input − n = 5, k = 2Output − 7Explanation −elements till 5 is 1, 2, 3, 4, 5 Selecting all XOR pairs: 1^2 = 3, 1^3 = 2, 1^4 = 5, 1^5 = 4 2^3 = 4, 2^4 = 6, 2^5 = 7 3^4 = 7, 3^5 = 6 4^5 = 1 The maximum here is 7.To solve this problem, the maximum XOR can be ...
Read MoreMeasure one litre using two vessels and infinite water supplys in C++
In this problem, we are given two vessels with capacities x and y and a supply of infinite water. Our task is to create a program that will be able to calculate exactly 1 liter in one vessel. Given the condition that x and y are co-primes. Co-primes also is known as relatively prime, mutually prime are numbers two numbers that have 1 as their only common divisor. So, this implies that their gcd(greatest common divisor) is 1.Here, let’s suppose we have two vessels V1 with capacity x and V2 with capacity y. To measure 1 liter using these two ...
Read MoreMedian after K additional integers in C++
In this problem, we are given an array of n integers and we are adding K elements to the array and then find the median of the resultant array. Given the condition, N+k is odd.Let’s take an example to understand the problem, Input −array = {23, 65, 76, 67} ; k =1Output −67To solve this problem, we will sort the given elements in ascending order and then add k elements at the end of the array i.e. we will take k greater elements.The condition is given that n+k is odd. So, the median can be calculated using the formula, (n+k)/2.ExampleProgram ...
Read MoreMinimum sum of two numbers formed from digits of an array in C++
DescriptionGiven an array of digits which contains values from 0 to 9. The task is to find the minimum possible sum of two numbers formed from digits of the array. Please note that we have to use all digits of given arrayExampleIf input array is {7, 5, 1, 3, 2, 4} then minimum sum is 382 as, we can create two number 135 and 247.AlgorithmSort the array in ascending orderCreate two number by picking a digit from sorted array alternatively i.e. from even and odd indexExample#include using namespace std; int getMinSum(int *arr, int n) { sort(arr, arr + ...
Read MoreMinimum sum path between two leaves of a binary trees in C++
Problem statementGiven a binary tree in which each node element contains a number. The task is to find the minimum possible sum from one leaf node to another.ExampleIn above tree minimum sub path is -6 as follows: (-4) + 3 + 2 + (-8) + 1AlgorithmThe idea is to maintain two values in recursive calls −Minimum root to leaf path sum for the subtree rooted under current nodeThe minimum path sum between leavesFor every visited node X, we have to find the minimum root to leaf sum in left and right sub trees of X. Then add the two values ...
Read MoreMinimum Sum Path in a Triangle in C++
Problem statementGiven a triangular structure of numbers, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.ExampleIf input is − 5 7 3 8 1 2 9 6 4 5Then minimum sum is 13 as follows −5 + 3 + 1 + 4AlgorithmUse memorization technique of dynamic programmingCreate 1-D array for memorization namely memorizationFor each K row use below formula −memorization[i] = min( memorization[i], memorization[i+1]) + A[k][i];Example#include using namespace std; int getMinSum(vector &arr) { int memorization[arr.size()]; int n = arr.size() - 1; for (int ...
Read MoreMinimum swaps required to bring all elements less than or equal to k together in C++
Problem statementGiven an array of n positive integers and a number k. Find the minimum number of swaps required to bring all the numbers less than or equal to k together.ExampleIf input array is = {1, 5, 4, 7, 2, 10} and k = 6 then 1 swap is required i.e. swap element 7 with 2.AlgorithmCount all elements which are less than or equals to ‘k’. Let’s say the count is ‘cnt’Using two pointer technique for window of length ‘cnt’, each time keep track of how many elements in this range are greater than ‘k’. Let’s say the total count ...
Read MoreMinimum Swaps required to group all 1's together in C++
Problem statementGiven an array of 0’s and 1’s. The task is to find the minimum number of swaps required to group all 1’s present in the array together.ExampleIf input array = {1, 0, 1, 1, 0, 1} then 1 swap is required. i.e. swap first 0 with last 1.AlgorithmCount total number of 1’s in the arrayIf count is x, then we need to find the subarray of length x of this array with maximum number of 1’sMinimum swaps required will be the number of 0’s in the subarray of length x with maximum number of 1’sExample#include using namespace std; ...
Read MoreMinimum swaps required to make a binary string alternating in C++
Problem statementGiven a binary string of even length and equal number of 0’s and 1’s. What is the minimum number of swaps to make the string alternating? A binary string is alternating if no two consecutive elements are equalExampleIf str = 11110000 then 2 swaps are required.AlgorithmCount number of zeroes at odd position and even position of the string. Let their count be oddZeroCnt and evenZeroCnt respectivelyCount number of ones at odd position and even position of the string. Let their count be oddOneCnt and evenOneCnt respectivelyWe will always swap a 1 with a 0. So we just check if ...
Read MoreMinimum toggles to partition a binary array so that it has first 0s then 1s in C++
Problem statementGiven an array of n integers containing only 0 and 1. Find the minimum toggles (switch from 0 to 1 or vice-versa) required such the array the array become partitioned, i.e., it has first 0s then 1s.ExampleIf arr[] = {1, 0, 0, 1, 1, 1, 0} then 2 toggle is required i.e. toggle first one and last zero.AlgorithmIf we observe the question, then we will find that there will definitely exist a point from 0 to n-1 where all elements left to that point should contains all 0’s and right to point should contains all 1’sThose indices which don’t ...
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