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# Python program to update every array element with # multiplication of previous and next numbers in array def modify(arr, n): # Nothing to do when array size is 1 if n <= 1: return # store current value of arr[0] and update it prev = arr[0] arr[0] = arr[0] * arr[1] # Update rest of the array elements for i in range(1, n-1): # Store current value of next interaction curr = arr[i]; # Update current value using previous value arr[i] = prev * arr[i+1] # Update previous value prev = curr # Update last array element arr[n-1] = prev * arr[n-1] # Driver program arr = [2, 3, 4, 5, 6] n = len(arr) modify(arr, n) for i in range (0, n): print(arr[i],end=" ") # This code is contributed by # Smitha Dinesh Semwal
constant
linear
# Python Program to shuffle a given array from random import randint # A function to generate a random permutation of arr[] def randomize (arr, n): # Start from the last element and swap one by one. We don't # need to run for the first element that's why i > 0 for i in range(n-1,0,-1): # Pick a random index from 0 to i j = randint(0,i+1) # Swap arr[i] with the element at random index arr[i],arr[j] = arr[j],arr[i] return arr # Driver program to test above function. arr = [1, 2, 3, 4, 5, 6, 7, 8] n = len(arr) print(randomize(arr, n)) # This code is contributed by Pratik Chhajer
constant
linear
# Python3 implementation of the above approach def arrayEvenAndOdd(arr, n): index = 0; a = [0 for i in range(n)] for i in range(n): if (arr[i] % 2 == 0): a[index] = arr[i] ind += 1 for i in range(n): if (arr[i] % 2 != 0): a[index] = arr[i] ind += 1 for i in range(n): print(a[i], end = " ") print() # Driver code arr = [ 1, 3, 2, 4, 7, 6, 9, 10 ] n = len(arr) # Function call arrayEvenAndOdd(arr, n) # This code is contributed by rohitsingh07052
linear
linear
# Python3 code to segregate even odd # numbers in an array # Function to segregate even odd numbers def arrayEvenAndOdd(arr,n): i = -1 j= 0 while (j!=n): if (arr[j] % 2 ==0): i = i+1 # Swapping even and odd numbers arr[i],arr[j] = arr[j],arr[i] j = j+1 # Printing segregated array for i in arr: print (str(i) + " " ,end='') # Driver Code if __name__=='__main__': arr = [ 1 ,3, 2, 4, 7, 6, 9, 10] n = len(arr) arrayEvenAndOdd(arr,n) # This code was contributed by # Yatin Gupta
constant
linear
# Python3 implementation of above implementation # This function returns k'th smallest element # in arr[l..r] using QuickSort based method. # ASSUMPTION: ALL ELEMENTS IN ARR[] ARE DISTINCT from random import randint def randomPartition(arr, l, r): n = r - l + 1 pivot = randint(1, 100) % n arr[l + pivot], arr[r] = arr[l + pivot], arr[r] return partition(arr, l, r) def kthSmallest(arr, l, r, k): # If k is smaller than # number of elements in array if (k > 0 and k <= r - l + 1): # Partition the array around last element and # get position of pivot element in sorted array pos = randomPartition(arr, l, r) # If position is same as k if (pos - l == k - 1): return arr[pos] # If position is more, recur for left subarray if (pos - l > k - 1): return kthSmallest(arr, l, pos - 1, k) # Else recur for right subarray return kthSmallest(arr, pos + 1, r, k - pos + l - 1) # If k is more than number of elements in array return 10**9 # Standard partition process of QuickSort(). # It considers the last element as pivot and # moves all smaller element to left of it # and greater elements to right def partition(arr, l, r): x = arr[r] i = l for j in range(l, r): if (arr[j] <= x): arr[i], arr[j] = arr[j], arr[i] i += 1 arr[i], arr[r] = arr[r], arr[i] return i # Driver Code arr = [12, 3, 5, 7, 4, 19, 26] n = len(arr) k = 3 print("K'th smallest element is", kthSmallest(arr, 0, n - 1, k)) # This code is contributed by Mohit Kumar
constant
nlogn
# Program for kth largest element in a 2d array # sorted row-wise and column-wise from sys import maxsize # A structure to store an entry of heap. # The entry contains a value from 2D array, # row and column numbers of the value class HeapNode: def __init__(self, val, r, c): self.val = val # value to be stored self.r = r # Row number of value in 2D array self.c = c # Column number of value in 2D array # A utility function to minheapify the node harr[i] # of a heap stored in harr[] def minHeapify(harr, i, heap_size): l = i * 2 + 1 r = i * 2 + 2 if(l < heap_size and r<heap_size and harr[l].val < harr[i].val and harr[r].val < harr[i].val): temp= HeapNode(0,0,0) temp=harr[r] harr[r]=harr[i] harr[i]=harr[l] harr[l]=temp minHeapify(harr ,l,heap_size) minHeapify(harr ,r,heap_size) if (l < heap_size and harr[l].val < harr[i].val): temp= HeapNode(0,0,0) temp=harr[i] harr[i]=harr[l] harr[l]=temp minHeapify(harr ,l,heap_size) # This function returns kth smallest element # in a 2D array mat[][] def kthSmallest(mat, n, k): # k must be greater than 0 and smaller than n*n if k < 0 or k > n * n: return maxsize # Create a min heap of elements from # first row of 2D array harr = [0] * n for i in range(n): harr[i] = HeapNode(mat[0][i], 0, i) hr = HeapNode(0, 0, 0) for i in range(k): # Get current heap root hr = harr[0] # Get next value from column of root's value. # If the value stored at root was last value # in its column, then assign INFINITE as next value nextval = mat[hr.r + 1][hr.c] if (hr.r < n - 1) else maxsize # Update heap root with next value harr[0] = HeapNode(nextval, hr.r + 1, hr.c) # Heapify root minHeapify(harr, 0, n) # Return the value at last extracted root return hr.val # Driver Code if __name__ == "__main__": mat = [[10, 20, 30, 40], [15, 25, 35, 45], [25, 29, 37, 48], [32, 33, 39, 50]] print("7th smallest element is", kthSmallest(mat, 4, 7)) # This code is contributed by Rishabh Chauhan
linear
nlogn
# This returns count of elements in matrix # less than of equal to num def getElementsGreaterThanOrEqual(num,n,mat): ans = 0 for i in range(n): # if num is less than the first element # then no more element in matrix # further are less than or equal to num if (mat[i][0] > num): return ans # if num is greater than last element, # it is greater than all elements # in that row if (mat[i][n - 1] <= num): ans += n continue # This contain the col index of last element # in matrix less than of equal # to num greaterThan = 0 jump = n // 2 while(jump >= 1): while (greaterThan + jump < n and mat[i][greaterThan + jump] <= num): greaterThan += jump jump //= 2 ans += greaterThan + 1 return ans # returns kth smallest index in the matrix def kthSmallest(mat, n, k): # We know the answer lies between # the first and the last element # So do a binary search on answer # based on the number of elements # our current element is greater than # the elements in the matrix l,r = mat[0][0],mat[n - 1][n - 1] while (l <= r): mid = l + (r - l) // 2 greaterThanOrEqualMid = getElementsGreaterThanOrEqual(mid, n, mat) if (greaterThanOrEqualMid >= k): r = mid - 1 else: l = mid + 1 return l # driver code n = 4 mat = [[10, 20, 30, 40],[15, 25, 35, 45],[25, 29, 37, 48],[32, 33, 39, 50]] print(f"7th smallest element is {kthSmallest(mat, 4, 7)}") # This code is contributed by shinjanpatra
linear
nlogn
# Python program to implement above approach def kthSmallest(mat, n, k): a = [0 for i in range(n*n)] v=0 for i in range(n): for j in range(n): a[v] = mat[i][j] v += 1 a.sort() result = a[k - 1] return result # driver program mat = [ [ 10, 20, 30, 40 ], [ 15, 25, 35, 45 ], [ 25, 29, 37, 48 ], [ 32, 33, 39, 50 ] ] res = kthSmallest(mat, 4, 7) print("7th smallest element is "+ str(res)) # This code is contributed by shinjanpatra
quadratic
quadratic
import heapq def kthSmallest(matrix, k): # n = size of matrix n = len(matrix) # using built-in priority queue which acts as max Heap i.e. largest element will be on top # Kth smallest element can also be seen as largest element in a priority queue of size k # By this logic we pop elements from priority queue when its size becomes greater than k # thus top of priority queue is kth smallest element in matrix maxH = [] for i in range(n): for j in range(n): heapq.heappush(maxH, -matrix[i][j]) if len(maxH) > k: heapq.heappop(maxH) return -maxH[0] matrix = [[1, 5, 9], [10, 11, 13], [12, 13, 15]] k = 8 print("8th smallest element is", kthSmallest(matrix, k)) # This code is comtributed by Tapesh (tapeshdua420)
linear
quadratic
# Python3 program to find maximum # in arr[] of size n # Function to find maximum # in arr[] of size n def largest(arr,n): # Initialize maximum element mx = arr[0] # Traverse array elements from second # and compare every element with # current max for i in range(1, n): if arr[i] > mx: mx = arr[i] return mx # Driver Code arr = [10, 324, 45, 90, 9808] n = len(arr) #calculating length of an array Ans = largest(arr,n) # display max print ("Largest in given array is",Ans) # This code is contributed by Jai Parkash Bhardwaj # and improved by prophet1999
constant
linear
import math class GFG : @staticmethod def largest( arr, n, i) : # last index # return the element if (i == n - 1) : return arr[i] # find the maximum from rest of the array recMax = GFG.largest(arr, n, i + 1) # compare with i-th element and return return max(recMax,arr[i]) # Driver Code @staticmethod def main( args) : arr = [10, 324, 45, 90, 9808] n = len(arr) print("Largest in given array is " + str(GFG.largest(arr, n, 0))) if __name__=="__main__": GFG.main([]) # This code is contributed by aadityaburujwale.
linear
linear
# Python 3 program to find # maximum in arr[] of size n # returns maximum # in arr[] of size n def largest(arr, n): return max(arr) # driver code arr = [10, 324, 45, 90, 9808] n = len(arr) print(largest(arr, n)) # This code is contributed by # Smitha Dinesh Semwal
constant
linear
# Python3 code to find largest three # elements in an array import sys # Function to print three largest # elements def print3largest(arr, arr_size): # There should be atleast three # elements if (arr_size < 3): print(" Invalid Input ") return third = first = second = -sys.maxsize for i in range(0, arr_size): # If current element is greater # than first if (arr[i] > first): third = second second = first first = arr[i] # If arr[i] is in between first # and second then update second elif (arr[i] > second): third = second second = arr[i] elif (arr[i] > third): third = arr[i] print("Three largest elements are", first, second, third) # Driver program to test above function arr = [12, 13, 1, 10, 34, 1] n = len(arr) print3largest(arr, n) # This code is contributed by Smitha Dinesh Semwal # and edited by Ayush Singla(@ayusin51).
constant
linear
# Python3 code to find largest # three elements in an array def find3largest(arr, n): arr = sorted(arr) # It uses Tuned Quicksort with # avg. case Time complexity = O(nLogn) check = 0 count = 1 for i in range(1, n + 1): if(count < 4): if(check != arr[n - i]): # to handle duplicate values print(arr[n - i], end = " ") check = arr[n - i] count += 1 else: break # Driver code arr = [12, 45, 1, -1, 45, 54, 23, 5, 0, -10] n = len(arr) find3largest(arr, n) # This code is contributed by mohit kumar
constant
nlogn
# Python program to implement # the above approach # Driver Code V = [ 11, 65, 193, 36, 209, 664, 32 ]; V.sort() V.reverse() print(f"first = {V[0]}"); print(f"second = {V[1]}"); print(f"third = {V[2]}"); # This code is contributed by Saurabh Jaiswal
constant
nlogn
# Python3 program to find # all elements in array # which have at-least two # greater elements itself. def findElements( arr, n): # Pick elements one by # one and count greater # elements. If count # is more than 2, print # that element. for i in range(n): count = 0 for j in range(0, n): if arr[j] > arr[i]: count = count + 1 if count >= 2 : print(arr[i], end=" ") # Driver code arr = [ 2, -6 ,3 , 5, 1] n = len(arr) findElements(arr, n) # This code is contributed by sunnysingh
constant
quadratic
# Sorting based Python 3 program # to find all elements in array # which have atleast two greater # elements itself. def findElements(arr, n): arr.sort() for i in range(0, n-2): print(arr[i], end =" ") # Driven source arr = [2, -6, 3, 5, 1] n = len(arr) findElements(arr, n) # This code is contributed # by Smitha Dinesh Semwal
constant
nlogn
# Python3 program to find all elements # in array which have atleast two # greater elements itself. import sys def findElements(arr, n): first = -sys.maxsize second = -sys.maxsize for i in range(0, n): # If current element is smaller # than first then update both # first and second if (arr[i] > first): second = first first = arr[i] # If arr[i] is in between first # and second then update second elif (arr[i] > second): second = arr[i] for i in range(0, n): if (arr[i] < second): print(arr[i], end =" ") # Driver code arr = [2, -6, 3, 5, 1] n = len(arr) findElements(arr, n) # This code is contributed # by Smitha Dinesh Semwal
constant
linear
# Python3 program to find mean # and median of an array # Function for calculating mean def findMean(a, n): sum = 0 for i in range(0, n): sum += a[i] return float(sum/n) # Function for calculating median def findMedian(a, n): # First we sort the array sorted(a) # check for even case if n % 2 != 0: return float(a[int(n/2)]) return float((a[int((n-1)/2)] + a[int(n/2)])/2.0) # Driver code a = [1, 3, 4, 2, 7, 5, 8, 6] n = len(a) # Function call print("Mean =", findMean(a, n)) print("Median =", findMedian(a, n)) # This code is contributed by Smitha Dinesh Semwal
constant
nlogn
# python3 program to find med in # stream of running integers from heapq import * # function to calculate med of stream def printMedians(arr, n): # max heap to store the smaller half elements s = [] # min heap to store the greater half elements g = [] heapify(s) heapify(g) med = arr[0] heappush(s, arr[0]) print(med) # reading elements of stream one by one for i in range(1, n): x = arr[i] # case1(left side heap has more elements) if len(s) > len(g): if x < med: heappush(g, heappop(s)) heappush(s, x) else: heappush(g, x) med = (nlargest(1, s)[0] + nsmallest(1, g)[0])/2 # case2(both heaps are balanced) elif len(s) == len(g): if x < med: heappush(s, x) med = nlargest(1, s)[0] else: heappush(g, x) med = nsmallest(1, g)[0] # case3(right side heap has more elements) else: if x > med: heappush(s, heappop(g)) heappush(g, x) else: heappush(s, x) med = (nlargest(1, s)[0] + nsmallest(1, g)[0])/2 print(med) # Driver program to test above functions arr = [5, 15, 10, 20, 3] printMedians(arr, len(arr)) # This code is contributed by cavi4762.
linear
nlogn
# Python3 program to find minimum # product of k elements in an array import math import heapq def minProduct(arr, n, k): heapq.heapify(arr) count = 0 ans = 1 # One by one extract # items from min heap while ( arr ) and count < k: x = heapq.heappop(arr) ans = ans * x count = count + 1 return ans; # Driver method arr = [198, 76, 544, 123, 154, 675] k = 2 n = len(arr) print ("Minimum product is", minProduct(arr, n, k))
linear
nlogn
# Python program to find out k maximum # non-overlapping subarray sums. # Function to compute k # maximum sub-array sums. def kmax(arr, k, n): # In each iteration it will give # the ith maximum subarray sum. for c in range(k): # Kadane's algorithm max_so_far = -float("inf") max_here = 0 # compute starting and ending # index of each of the subarray start = 0 end = 0 s = 0 for i in range(n): max_here += arr[i] if (max_so_far < max_here): max_so_far = max_here start = s end = i if (max_here < 0): max_here = 0 s = i + 1 # Print out the result print("Maximum non-overlapping sub-array sum", c + 1, ": ", max_so_far, ", starting index: ", start, ", ending index: ", end, ".", sep = "") # Replace all elements of the maximum subarray # by -infinity. Hence these places cannot form # maximum sum subarray again. for l in range(start, end+1): arr[l] = -float("inf") print() # Driver Program # Test case 1 arr1 = [4, 1, 1, -1, -3, -5, 6, 2, -6, -2] k1 = 3 n1 = len(arr1) # Function calling kmax(arr1, k1, n1) # Test case 2 arr2 = [5, 1, 2, -6, 2, -1, 3, 1] k2 = 2 n2 = len(arr2) # Function calling kmax(arr2, k2, n2)
constant
quadratic
# Python 3 for printing smallest # k numbers in order # Function to print smallest k # numbers in arr[0..n-1] def printSmall(arr, n, k): # For each arr[i] find whether # it is a part of n-smallest # with insertion sort concept for i in range(k, n): # find largest from first k-elements max_var = arr[k - 1] pos = k - 1 for j in range(k - 2, -1, -1): if (arr[j] > max_var): max_var = arr[j] pos = j # if largest is greater than arr[i] # shift all element one place left if (max_var > arr[i]): j = pos while (j < k - 1): arr[j] = arr[j + 1] j += 1 # make arr[k-1] = arr[i] arr[k - 1] = arr[i] # print result for i in range(0, k): print(arr[i], end=" ") # Driver program arr = [1, 5, 8, 9, 6, 7, 3, 4, 2, 0] n = len(arr) k = 5 printSmall(arr, n, k)
constant
quadratic
# Python3 program to find # k-th absolute difference # between two elements from bisect import bisect as upper_bound # returns number of pairs with # absolute difference less than # or equal to mid. def countPairs(a, n, mid): res = 0 for i in range(n): # Upper bound returns pointer to position # of next higher number than a[i]+mid in # a[i..n-1]. We subtract (a + i + 1) from # this position to count res += upper_bound(a, a[i] + mid) return res # Returns k-th absolute difference def kthDiff(a, n, k): # Sort array a = sorted(a) # Minimum absolute difference low = a[1] - a[0] for i in range(1, n - 1): low = min(low, a[i + 1] - a[i]) # Maximum absolute difference high = a[n - 1] - a[0] # Do binary search for k-th absolute difference while (low < high): mid = (low + high) >> 1 if (countPairs(a, n, mid) < k): low = mid + 1 else: high = mid return low # Driver code k = 3 a = [1, 2, 3, 4] n = len(a) print(kthDiff(a, n, k)) # This code is contributed by Mohit Kumar
constant
nlogn
# Python3 program to find second # largest element in an array # Function to print the # second largest elements def print2largest(arr, arr_size): # There should be # atleast two elements if (arr_size < 2): print(" Invalid Input ") return # Sort the array arr.sort # Start from second last # element as the largest # element is at last for i in range(arr_size-2, -1, -1): # If the element is not # equal to largest element if (arr[i] != arr[arr_size - 1]) : print("The second largest element is", arr[i]) return print("There is no second largest element") # Driver code arr = [12, 35, 1, 10, 34, 1] n = len(arr) print2largest(arr, n) # This code is contributed by divyeshrabadiya07
constant
nlogn
# Python3 program to find # second largest element # in an array # Function to print # second largest elements def print2largest(arr, arr_size): # There should be atleast # two elements if (arr_size < 2): print(" Invalid Input "); return; largest = second = -2454635434; # Find the largest element for i in range(0, arr_size): largest = max(largest, arr[i]); # Find the second largest element for i in range(0, arr_size): if (arr[i] != largest): second = max(second, arr[i]); if (second == -2454635434): print("There is no second " + "largest element"); else: print("The second largest " + "element is \n", second); # Driver code if __name__ == '__main__': arr = [12, 35, 1, 10, 34, 1]; n = len(arr); print2largest(arr, n); # This code is contributed by shikhasingrajput
constant
linear
# Python program to # find second largest # element in an array # Function to print the # second largest elements def print2largest(arr, arr_size): # There should be atleast # two elements if (arr_size < 2): print(" Invalid Input ") return first = second = -2147483648 for i in range(arr_size): # If current element is # smaller than first # then update both # first and second if (arr[i] > first): second = first first = arr[i] # If arr[i] is in # between first and # second then update second elif (arr[i] > second and arr[i] != first): second = arr[i] if (second == -2147483648): print("There is no second largest element") else: print("The second largest element is", second) # Driver program to test # above function arr = [12, 35, 1, 10, 34, 1] n = len(arr) print2largest(arr, n) # This code is contributed # by Anant Agarwal.
constant
linear
# Python3 implementation to find k numbers # with most occurrences in the given array # Function to print the k numbers with # most occurrences def pr_N_mostFrequentNumber(arr, N, K): mp = {} for i in range(N): if arr[i] in mp: mp[arr[i]] += 1 else: mp[arr[i]] = 1 a = [0] * (len(mp)) j = 0 for i in mp: a[j] = [i, mp[i]] j += 1 a = sorted(a, key=lambda x: x[0], reverse=True) a = sorted(a, key=lambda x: x[1], reverse=True) # Display the top k numbers print(K, "numbers with most occurrences are:") for i in range(K): print(a[i][0], end=" ") # Driver code if __name__ == "__main__": arr = [3, 1, 4, 4, 5, 2, 6, 1] N = 8 K = 2 # Function call pr_N_mostFrequentNumber(arr, N, K) # This code is contributed by # Shubham Singh(SHUBHAMSINGH10)
linear
nlogn
def print_N_mostFrequentNumber(arr, N, K): # HashMap to store count of the elements count = {} # Array to store the elements according # to their frequency freq = [[] for i in range(len(arr) + 1)] for n in arr: count[n] = 1 + count.get(n, 0) for n, c in count.items(): freq.append(n) res = [] # if K elements have been printed for i in range(len(freq)-1, 0, -1): for n in freq[i]: res.append(n) if len(res) == K: return res[-1::-1] # Driver's code if __name__ == "__main__": arr = [3, 1, 4, 4, 5, 2, 6, 1] N = len(arr) K = 2 # Function call print(print_N_mostFrequentNumber(arr, N, K))
linear
linear
# Python3 simple approach to print smallest # and second smallest element. # driver code arr = [111, 13, 25, 9, 34, 1] n = len(arr) # sorting the array using # in-built sort function arr.sort() # printing the desired element print("smallest element is "+str(arr[0])) print("second smallest element is "+str(arr[1])) # This code is contributed by shinjanpatra
constant
nlogn
# Python program to find smallest and second smallest elements import math def print2Smallest(arr): # There should be atleast two elements arr_size = len(arr) if arr_size < 2: print ("Invalid Input") return first = second = math.inf for i in range(0, arr_size): # If current element is smaller than first then # update both first and second if arr[i] < first: second = first first = arr[i] # If arr[i] is in between first and second then # update second elif (arr[i] < second and arr[i] != first): second = arr[i]; if (second == math.inf): print ("No second smallest element") else: print ('The smallest element is',first,'and', \ ' second smallest element is',second) # Driver function to test above function arr = [12, 13, 1, 10, 34, 1] print2Smallest(arr) # This code is contributed by Devesh Agrawal
constant
linear
# Python3 program to find the smallest # elements missing in a sorted array. def findFirstMissing(array, start, end): if (start > end): return end + 1 if (start != array[start]): return start; mid = int((start + end) / 2) # Left half has all elements # from 0 to mid if (array[mid] == mid): return findFirstMissing(array, mid+1, end) return findFirstMissing(array, start, mid) # driver program to test above function arr = [0, 1, 2, 3, 4, 5, 6, 7, 10] n = len(arr) print("Smallest missing element is", findFirstMissing(arr, 0, n-1)) # This code is contributed by Smitha Dinesh Semwal
logn
logn
# Python3 program for above approach # Function to find Smallest # Missing in Sorted Array def findSmallestMissinginSortedArray(arr): # Check if 0 is missing # in the array if (arr[0] != 0): return 0 # Check is all numbers 0 to n - 1 # are present in array if (arr[-1] == len(arr) - 1): return len(arr) first = arr[0] return findFirstMissing(arr, 0, len(arr) - 1, first) # Function to find missing element def findFirstMissing(arr, start, end, first): if (start < end): mid = int((start + end) / 2) # Index matches with value # at that index, means missing # element cannot be upto that point if (arr[mid] != mid + first): return findFirstMissing(arr, start, mid, first) else: return findFirstMissing(arr, mid + 1, end, first) return start + first # Driver code arr = [ 0, 1, 2, 3, 4, 5, 7 ] n = len(arr) # Function Call print("First Missing element is :", findSmallestMissinginSortedArray(arr)) # This code is contributed by rag2127
logn
logn
# Python code to implement the approach # Function to find the maximum sum def findMaxSum(arr, N): # Declare dp array dp = [[0 for i in range(2)] for j in range(N)] if (N == 1): return arr[0] # Initialize the values in dp array dp[0][0] = 0 dp[0][1] = arr[0] # Loop to find the maximum possible sum for i in range(1,N): dp[i][1] = dp[i - 1][0] + arr[i] dp[i][0] = max(dp[i - 1][1], dp[i - 1][0]) # Return the maximum sum return max(dp[N - 1][0], dp[N - 1][1]) # Driver Code # Creating the array arr = [ 5, 5, 10, 100, 10, 5 ] N = len(arr) # Function call print(findMaxSum(arr, N)) # This code is contributed by shinjanpatra
linear
linear
# Python code to implement the approach # Function to return max sum such that # no two elements are adjacent def findMaxSum(arr, n): incl = 0 excl = 0 for i in arr: # Current max excluding i new_excl = max (excl, incl) # Current max including i incl = excl + i excl = new_excl # Return max of incl and excl return max(excl, incl) # Driver code if __name__ == "__main__": arr = [5, 5, 10, 100, 10, 5] N = 6 # Function call print (findMaxSum(arr, N)) # This code is contributed by Kalai Selvan
constant
linear
# Python 3 program to demonstrate working of Square Root # Decomposition. from math import sqrt MAXN = 10000 SQRSIZE = 100 arr = [0]*(MAXN) # original array block = [0]*(SQRSIZE) # decomposed array blk_sz = 0 # block size # Time Complexity : O(1) def update(idx, val): blockNumber = idx // blk_sz block[blockNumber] += val - arr[idx] arr[idx] = val # Time Complexity : O(sqrt(n)) def query(l, r): sum = 0 while (l < r and l % blk_sz != 0 and l != 0): # traversing first block in range sum += arr[l] l += 1 while (l + blk_sz - 1 <= r): # traversing completely overlapped blocks in range sum += block[l//blk_sz] l += blk_sz while (l <= r): # traversing last block in range sum += arr[l] l += 1 return sum # Fills values in input[] def preprocess(input, n): # initiating block pointer blk_idx = -1 # calculating size of block global blk_sz blk_sz = int(sqrt(n)) # building the decomposed array for i in range(n): arr[i] = input[i]; if (i % blk_sz == 0): # entering next block # incrementing block pointer blk_idx += 1; block[blk_idx] += arr[i] # Driver code # We have used separate array for input because # the purpose of this code is to explain SQRT # decomposition in competitive programming where # we have multiple inputs. input= [1, 5, 2, 4, 6, 1, 3, 5, 7, 10] n = len(input) preprocess(input, n) print("query(3,8) : ",query(3, 8)) print("query(1,6) : ",query(1, 6)) update(8, 0) print("query(8,8) : ",query(8, 8)) # This code is contributed by Sanjit_Prasad
linear
linear
# Python3 program to do range minimum # query using sparse table import math # Fills lookup array lookup[][] in # bottom up manner. def buildSparseTable(arr, n): # Initialize M for the intervals # with length 1 for i in range(0, n): lookup[i][0] = arr[i] j = 1 # Compute values from smaller to # bigger intervals while (1 << j) <= n: # Compute minimum value for all # intervals with size 2^j i = 0 while (i + (1 << j) - 1) < n: # For arr[2][10], we compare arr[lookup[0][7]] # and arr[lookup[3][10]] if (lookup[i][j - 1] < lookup[i + (1 << (j - 1))][j - 1]): lookup[i][j] = lookup[i][j - 1] else: lookup[i][j] = \ lookup[i + (1 << (j - 1))][j - 1] i += 1 j += 1 # Returns minimum of arr[L..R] def query(L, R): # Find highest power of 2 that is smaller # than or equal to count of elements in # given range. For [2, 10], j = 3 j = int(math.log2(R - L + 1)) # Compute minimum of last 2^j elements # with first 2^j elements in range. # For [2, 10], we compare arr[lookup[0][3]] # and arr[lookup[3][3]], if lookup[L][j] <= lookup[R - (1 << j) + 1][j]: return lookup[L][j] else: return lookup[R - (1 << j) + 1][j] # Driver Code if __name__ == "__main__": a = [7, 2, 3, 0, 5, 10, 3, 12, 18] n = len(a) MAX = 500 # lookup[i][j] is going to store minimum # value in arr[i..j]. Ideally lookup table # size should not be fixed and should be # determined using n Log n. It is kept # constant to keep code simple. lookup = [[0 for i in range(MAX)] for j in range(MAX)] buildSparseTable(a, n) print(query(0, 4)) print(query(4, 7)) print(query(7, 8)) # This code is contributed by Rituraj Jain
nlogn
nlogn
# Python3 program to do range minimum # query using sparse table import math # Fills lookup array lookup[][] in # bottom up manner. def buildSparseTable(arr, n): # GCD of single element is element itself for i in range(0, n): table[i][0] = arr[i] # Build sparse table j = 1 while (1 << j) <= n: i = 0 while i <= n - (1 << j): table[i][j] = math.gcd(table[i][j - 1], table[i + (1 << (j - 1))][j - 1]) i += 1 j += 1 # Returns minimum of arr[L..R] def query(L, R): # Find highest power of 2 that is smaller # than or equal to count of elements in # given range. For [2, 10], j = 3 j = int(math.log2(R - L + 1)) # Compute GCD of last 2^j elements with # first 2^j elements in range. # For [2, 10], we find GCD of arr[lookup[0][3]] # and arr[lookup[3][3]], return math.gcd(table[L][j], table[R - (1 << j) + 1][j]) # Driver Code if __name__ == "__main__": a = [7, 2, 3, 0, 5, 10, 3, 12, 18] n = len(a) MAX = 500 # lookup[i][j] is going to store minimum # value in arr[i..j]. Ideally lookup table # size should not be fixed and should be # determined using n Log n. It is kept # constant to keep code simple. table = [[0 for i in range(MAX)] for j in range(MAX)] buildSparseTable(a, n) print(query(0, 2)) print(query(1, 3)) print(query(4, 5)) # This code is contributed by Rituraj Jain
nlogn
nlogn
# Python program to find total # count of an element in a range # Returns count of element # in arr[left-1..right-1] def findFrequency(arr, n, left, right, element): count = 0 for i in range(left - 1, right): if (arr[i] == element): count += 1 return count # Driver Code arr = [2, 8, 6, 9, 8, 6, 8, 2, 11] n = len(arr) # Print frequency of 2 from position 1 to 6 print("Frequency of 2 from 1 to 6 = ", findFrequency(arr, n, 1, 6, 2)) # Print frequency of 8 from position 4 to 9 print("Frequency of 8 from 4 to 9 = ", findFrequency(arr, n, 4, 9, 8)) # This code is contributed by Anant Agarwal.
constant
linear
# Python3 program to get updated array # after many array range add operation # Utility method to add value # val, to range [lo, hi] def add(arr, N, lo, hi, val): arr[lo] += val if (hi != N - 1): arr[hi + 1] -= val # Utility method to get actual # array from operation array def updateArray(arr, N): # convert array into prefix sum array for i in range(1, N): arr[i] += arr[i - 1] # method to print final updated array def printArr(arr, N): updateArray(arr, N) for i in range(N): print(arr[i], end=" ") print() # Driver code N = 6 arr = [0 for i in range(N)] # Range add Queries add(arr, N, 0, 2, 100) add(arr, N, 1, 5, 100) add(arr, N, 2, 3, 100) printArr(arr, N) # This code is contributed by Anant Agarwal.
constant
linear
# Python program for # queries of GCD excluding # given range of elements. # Calculating GCD # using euclid algorithm def GCD(a,b): if (b==0): return a return GCD (b, a%b) # Filling the prefix # and suffix array def FillPrefixSuffix(prefix,arr,suffix,n): # Filling the prefix array # following relation # prefix(i) = GCD(prefix(i-1), arr(i)) prefix[0] = arr[0] for i in range(1,n): prefix[i] = GCD (prefix[i-1], arr[i]) # Filling the suffix # array following the # relation suffix(i) = GCD(suffix(i+1), arr(i)) suffix[n-1] = arr[n-1] for i in range(n-2,-1,-1): suffix[i] = GCD (suffix[i+1], arr[i]) # To calculate gcd of # the numbers outside range def GCDoutsideRange(l,r,prefix,suffix,n): # If l=0, we need to tell GCD of numbers # from r+1 to n if (l==0): return suffix[r+1] # If r=n-1 we need to return the gcd of # numbers from 1 to l if (r==n-1): return prefix[l-1] return GCD(prefix[l-1], suffix[r+1]) # Driver code arr = [2, 6, 9] n = len(arr) prefix=[] suffix=[] for i in range(n+1): prefix.append(0) suffix.append(0) FillPrefixSuffix(prefix, arr, suffix, n) l = 0 r = 0 print(GCDoutsideRange(l, r, prefix, suffix, n)) l = 1 r = 1 print(GCDoutsideRange(l, r, prefix, suffix, n)) l = 1 r = 2 print(GCDoutsideRange(l, r, prefix, suffix, n)) # This code is contributed # by Anant Agarwal.
linear
nlogn
# function to count elements within given range def countInRange(arr, n, x, y): # initialize result count = 0; for i in range(n): # check if element is in range if (arr[i] >= x and arr[i] <= y): count += 1 return count # driver function arr = [1, 3, 4, 9, 10, 3] n = len(arr) # Answer queries i = 1 j = 4 print(countInRange(arr, n, i, j)) i = 9 j = 12 print(countInRange(arr, n, i, j))
constant
linear
# function to find first index >= x def lowerIndex(arr, n, x): l = 0 h = n-1 while (l <= h): mid = int((l + h)//2) if (arr[mid] >= x): h = mid - 1 else: l = mid + 1 return l # function to find last index <= x def upperIndex(arr, n, x): l = 0 h = n-1 while (l <= h): mid = int((l + h)//2) if (arr[mid] <= x): l = mid + 1 else: h = mid - 1 return h # function to count elements within given range def countInRange(arr, n, x, y): # initialize result count = 0; count = upperIndex(arr, n, y) - lowerIndex(arr, n, x) + 1; return count # driver function arr = [1, 3, 4, 9, 10, 3] # Preprocess array arr.sort() n = len(arr) # Answer queries i = 1 j = 4 print(countInRange(arr, n, i, j)) i = 9 j = 12 print(countInRange(arr, n, i, j))
constant
nlogn
# implementation of finding number # represented by binary subarray from math import pow # Fills pre[] def precompute(arr, n, pre): pre[n - 1] = arr[n - 1] * pow(2, 0) i = n - 2 while(i >= 0): pre[i] = (pre[i + 1] + arr[i] * (1 << (n - 1 - i))) i -= 1 # returns the number represented by # a binary subarray l to r def decimalOfSubarr(arr, l, r, n, pre): # if r is equal to n-1 r+1 does not exist if (r != n - 1): return ((pre[l] - pre[r + 1]) / (1 << (n - 1 - r))) return pre[l] / (1 << (n - 1 - r)) # Driver Code if __name__ == '__main__': arr = [1, 0, 1, 0, 1, 1] n = len(arr) pre = [0 for i in range(n)] precompute(arr, n, pre) print(int(decimalOfSubarr(arr, 2, 4, n, pre))) print(int(decimalOfSubarr(arr, 4, 5, n, pre))) # This code is contributed by # Surendra_Gangwar
linear
linear
# Python3 program to perform range # queries over range queries. import math max = 10000 # For prefix sum array def update(arr, l): arr[l] += arr[l - 1] # This function is used to apply square root # decomposition in the record array def record_func(block_size, block, record, l, r, value): # Traversing first block in range while (l < r and l % block_size != 0 and l != 0): record[l] += value l += 1 # Traversing completely overlapped # blocks in range while (l + block_size <= r + 1): block[l // block_size] += value l += block_size # Traversing last block in range while (l <= r): record[l] += value l += 1 # Function to print the resultant array def print_array(arr, n): for i in range(n): print(arr[i], end = " ") # Driver code if __name__ == "__main__": n = 5 m = 5 arr = [0] * n record = [0] * m block_size = (int)(math.sqrt(m)) block = [0] * max command = [ [ 1, 1, 2 ], [ 1, 4, 5 ], [ 2, 1, 2 ], [ 2, 1, 3 ], [ 2, 3, 4 ] ] for i in range(m - 1, -1, -1): # If query is of type 2 then function # call to record_func if (command[i][0] == 2): x = i // (block_size) record_func(block_size, block, record, command[i][1] - 1, command[i][2] - 1, (block[x] + record[i] + 1)) # If query is of type 1 then simply add # 1 to the record array else: record[i] += 1 # Merging the value of the block # in the record array for i in range(m): check = (i // block_size) record[i] += block[check] for i in range(m): # If query is of type 1 then the array # elements are over-written by the record # array if (command[i][0] == 1): arr[command[i][1] - 1] += record[i] if ((command[i][2] - 1) < n - 1): arr[(command[i][2])] -= record[i] # The prefix sum of the array for i in range(1, n): update(arr, i) # Printing the resultant array print_array(arr, n) # This code is contributed by chitranayal
linear
logn
# Python 3 program to count the # number of indexes in range L R # such that Ai = Ai + 1 # function that answers every # query in O(r-l) def answer_query(a, n, l, r): # traverse from l to r and # count the required indexes count = 0 for i in range(l, r): if (a[i] == a[i + 1]): count += 1 return count # Driver Code a = [1, 2, 2, 2, 3, 3, 4, 4, 4] n = len(a) # 1-st query L = 1 R = 8 print(answer_query(a, n, L, R)) # 2nd query L = 0 R = 4 print(answer_query(a, n, L, R)) # This code is contributed by # Smitha Dinesh Semwal
constant
constant
# Python program to count # the number of indexes in # range L R such that Ai=Ai+1 N = 1000 # array to store count # of index from 0 to # i that obey condition prefixans = [0] * N; # precomputing # prefixans[] array def countIndex(a, n) : global N, prefixans # traverse to compute # the prefixans[] array for i in range(0, n - 1) : if (a[i] == a[i + 1]) : prefixans[i] = 1 if (i != 0) : prefixans[i] = (prefixans[i] + prefixans[i - 1]) # def that answers # every query in O(1) def answer_query(l, r) : global N, prefixans if (l == 0) : return prefixans[r - 1] else : return (prefixans[r - 1] - prefixans[l - 1]) # Driver Code a = [1, 2, 2, 2, 3, 3, 4, 4, 4] n = len(a) # pre-computation countIndex(a, n) # 1-st query L = 1 R = 8 print (answer_query(L, R)) # 2nd query L = 0 R = 4 print (answer_query(L, R)) # This code is contributed by # Manish Shaw(manishshaw1)
linear
linear
# Python program to find maximum contiguous subarray # Function to find the maximum contiguous subarray from sys import maxint def maxSubArraySum(a, size): max_so_far = -maxint - 1 max_ending_here = 0 for i in range(0, size): max_ending_here = max_ending_here + a[i] if (max_so_far < max_ending_here): max_so_far = max_ending_here if max_ending_here < 0: max_ending_here = 0 return max_so_far # Driver function to check the above function a = [-2, -3, 4, -1, -2, 1, 5, -3] print "Maximum contiguous sum is", maxSubArraySum(a, len(a)) # This code is contributed by _Devesh Agrawal_
constant
linear
# Python program to print largest contiguous array sum from sys import maxsize # Function to find the maximum contiguous subarray # and print its starting and end index def maxSubArraySum(a, size): max_so_far = -maxsize - 1 max_ending_here = 0 start = 0 end = 0 s = 0 for i in range(0, size): max_ending_here += a[i] if max_so_far < max_ending_here: max_so_far = max_ending_here start = s end = i if max_ending_here < 0: max_ending_here = 0 s = i+1 print("Maximum contiguous sum is %d" % (max_so_far)) print("Starting Index %d" % (start)) print("Ending Index %d" % (end)) # Driver program to test maxSubArraySum a = [-2, -3, 4, -1, -2, 1, 5, -3] maxSubArraySum(a, len(a))
constant
linear
# Returns maximum profit with # two transactions on a given # list of stock prices price[0..n-1] def maxProfit(price, n): # Create profit array and initialize it as 0 profit = [0]*n # Get the maximum profit # with only one transaction # allowed. After this loop, # profit[i] contains maximum # profit from price[i..n-1] # using at most one trans. max_price = price[n-1] for i in range(n-2, 0, -1): if price[i] > max_price: max_price = price[i] # we can get profit[i] by # taking maximum of: # a) previous maximum, # i.e., profit[i+1] # b) profit by buying at # price[i] and selling at # max_price profit[i] = max(profit[i+1], max_price - price[i]) # Get the maximum profit # with two transactions allowed # After this loop, profit[n-1] # contains the result min_price = price[0] for i in range(1, n): if price[i] < min_price: min_price = price[i] # Maximum profit is maximum of: # a) previous maximum, # i.e., profit[i-1] # b) (Buy, Sell) at # (min_price, A[i]) and add # profit of other trans. # stored in profit[i] profit[i] = max(profit[i-1], profit[i]+(price[i]-min_price)) result = profit[n-1] return result # Driver function price = [2, 30, 15, 10, 8, 25, 80] print ("Maximum profit is", maxProfit(price, len(price))) # This code is contributed by __Devesh Agrawal__
linear
linear
import sys def maxtwobuysell(arr, size): first_buy = -sys.maxsize; first_sell = 0; second_buy = -sys.maxsize; second_sell = 0; for i in range(size): first_buy = max(first_buy, -arr[i]); first_sell = max(first_sell, first_buy + arr[i]); second_buy = max(second_buy, first_sell - arr[i]); second_sell = max(second_sell, second_buy + arr[i]); return second_sell; if __name__ == '__main__': arr = [ 2, 30, 15, 10, 8, 25, 80 ]; size = len(arr); print(maxtwobuysell(arr, size)); # This code is contributed by gauravrajput1
constant
linear
# Python3 program to find # minimum average subarray # Prints beginning and ending # indexes of subarray of size k # with minimum average def findsubarrayleast(arr, k, n): min = 999999 minindex = 0 for i in range(n-k+1): sum = 0 j = i for j in range(i, i+k): sum += arr[j] if sum < min: min = sum minindex = i # printing the desired subarray print("subarray with minimum average is: ", end='') for i in range(minindex, minindex+k): print(arr[i], end=" ") # Driver Code arr = [20, 3, 13, 5, 10, 14, 8, 5, 11, 9, 1, 11] k = 9 # Subarray size n = len(arr) findsubarrayleast(arr, k, n) # This code is contributed by Aarti_Rathi
constant
quadratic
# Python3 program to find # minimum average subarray # Prints beginning and ending # indexes of subarray of size k # with minimum average def findMinAvgSubarray(arr, n, k): # k must be smaller than or equal to n if (n < k): return 0 # Initialize beginning index of result res_index = 0 # Compute sum of first subarray of size k curr_sum = 0 for i in range(k): curr_sum += arr[i] # Initialize minimum sum as current sum min_sum = curr_sum # Traverse from (k + 1)'th # element to n'th element for i in range(k, n): # Add current item and remove first # item of previous subarray curr_sum += arr[i] - arr[i-k] # Update result if needed if (curr_sum < min_sum): min_sum = curr_sum res_index = (i - k + 1) print("Subarray between [", res_index, ", ", (res_index + k - 1), "] has minimum average") # Driver Code arr = [3, 7, 90, 20, 10, 50, 40] k = 3 # Subarray size n = len(arr) findMinAvgSubarray(arr, n, k) # This code is contributed by Anant Agarwal.
constant
linear
# Python3 code to Find the minimum # distance between two numbers def minDist(arr, n, x, y): min_dist = 99999999 for i in range(n): for j in range(i + 1, n): if (x == arr[i] and y == arr[j] or y == arr[i] and x == arr[j]) and min_dist > abs(i-j): min_dist = abs(i-j) return min_dist # Driver code arr = [3, 5, 4, 2, 6, 5, 6, 6, 5, 4, 8, 3] n = len(arr) x = 3 y = 6 print("Minimum distance between ", x, " and ", y, "is", minDist(arr, n, x, y)) # This code is contributed by "Abhishek Sharma 44"
constant
quadratic
import sys def minDist(arr, n, x, y): #previous index and min distance i=0 p=-1 min_dist = sys.maxsize; for i in range(n): if(arr[i] ==x or arr[i] == y): #we will check if p is not equal to -1 and #If the element at current index matches with #the element at index p , If yes then update #the minimum distance if needed if(p != -1 and arr[i] != arr[p]): min_dist = min(min_dist,i-p) #update the previous index p=i #If distance is equal to int max if(min_dist == sys.maxsize): return -1 return min_dist # Driver program to test above function */ arr = [3, 5, 4, 2, 6, 3, 0, 0, 5, 4, 8, 3] n = len(arr) x = 3 y = 6 print ("Minimum distance between %d and %d is %d\n"%( x, y,minDist(arr, n, x, y))); # This code is contributed by Shreyanshi Arun.
constant
linear
# Python program to Find the minimum # distance between two numbers import sys def minDist(arr, n, x, y) : # idx1 and idx2 will store indices of # x or y and min_dist will store the minimum difference idx1=-1; idx2=-1; min_dist = sys.maxsize; for i in range(n) : # if current element is x then change idx1 if arr[i]==x : idx1=i # if current element is y then change idx2 elif arr[i]==y : idx2=i # if x and y both found in array # then only find the difference and store it in min_dist if idx1!=-1 and idx2!=-1 : min_dist=min(min_dist,abs(idx1-idx2)); # if left or right did not found in array # then return -1 if idx1==-1 or idx2==-1 : return -1 # return the minimum distance else : return min_dist # Driver code if __name__ == "__main__" : arr = [ 3, 5, 4, 2, 6, 5, 6, 6, 5, 4, 8, 3] n = len(arr) x = 3 y = 6 print ("Minimum distance between %d and %d is %d\n"%( x, y,minDist(arr, n, x, y))); # this code is contributed by aditya942003patil
constant
linear
# User function Template def getMinDiff(arr, n, k): arr.sort() ans = arr[n - 1] - arr[0] # Maximum possible height difference tempmin = arr[0] tempmax = arr[n - 1] for i in range(1, n): if arr[i] < k: continue tempmin = min(arr[0] + k, arr[i] - k) # Minimum element when we # add k to whole array # Maximum element when we tempmax = max(arr[i - 1] + k, arr[n - 1] - k) # subtract k from whole array ans = min(ans, tempmax - tempmin) return ans # Driver Code Starts k = 6 n = 6 arr = [7, 4, 8, 8, 8, 9] ans = getMinDiff(arr, n, k) print(ans) # This code is contributed by ninja_hattori.
constant
nlogn
# Python3 program to find Minimum # number of jumps to reach end # Returns minimum number of jumps # to reach arr[h] from arr[l] def minJumps(arr, l, h): # Base case: when source and # destination are same if (h == l): return 0 # when nothing is reachable # from the given source if (arr[l] == 0): return float('inf') # Traverse through all the points # reachable from arr[l]. Recursively # get the minimum number of jumps # needed to reach arr[h] from # these reachable points. min = float('inf') for i in range(l + 1, h + 1): if (i < l + arr[l] + 1): jumps = minJumps(arr, i, h) if (jumps != float('inf') and jumps + 1 < min): min = jumps + 1 return min # Driver program to test above function arr = [1, 3, 5, 8, 9, 2, 6, 7, 6, 8, 9] n = len(arr) print('Minimum number of jumps to reach', 'end is', minJumps(arr, 0, n-1)) # This code is contributed by Soumen Ghosh
linear
np
# Python3 program to find Minimum # number of jumps to reach end # Returns minimum number of jumps # to reach arr[n-1] from arr[0] def minJumps(arr, n): jumps = [0 for i in range(n)] if (n == 0) or (arr[0] == 0): return float('inf') jumps[0] = 0 # Find the minimum number of # jumps to reach arr[i] from # arr[0] and assign this # value to jumps[i] for i in range(1, n): jumps[i] = float('inf') for j in range(i): if (i <= j + arr[j]) and (jumps[j] != float('inf')): jumps[i] = min(jumps[i], jumps[j] + 1) break return jumps[n-1] # Driver Program to test above function arr = [1, 3, 5, 8, 9, 2, 6, 7, 6, 8, 9] size = len(arr) print('Minimum number of jumps to reach', 'end is', minJumps(arr, size)) # This code is contributed by Soumen Ghosh
linear
np
# Python3 program to find Minimum # number of jumps to reach end # Returns Minimum number of # jumps to reach end def minJumps(arr, n): # jumps[0] will hold the result jumps = [0 for i in range(n)] # Minimum number of jumps needed # to reach last element from # last elements itself is always 0 # jumps[n-1] is also initialized to 0 # Start from the second element, # move from right to left and # construct the jumps[] array where # jumps[i] represents minimum number # of jumps needed to reach arr[m-1] # form arr[i] for i in range(n-2, -1, -1): # If arr[i] is 0 then arr[n-1] # can't be reached from here if (arr[i] == 0): jumps[i] = float('inf') # If we can directly reach to # the end point from here then # jumps[i] is 1 elif (arr[i] >= n - i - 1): jumps[i] = 1 # Otherwise, to find out the # minimum number of jumps # needed to reach arr[n-1], # check all the points # reachable from here and # jumps[] value for those points else: # initialize min value min = float('inf') # following loop checks with # all reachable points and # takes the minimum for j in range(i + 1, n): if (j <= arr[i] + i): if (min > jumps[j]): min = jumps[j] # Handle overflow if (min != float('inf')): jumps[i] = min + 1 else: # or INT_MAX jumps[i] = min return jumps[0] # Driver program to test above function arr = [1, 3, 5, 8, 9, 2, 6, 7, 6, 8, 9] n = len(arr) print('Minimum number of jumps to reach', 'end is', minJumps(arr, n-1)) # This code is contributed by Soumen Ghosh
linear
quadratic
# Dynamic Programming based Python # implementation of Maximum Sum # Increasing Subsequence (MSIS) # problem # maxSumIS() returns the maximum # sum of increasing subsequence # in arr[] of size n def maxSumIS(arr, n): max = 0 msis = [0 for x in range(n)] # Initialize msis values # for all indexes for i in range(n): msis[i] = arr[i] # Compute maximum sum # values in bottom up manner for i in range(1, n): for j in range(i): if (arr[i] > arr[j] and msis[i] < msis[j] + arr[i]): msis[i] = msis[j] + arr[i] # Pick maximum of # all msis values for i in range(n): if max < msis[i]: max = msis[i] return max # Driver Code arr = [1, 101, 2, 3, 100, 4, 5] n = len(arr) print("Sum of maximum sum increasing " + "subsequence is " + str(maxSumIS(arr, n))) # This code is contributed # by Bhavya Jain
linear
quadratic
# Python3 program to find Smallest # subarray with sum greater # than a given value # Returns length of smallest subarray # with sum greater than x. If there # is no subarray with given sum, # then returns n+1 def smallestSubWithSum(arr, n, x): # Initialize length of smallest # subarray as n+1 min_len = n + 1 # Pick every element as starting point for start in range(0,n): # Initialize sum starting # with current start curr_sum = arr[start] # If first element itself is greater if (curr_sum > x): return 1 # Try different ending points # for curremt start for end in range(start+1,n): # add last element to current sum curr_sum += arr[end] # If sum becomes more than x # and length of this subarray # is smaller than current smallest # length, update the smallest # length (or result) if curr_sum > x and (end - start + 1) < min_len: min_len = (end - start + 1) return min_len; # Driver program to test above function */ arr1 = [1, 4, 45, 6, 10, 19] x = 51 n1 = len(arr1) res1 = smallestSubWithSum(arr1, n1, x); if res1 == n1+1: print("Not possible") else: print(res1) arr2 = [1, 10, 5, 2, 7] n2 = len(arr2) x = 9 res2 = smallestSubWithSum(arr2, n2, x); if res2 == n2+1: print("Not possible") else: print(res2) arr3 = [1, 11, 100, 1, 0, 200, 3, 2, 1, 250] n3 = len(arr3) x = 280 res3 = smallestSubWithSum(arr3, n3, x) if res3 == n3+1: print("Not possible") else: print(res3) # This code is contributed by Smitha Dinesh Semwal
constant
quadratic
# O(n) solution for finding smallest # subarray with sum greater than x # Returns length of smallest subarray # with sum greater than x. If there # is no subarray with given sum, then # returns n + 1 def smallestSubWithSum(arr, n, x): # Initialize current sum and minimum length curr_sum = 0 min_len = n + 1 # Initialize starting and ending indexes start = 0 end = 0 while (end < n): # Keep adding array elements while current # sum is smaller than or equal to x while (curr_sum <= x and end < n): curr_sum += arr[end] end += 1 # If current sum becomes greater than x. while (curr_sum > x and start < n): # Update minimum length if needed if (end - start < min_len): min_len = end - start # remove starting elements curr_sum -= arr[start] start += 1 return min_len # Driver program arr1 = [1, 4, 45, 6, 10, 19] x = 51 n1 = len(arr1) res1 = smallestSubWithSum(arr1, n1, x) print("Not possible") if (res1 == n1 + 1) else print(res1) arr2 = [1, 10, 5, 2, 7] n2 = len(arr2) x = 9 res2 = smallestSubWithSum(arr2, n2, x) print("Not possible") if (res2 == n2 + 1) else print(res2) arr3 = [1, 11, 100, 1, 0, 200, 3, 2, 1, 250] n3 = len(arr3) x = 280 res3 = smallestSubWithSum(arr3, n3, x) print("Not possible") if (res3 == n3 + 1) else print(res3) # This code is contributed by # Smitha Dinesh Semwal
constant
linear
# Python program to find maximum average subarray # of given length. # Returns beginning index of maximum average # subarray of length 'k' def findMaxAverage(arr, n, k): # Check if 'k' is valid if k > n: return -1 # Create and fill array to store cumulative # sum. csum[i] stores sum of arr[0] to arr[i] csum = [0]*n csum[0] = arr[0] for i in range(1, n): csum[i] = csum[i-1] + arr[i]; # Initialize max_sm as sum of first subarray max_sum = csum[k-1] max_end = k-1 # Find sum of other subarrays and update # max_sum if required. for i in range(k, n): curr_sum = csum[i] - csum[i-k] if curr_sum > max_sum: max_sum = curr_sum max_end = i # Return starting index return max_end - k + 1 # Driver program arr = [1, 12, -5, -6, 50, 3] k = 4 n = len(arr) print("The maximum average subarray of length",k, "begins at index",findMaxAverage(arr, n, k)) #This code is contributed by #Smitha Dinesh Semwal
linear
linear
# Python 3 program to find maximum # average subarray of given length. # Returns beginning index of maximum # average subarray of length 'k' def findMaxAverage(arr, n, k): # Check if 'k' is valid if (k > n): return -1 # Compute sum of first 'k' elements sum = arr[0] for i in range(1, k): sum += arr[i] max_sum = sum max_end = k - 1 # Compute sum of remaining subarrays for i in range(k, n): sum = sum + arr[i] - arr[i - k] if (sum > max_sum): max_sum = sum max_end = i # Return starting index return max_end - k + 1 # Driver program arr = [1, 12, -5, -6, 50, 3] k = 4 n = len(arr) print("The maximum average subarray of length", k, "begins at index", findMaxAverage(arr, n, k)) # This code is contributed by # Smitha Dinesh Semwal
constant
linear
# Python3 program to count minimum number of # operations to get the given target array # Returns count of minimum operations to # convert a zero array to target array # with increment and doubling operations. # This function computes count by doing reverse # steps, i.e., convert target to zero array. def countMinOperations(target, n): # Initialize result (Count of minimum moves) result = 0; # Keep looping while all elements of # target don't become 0. while (True): # To store count of zeroes in # current target array zero_count = 0; # To find first odd element i = 0; while (i < n): # If odd number found if ((target[i] & 1) > 0): break; # If 0, then increment # zero_count elif (target[i] == 0): zero_count += 1; i += 1; # All numbers are 0 if (zero_count == n): return result; # All numbers are even if (i == n): # Divide the whole array by 2 # and increment result for j in range(n): target[j] = target[j] // 2; result += 1; # Make all odd numbers even by # subtracting one and increment result. for j in range(i, n): if (target[j] & 1): target[j] -= 1; result += 1; # Driver Code arr = [16, 16, 16]; n = len(arr); print("Minimum number of steps required to", "\nget the given target array is", countMinOperations(arr, n)); # This code is contributed by mits
constant
linear
# Python program to find number of operations # to make an array palindrome # Returns minimum number of count operations # required to make arr[] palindrome def findMinOps(arr, n): ans = 0 # Initialize result # Start from two corners i,j = 0,n-1 while i<=j: # If corner elements are same, # problem reduces arr[i+1..j-1] if arr[i] == arr[j]: i += 1 j -= 1 # If left element is greater, then # we merge right two elements elif arr[i] > arr[j]: # need to merge from tail. j -= 1 arr[j] += arr[j+1] ans += 1 # Else we merge left two elements else: i += 1 arr[i] += arr[i-1] ans += 1 return ans # Driver program to test above arr = [1, 4, 5, 9, 1] n = len(arr) print("Count of minimum operations is " + str(findMinOps(arr, n))) # This code is contributed by Pratik Chhajer
constant
linear
# Python3 program to find the smallest # positive value that cannot be # represented as sum of subsets # of a given sorted array # Returns the smallest number # that cannot be represented as sum # of subset of elements from set # represented by sorted array arr[0..n-1] def findSmallest(arr, n): res = 1 #Initialize result # Traverse the array and increment # 'res' if arr[i] is smaller than # or equal to 'res'. for i in range (0, n ): if arr[i] <= res: res = res + arr[i] else: break return res # Driver program to test above function arr1 = [1, 3, 4, 5] n1 = len(arr1) print(findSmallest(arr1, n1)) arr2= [1, 2, 6, 10, 11, 15] n2 = len(arr2) print(findSmallest(arr2, n2)) arr3= [1, 1, 1, 1] n3 = len(arr3) print(findSmallest(arr3, n3)) arr4 = [1, 1, 3, 4] n4 = len(arr4) print(findSmallest(arr4, n4)) # This code is.contributed by Smitha Dinesh Semwal
constant
nlogn
# Python3 program to print largest contiguous array sum from sys import maxsize # Function to find the maximum contiguous subarray # and print its starting and end index def maxSubArraySum(a,size): max_so_far = -maxsize - 1 max_ending_here = 0 start = 0 end = 0 s = 0 for i in range(0,size): max_ending_here += a[i] if max_so_far < max_ending_here: max_so_far = max_ending_here start = s end = i if max_ending_here < 0: max_ending_here = 0 s = i+1 return (end - start + 1) # Driver program to test maxSubArraySum a = [-2, -3, 4, -1, -2, 1, 5, -3] print(maxSubArraySum(a,len(a)))
constant
linear
# Python implementation of simple method to find # minimum difference between any pair # Returns minimum difference between any pair def findMinDiff(arr, n): # Initialize difference as infinite diff = 10**20 # Find the min diff by comparing difference # of all possible pairs in given array for i in range(n-1): for j in range(i+1, n): if abs(arr[i]-arr[j]) < diff: diff = abs(arr[i] - arr[j]) # Return min diff return diff # Driver code if __name__ == "__main__": arr = [1, 5, 3, 19, 18, 25] n = len(arr) # Function call print("Minimum difference is " + str(findMinDiff(arr, n))) # This code is contributed by Pratik Chhajer
constant
quadratic
# Python3 program to find minimum difference between # any pair in an unsorted array # Returns minimum difference between any pair def findMinDiff(arr, n): # Sort array in non-decreasing order arr = sorted(arr) # Initialize difference as infinite diff = 10**20 # Find the min diff by comparing adjacent # pairs in sorted array for i in range(n-1): if arr[i+1] - arr[i] < diff: diff = arr[i+1] - arr[i] # Return min diff return diff # Driver code if __name__ == "__main__": arr = [1, 5, 3, 19, 18, 25] n = len(arr) # Function call print("Minimum difference is " + str(findMinDiff(arr, n))) # This code is contributed by Pratik Chhajer
constant
nlogn
# A Simple python program to find longest common # subarray of two binary arrays with same sum # Returns length of the longest common subarray # with same sum def longestCommonSum(arr1, arr2, n): # Initialize result maxLen = 0 # One by one pick all possible starting points # of subarrays for i in range(0,n): # Initialize sums of current subarrays sum1 = 0 sum2 = 0 # Consider all points for starting with arr[i] for j in range(i,n): # Update sums sum1 += arr1[j] sum2 += arr2[j] # If sums are same and current length is # more than maxLen, update maxLen if (sum1 == sum2): len = j-i+1 if (len > maxLen): maxLen = len return maxLen # Driver program to test above function arr1 = [0, 1, 0, 1, 1, 1, 1] arr2 = [1, 1, 1, 1, 1, 0, 1] n = len(arr1) print("Length of the longest common span with same " "sum is",longestCommonSum(arr1, arr2, n)) # This code is contributed by # Smitha Dinesh Semwal
constant
quadratic
# Python program to find longest common # subarray of two binary arrays with # same sum def longestCommonSum(arr1, arr2, n): # Initialize result maxLen = 0 # Initialize prefix sums of two arrays presum1 = presum2 = 0 # Create a dictionary to store indices # of all possible sums diff = {} # Traverse both arrays for i in range(n): # Update prefix sums presum1 += arr1[i] presum2 += arr2[i] # Compute current diff which will be # used as index in diff dictionary curr_diff = presum1 - presum2 # If current diff is 0, then there # are same number of 1's so far in # both arrays, i.e., (i+1) is # maximum length. if curr_diff == 0: maxLen = i+1 elif curr_diff not in diff: # save the index for this diff diff[curr_diff] = i else: # calculate the span length length = i - diff[curr_diff] maxLen = max(maxLen, length) return maxLen # Driver program arr1 = [0, 1, 0, 1, 1, 1, 1] arr2 = [1, 1, 1, 1, 1, 0, 1] print("Length of the longest common", " span with same", end = " ") print("sum is",longestCommonSum(arr1, arr2, len(arr1))) # This code is contributed by Abhijeet Nautiyal
linear
linear
# Python program to find largest subarray # with equal number of 0's and 1's. # Returns largest common subarray with equal # number of 0s and 1s def longestCommonSum(arr1, arr2, n): # Find difference between the two arr = [0 for i in range(n)] for i in range(n): arr[i] = arr1[i] - arr2[i]; # Creates an empty hashMap hM hm = {} sum = 0 # Initialize sum of elements max_len = 0 #Initialize result # Traverse through the given array for i in range(n): # Add current element to sum sum += arr[i] # To handle sum=0 at last index if (sum == 0): max_len = i + 1 # If this sum is seen before, # then update max_len if required if sum in hm: max_len = max(max_len, i - hm[sum]) else: # Else put this sum in hash table hm[sum] = i return max_len # Driver code arr1 = [0, 1, 0, 1, 1, 1, 1] arr2 = [1, 1, 1, 1, 1, 0, 1] n = len(arr1) print(longestCommonSum(arr1, arr2, n)) # This code is contributed by rag2127
linear
linear
# Python 3 program to print an array # in alternate sorted manner. # Function to print alternate sorted # values def alternateSort(arr, n): # Sorting the array arr.sort() # Printing the last element of array # first and then first element and then # second last element and then second # element and so on. i = 0 j = n-1 while (i < j): print(arr[j], end =" ") j-= 1 print(arr[i], end =" ") i+= 1 # If the total element in array is odd # then print the last middle element. if (n % 2 != 0): print(arr[i]) # Driver code arr = [1, 12, 4, 6, 7, 10] n = len(arr) alternateSort(arr, n) # This code is contributed by # Smitha Dinesh Semwal
constant
nlogn
# Function to sort an array using # insertion sort def insertionSort(A, size): i, key, j = 0, 0, 0 for i in range(size): key = A[i] j = i-1 # Move elements of A[0..i-1], that are # greater than key, to one position # ahead of their current position. # This loop will run at most k times while j >= 0 and A[j] > key: A[j + 1] = A[j] j = j - 1 A[j + 1] = key
constant
constant
# A Python3 program to sort a # nearly sorted array. from heapq import heappop, heappush, heapify # A utility function to print # array elements def print_array(arr: list): for elem in arr: print(elem, end=' ') # Given an array of size n, where every # element is k away from its target # position, sorts the array in O(nLogk) time. def sort_k(arr: list, n: int, k: int): """ :param arr: input array :param n: length of the array :param k: max distance, which every element is away from its target position. :return: None """ # List of first k+1 items heap = arr[:k + 1] # using heapify to convert list # into heap(or min heap) heapify(heap) # "rem_elmnts_index" is index for remaining # elements in arr and "target_index" is # target index of for current minimum element # in Min Heap "heap". target_index = 0 for rem_elmnts_index in range(k + 1, n): arr[target_index] = heappop(heap) heappush(heap, arr[rem_elmnts_index]) target_index += 1 while heap: arr[target_index] = heappop(heap) target_index += 1 # Driver Code k = 3 arr = [2, 6, 3, 12, 56, 8] n = len(arr) sort_k(arr, n, k) print('Following is sorted array') print_array(arr) # This code is contributed by # Veerat Beri(viratberi)
logn
nlogn
# Python function to sort the array arr[0..n-1] in wave form, # i.e., arr[0] >= arr[1] <= arr[2] >= arr[3] <= arr[4] >= arr[5] def sortInWave(arr, n): #sort the array arr.sort() # Swap adjacent elements for i in range(0,n-1,2): arr[i], arr[i+1] = arr[i+1], arr[i] # Driver program arr = [10, 90, 49, 2, 1, 5, 23] sortInWave(arr, len(arr)) for i in range(0,len(arr)): print (arr[i],end=" ") # This code is contributed by __Devesh Agrawal__
constant
nlogn
# Python function to sort the array arr[0..n-1] in wave form, # i.e., arr[0] >= arr[1] <= arr[2] >= arr[3] <= arr[4] >= arr[5] def sortInWave(arr, n): # Traverse all even elements for i in range(0, n - 1, 2): # If current even element is smaller than previous if (i > 0 and arr[i] < arr[i-1]): arr[i], arr[i-1] = arr[i-1], arr[i] # If current even element is smaller than next if (i < n-1 and arr[i] < arr[i+1]): arr[i], arr[i+1] = arr[i+1], arr[i] # Driver program arr = [10, 90, 49, 2, 1, 5, 23] sortInWave(arr, len(arr)) for i in range(0, len(arr)): print(arr[i], end=" ") # This code is contributed by __Devesh Agrawal__
constant
linear
# Python program to Merge an array of # size n into another array of size m + n NA = -1 # Function to move m elements # at the end of array mPlusN[] def moveToEnd(mPlusN, size): i = 0 j = size - 1 for i in range(size-1, -1, -1): if (mPlusN[i] != NA): mPlusN[j] = mPlusN[i] j -= 1 # Merges array N[] # of size n into array mPlusN[] # of size m+n def merge(mPlusN, N, m, n): i = n # Current index of i/p part of mPlusN[] j = 0 # Current index of N[] k = 0 # Current index of output mPlusN[] while (k < (m+n)): # Take an element from mPlusN[] if # a) value of the picked # element is smaller and we have # not reached end of it # b) We have reached end of N[] */ if ((j == n) or (i < (m+n) and mPlusN[i] <= N[j])): mPlusN[k] = mPlusN[i] k += 1 i += 1 else: # Otherwise take element from N[] mPlusN[k] = N[j] k += 1 j += 1 # Utility that prints # out an array on a line def printArray(arr, size): for i in range(size): print(arr[i], " ", end="") print() # Driver function to # test above functions # Initialize arrays mPlusN = [2, 8, NA, NA, NA, 13, NA, 15, 20] N = [5, 7, 9, 25] n = len(N) m = len(mPlusN) - n # Move the m elements # at the end of mPlusN moveToEnd(mPlusN, m+n) # Merge N[] into mPlusN[] merge(mPlusN, N, m, n) # Print the resultant mPlusN printArray(mPlusN, m+n) # This code is contributed # by Anant Agarwal.
constant
linear
# Python 3 program to test whether an array # can be sorted by swapping adjacent # elements using a boolean array # Return true if array can be # sorted otherwise false def sortedAfterSwap(A, B, n) : # Check bool array B and sorts # elements for continuous sequence of 1 for i in range(0, n - 1) : if (B[i]== 1) : j = i while (B[j]== 1) : j = j + 1 # Sort array A from i to j A = A[0:i] + sorted(A[i:j + 1]) + A[j + 1:] i = j # Check if array is sorted or not for i in range(0, n) : if (A[i] != i + 1) : return False return True # Driver program to test sortedAfterSwap() A = [ 1, 2, 5, 3, 4, 6 ] B = [ 0, 1, 1, 1, 0 ] n = len(A) if (sortedAfterSwap(A, B, n)) : print("A can be sorted") else : print("A can not be sorted") # This code is contributed # by Nikita Tiwari.
constant
quadratic
# Python3 program to test whether array # can be sorted by swapping adjacent # elements using boolean array # Return true if array can be # sorted otherwise false def sortedAfterSwap(A,B,n): for i in range(0,n-1): if B[i]: if A[i]!=i+1: A[i], A[i+1] = A[i+1], A[i] # Check if array is sorted or not for i in range(n): if A[i]!=i+1: return False return True # Driver program if __name__=='__main__': A = [1, 2, 5, 3, 4, 6] B = [0, 1, 1, 1, 0] n =len(A) if (sortedAfterSwap(A, B, n)) : print("A can be sorted") else : print("A can not be sorted") # This code is contributed by # Shrikant13
constant
linear
# Python3 program to sort an array with # two types of values in one traversal. # Method for segregation 0 and # 1 given input array def segregate0and1(arr, n): type0 = 0; type1 = n - 1 while (type0 < type1): if (arr[type0] == 1): arr[type0], arr[type1] = arr[type1], arr[type0] type1 -= 1 else: type0 += 1 # Driver Code arr = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1] n = len(arr) segregate0and1(arr, n) for i in range(0, n): print(arr[i], end = " ") # This code is contributed by Smitha Dinesh Semwal
constant
linear
# Python3 program that performs the following # operations: Sort elements by frequency. If two elements # have same count, then put the elements that appears first # Used for sorting class ele: def __init__(self): self.count = 0 self.index = 0 self.val = 0 def mycomp(a): return a.val # Used for sorting by frequency. And if frequency is same, # then by appearance def mycomp2(a): # using negative value for a.index # since the sorting should be in # descending order return (a.count, -a.index) def sortByFrequency(arr, n): element = [None for _ in range(n)] for i in range(n): element[i] = ele() # Fill Indexes element[i].index = i # Initialize counts as 0 element[i].count = 0 # Fill values in structure # elements element[i].val = arr[i] # Sort the structure elements according to value, # we used stable sort so relative order is maintained. # element.sort(key=mycomp) # initialize count of first element as 1 element[0].count = 1 # Count occurrences of remaining elements for i in range(1, n): if (element[i].val == element[i - 1].val): element[i].count += element[i - 1].count + 1 # Set count of previous element as -1, we are # doing this because we'll again sort on the # basis of counts (if counts are equal than on # the basis of index)*/ element[i - 1].count = -1 # Retain the first index (Remember first index # is always present in the first duplicate we # used stable sort. */ element[i].index = element[i - 1].index # Else If previous element is not equal to current # so set the count to 1 else: element[i].count = 1 # Now we have counts and first index for each element # so now sort on the basis of count and in case of tie # use index to sort.*/ element.sort(key=mycomp2) index = 0 for i in range(n - 1, -1, -1): if (element[i].count != -1): for j in range(element[i].count): arr[index] = element[i].val index += 1 # Driver code arr = [2, 5, 2, 6, -1, 9999999, 5, 8, 8, 8] n = len(arr) # Function call sortByFrequency(arr, n) print(*arr) # This code is contributed by phasing17
linear
nlogn
# Python3 program for above approach from collections import defaultdict # Sort by Frequency def sortByFreq(arr, n): # arr -> Array to be sorted # n -> Length of Array # d is a hashmap(referred as dictionary in python) d = defaultdict(lambda: 0) for i in range(n): d[arr[i]] += 1 # Sorting the array 'arr' where key # is the function based on which # the array is sorted # While sorting we want to give # first priority to Frequency # Then to value of item arr.sort(key=lambda x: (-d[x], x)) return (arr) # Driver code if __name__ == "__main__": arr = [2, 5, 2, 6, -1, 9999999, 5, 8, 8, 8] n = len(arr) # Function call solution = sortByFreq(arr, n) print(*solution)
linear
nlogn
# Python3 program to count # inversions in an array def getInvCount(arr, n): inv_count = 0 for i in range(n): for j in range(i + 1, n): if (arr[i] > arr[j]): inv_count += 1 return inv_count # Driver Code arr = [1, 20, 6, 4, 5] n = len(arr) print("Number of inversions are", getInvCount(arr, n)) # This code is contributed by Smitha Dinesh Semwal
constant
quadratic
# Python 3 program to count inversions in an array # Function to Use Inversion Count def mergeSort(arr, n): # A temp_arr is created to store # sorted array in merge function temp_arr = [0]*n return _mergeSort(arr, temp_arr, 0, n-1) # This Function will use MergeSort to count inversions def _mergeSort(arr, temp_arr, left, right): # A variable inv_count is used to store # inversion counts in each recursive call inv_count = 0 # We will make a recursive call if and only if # we have more than one elements if left < right: # mid is calculated to divide the array into two subarrays # Floor division is must in case of python mid = (left + right)//2 # It will calculate inversion # counts in the left subarray inv_count += _mergeSort(arr, temp_arr, left, mid) # It will calculate inversion # counts in right subarray inv_count += _mergeSort(arr, temp_arr, mid + 1, right) # It will merge two subarrays in # a sorted subarray inv_count += merge(arr, temp_arr, left, mid, right) return inv_count # This function will merge two subarrays # in a single sorted subarray def merge(arr, temp_arr, left, mid, right): i = left # Starting index of left subarray j = mid + 1 # Starting index of right subarray k = left # Starting index of to be sorted subarray inv_count = 0 # Conditions are checked to make sure that # i and j don't exceed their # subarray limits. while i <= mid and j <= right: # There will be no inversion if arr[i] <= arr[j] if arr[i] <= arr[j]: temp_arr[k] = arr[i] k += 1 i += 1 else: # Inversion will occur. temp_arr[k] = arr[j] inv_count += (mid-i + 1) k += 1 j += 1 # Copy the remaining elements of left # subarray into temporary array while i <= mid: temp_arr[k] = arr[i] k += 1 i += 1 # Copy the remaining elements of right # subarray into temporary array while j <= right: temp_arr[k] = arr[j] k += 1 j += 1 # Copy the sorted subarray into Original array for loop_var in range(left, right + 1): arr[loop_var] = temp_arr[loop_var] return inv_count # Driver Code # Given array is arr = [1, 20, 6, 4, 5] n = len(arr) result = mergeSort(arr, n) print("Number of inversions are", result) # This code is contributed by ankush_953
linear
nlogn
from heapq import heappush, heappop from bisect import bisect, insort def getNumOfInversions(A): N = len(A) if N <= 1: return 0 sortList = [] result = 0 # Heapsort, O(N*log(N)) for i, v in enumerate(A): heappush(sortList, (v, i)) # Create a sorted list of indexes x = [] while sortList: # O(log(N)) v, i = heappop(sortList) # Find the current minimum's index # the index y can represent how many minimums on the left y = bisect(x, i) # i can represent how many elements on the left # i - y can find how many bigger nums on the left result += i - y insort(x, i) return result # Driver Code if __name__ == '__main__': A = [1, 20, 6, 4, 5] result = getNumOfInversions(A) print(f'Number of inversions are {result}')
linear
nlogn
# Python3 program to find shortest # subarray which is unsorted # Bool function for checking an array # elements are in increasing def increasing(a, n): for i in range(0, n - 1): if (a[i] >= a[i + 1]): return False return True # Bool function for checking an array # elements are in decreasing def decreasing(a, n): for i in range(0, n - 1): if (a[i] < a[i + 1]): return False return True def shortestUnsorted(a, n): # increasing and decreasing are two functions. # if function return True value then print # 0 otherwise 3. if (increasing(a, n) == True or decreasing(a, n) == True): return 0 else: return 3 # Driver code ar = [7, 9, 10, 8, 11] n = len(ar) print(shortestUnsorted(ar, n)) # This code is contributed by Smitha Dinesh Semwal.
constant
linear
# Python3 program to find # minimum number of swaps # required to sort an array # Function returns the minimum # number of swaps required to # sort the array def minSwaps(arr): n = len(arr) # Create two arrays and use # as pairs where first array # is element and second array # is position of first element arrpos = [*enumerate(arr)] # Sort the array by array element # values to get right position of # every element as the elements # of second array. arrpos.sort(key = lambda it : it[1]) # To keep track of visited elements. # Initialize all elements as not # visited or false. vis = {k : False for k in range(n)} # Initialize result ans = 0 for i in range(n): # already swapped or # already present at # correct position if vis[i] or arrpos[i][0] == i: continue # find number of nodes # in this cycle and # add it to ans cycle_size = 0 j = i while not vis[j]: # mark node as visited vis[j] = True # move to next node j = arrpos[j][0] cycle_size += 1 # update answer by adding # current cycle if cycle_size > 0: ans += (cycle_size - 1) # return answer return ans # Driver Code arr = [1, 5, 4, 3, 2] print(minSwaps(arr)) # This code is contributed # by Dharan Aditya
linear
nlogn
# Function returns the # minimum number of swaps # required to sort the array from functools import cmp_to_key def cmp(a, b): return a - b def minSwaps(nums): Len = len(nums) map = {} for i in range(Len): map[nums[i]] = i nums = sorted(nums, key = cmp_to_key(cmp)) # To keep track of visited elements. Initialize # all elements as not visited or false. visited = [False for col in range(Len)] # Initialize result ans = 0 for i in range(Len): # already swapped and corrected or # already present at correct pos if (visited[i] or map[nums[i]] == i): continue j,cycle_size = i, 0 while (visited[j] == False): visited[j] = True # move to next node j = map[nums[j]] cycle_size += 1 # Update answer by adding current cycle. if (cycle_size > 0): ans += (cycle_size - 1) return ans # Driver program to test the above function a = [ 1, 5, 4, 3, 2 ] print(minSwaps(a)) # This code is contributed by shinjanpatra
linear
nlogn
# Python3 program to find #minimum number of swaps # required to sort an array # Return the minimum number # of swaps required to sort # the array def minSwaps(arr, N): ans = 0 temp = arr.copy() temp.sort() for i in range(N): # This is checking whether # the current element is # at the right place or not if (arr[i] != temp[i]): ans += 1 # Swap the current element # with the right index # so that arr[0] to arr[i] # is sorted swap(arr, i, indexOf(arr, temp[i])) return ans def swap(arr, i, j): temp = arr[i] arr[i] = arr[j] arr[j] = temp def indexOf(arr, ele): for i in range(len(arr)): if (arr[i] == ele): return i return -1 # Driver code if __name__ == "__main__": a = [101, 758, 315, 730, 472, 619, 460, 479] n = len(a) # Output will be 5 print(minSwaps(a, n)) # This code is contributed by Chitranayal
linear
quadratic
# Python3 program to find # minimum number of swaps # required to sort an array # Return the minimum number # of swaps required to sort # the array def minSwap(arr, n): ans = 0 temp = arr.copy() # Dictionary which stores the # indexes of the input array h = {} temp.sort() for i in range(n): #h.[arr[i] h[arr[i]] = i init = 0 for i in range(n): # This is checking whether # the current element is # at the right place or not if (arr[i] != temp[i]): ans += 1 init = arr[i] # If not, swap this element # with the index of the # element which should come here arr[i], arr[h[temp[i]]] = arr[h[temp[i]]], arr[i] # Update the indexes in # the hashmap accordingly h[init] = h[temp[i]] h[temp[i]] = i return ans # Driver code a = [ 101, 758, 315, 730, 472, 619, 460, 479 ] n = len(a) # Output will be 5 print(minSwap(a, n)) # This code is contributed by avanitrachhadiya2155
linear
nlogn
# Python program to sort an array with # 0, 1 and 2 in a single pass # Function to sort array def sort012(a, arr_size): lo = 0 hi = arr_size - 1 mid = 0 # Iterate till all the elements # are sorted while mid <= hi: # If the element is 0 if a[mid] == 0: a[lo], a[mid] = a[mid], a[lo] lo = lo + 1 mid = mid + 1 # If the element is 1 elif a[mid] == 1: mid = mid + 1 # If the element is 2 else: a[mid], a[hi] = a[hi], a[mid] hi = hi - 1 return a # Function to print array def printArray(a): for k in a: print(k, end=' ') # Driver Program arr = [0, 1, 1, 0, 1, 2, 1, 2, 0, 0, 0, 1] arr_size = len(arr) arr = sort012(arr, arr_size) printArray(arr) # Contributed by Harshit Agrawal
constant
linear
# Python implementation of the approach # Utility function to print contents of an array def printArr(arr, n): for i in range(n): print(arr[i], end=" ") # Function to sort the array of 0s, 1s and 2s def sortArr(arr, n): cnt0 = 0 cnt1 = 0 cnt2 = 0 # Count the number of 0s, 1s and 2s in the array for i in range(n): if arr[i] == 0: cnt0 += 1 elif arr[i] == 1: cnt1 += 1 elif arr[i] == 2: cnt2 += 1 # Update the array i = 0 # Store all the 0s in the beginning while (cnt0 > 0): arr[i] = 0 i += 1 cnt0 -= 1 # Then all the 1s while (cnt1 > 0): arr[i] = 1 i += 1 cnt1 -= 1 # Finally all the 2s while (cnt2 > 0): arr[i] = 2 i += 1 cnt2 -= 1 # Print the sorted array printArr(arr, n) # Driver code arr = [0, 1, 1, 0, 1, 2, 1, 2, 0, 0, 0, 1] n = len(arr) sortArr(arr, n) # This code is contributed by shubhamsingh10
constant
linear
# Function to find position to insert current element of # stream using binary search def binarySearch(arr, item, low, high): if (low >= high): return (low + 1) if (item > arr[low]) else low mid = (low + high) // 2 if (item == arr[mid]): return mid + 1 if (item > arr[mid]): return binarySearch(arr, item, mid + 1, high) return binarySearch(arr, item, low, mid - 1) # Function to print median of stream of integers def printMedian(arr, n): i, j, pos, num = 0, 0, 0, 0 count = 1 print(f"Median after reading 1 element is {arr[0]}") for i in range(1, n): median = 0 j = i - 1 num = arr[i] # find position to insert current element in sorted # part of array pos = binarySearch(arr, num, 0, j) # move elements to right to create space to insert # the current element while (j >= pos): arr[j + 1] = arr[j] j -= 1 arr[j + 1] = num # increment count of sorted elements in array count += 1 # if odd number of integers are read from stream # then middle element in sorted order is median # else average of middle elements is median if (count % 2 != 0): median = arr[count // 2] else: median = (arr[(count // 2) - 1] + arr[count // 2]) // 2 print(f"Median after reading {i + 1} elements is {median} ") # Driver Code if __name__ == "__main__": arr = [5, 15, 1, 3, 2, 8, 7, 9, 10, 6, 11, 4] n = len(arr) printMedian(arr, n) # This code is contributed by rakeshsahni
constant
quadratic
# Python code to implement the approach from heapq import heappush, heappop, heapify import math # Function to find the median of stream of data def streamMed(arr, N): # Declaring two min heap g = [] s = [] for i in range(len(arr)): # Negation for treating it as max heap heappush(s, -arr[i]) heappush(g, -heappop(s)) if len(g) > len(s): heappush(s, -heappop(g)) if len(g) != len(s): print(-s[0]) else: print((g[0] - s[0])/2) # Driver code if __name__ == '__main__': A = [5, 15, 1, 3, 2, 8, 7, 9, 10, 6, 11, 4] N = len(A) # Function call streamMed(A, N)
linear
nlogn
# Python3 code to count the number of # possible triangles using brute # force approach # Function to count all possible # triangles with arr[] elements def findNumberOfTriangles(arr, n): # Count of triangles count = 0 # The three loops select three # different values from array for i in range(n): for j in range(i + 1, n): # The innermost loop checks for # the triangle property for k in range(j + 1, n): # Sum of two sides is greater # than the third if (arr[i] + arr[j] > arr[k] and arr[i] + arr[k] > arr[j] and arr[k] + arr[j] > arr[i]): count += 1 return count # Driver code if __name__ == "__main__": arr = [10, 21, 22, 100, 101, 200, 300] size = len(arr) # Function call print("Total number of triangles possible is", findNumberOfTriangles(arr, size)) # This code is contributed by shubhamsingh10
constant
cubic
# Python3 function to count all possible triangles with arr[] # elements def findnumberofTriangles(arr): # Sort array and initialize count as 0 n = len(arr) arr.sort() count = 0 # Fix the first element. We need to run till n-3 as # the other two elements are selected from arr[i + 1...n-1] for i in range(0, n-2): # Initialize index of the rightmost third element k = i + 2 # Fix the second element for j in range(i + 1, n): # Find the rightmost element which is smaller # than the sum of two fixed elements # The important thing to note here is, we use # the previous value of k. If value of arr[i] + # arr[j-1] was greater than arr[k], then arr[i] + # arr[j] must be greater than k, because the array # is sorted. while (k < n and arr[i] + arr[j] > arr[k]): k += 1 # Total number of possible triangles that can be # formed with the two fixed elements is k - j - 1. # The two fixed elements are arr[i] and arr[j]. All # elements between arr[j + 1] to arr[k-1] can form a # triangle with arr[i] and arr[j]. One is subtracted # from k because k is incremented one extra in above # while loop. k will always be greater than j. If j # becomes equal to k, then above loop will increment k, # because arr[k] + arr[i] is always greater than arr[k] if(k > j): count += k - j - 1 return count # Driver code if __name__ == "__main__": arr = [10, 21, 22, 100, 101, 200, 300] # Function call print("Total number of Triangles:", findnumberofTriangles(arr)) # This code is contributed by Devesh Agrawal
constant
quadratic
# Python implementation of the above approach def CountTriangles(A): n = len(A) A.sort() count = 0 for i in range(n - 1, 0, -1): l = 0 r = i - 1 while(l < r): if(A[l] + A[r] > A[i]): # If it is possible with a[l], a[r] # and a[i] then it is also possible # with a[l + 1]..a[r-1], a[r] and a[i] count += r - l # checking for more possible solutions r -= 1 else: # if not possible check for # higher values of arr[l] l += 1 print("No of possible solutions: ", count) # Driver Code if __name__ == '__main__': A = [10, 21, 22, 100, 101, 200, 300] # Function call CountTriangles(A) # This code is contributed by PrinciRaj1992
constant
quadratic