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Check if i * 5 <= n | if ( i * 5 <= n ) : NEW_LINE INDENT dp [ i * 5 ] = min ( dp [ i * 5 ] , dp [ i ] + 1 ) NEW_LINE DEDENT |
Check if i + 3 <= n | if ( i + 3 <= n ) : NEW_LINE INDENT dp [ i + 3 ] = min ( dp [ i + 3 ] , dp [ i ] + 1 ) NEW_LINE DEDENT |
Return the result | return dp [ n ] NEW_LINE |
Driver code | if __name__ == ' _ _ main _ _ ' : NEW_LINE |
Given Input | n = 28 NEW_LINE |
Function Call | m = findMinOperations ( n ) NEW_LINE |
Print the result | if ( m != 9999 ) : NEW_LINE INDENT print ( m ) NEW_LINE DEDENT else : NEW_LINE INDENT print ( - 1 ) NEW_LINE DEDENT |
Function to find maximum sum of difference between maximums and minimums in the splitted subarrays | def getValue ( arr , N ) : NEW_LINE INDENT dp = [ 0 for i in range ( N ) ] NEW_LINE DEDENT |
Traverse the array | for i in range ( 1 , N ) : NEW_LINE |
Stores the maximum and minimum elements upto the i - th index | minn = arr [ i ] NEW_LINE maxx = arr [ i ] NEW_LINE j = i NEW_LINE |
Traverse the range [ 0 , i ] | while ( j >= 0 ) : NEW_LINE |
Update the minimum | minn = min ( arr [ j ] , minn ) NEW_LINE |
Update the maximum | maxx = max ( arr [ j ] , maxx ) NEW_LINE |
Update dp [ i ] | dp [ i ] = max ( dp [ i ] , maxx - minn + ( dp [ j - 1 ] if ( j >= 1 ) else 0 ) ) NEW_LINE j -= 1 NEW_LINE |
Return the maximum sum of difference | return dp [ N - 1 ] NEW_LINE |
Driver code | if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT arr = [ 8 , 1 , 7 , 9 , 2 ] NEW_LINE N = len ( arr ) NEW_LINE print ( getValue ( arr , N ) ) NEW_LINE DEDENT |
Function to count 0 's in a string | def count0 ( s ) : NEW_LINE |
Stores count of 0 s | count = 0 NEW_LINE |
Iterate over characters of string | for i in range ( len ( s ) ) : NEW_LINE |
Recursive function to find the length of longest subset from an array of strings with at most A 0 ' s ▁ and ▁ B ▁ 1' s | def solve ( vec , A , B , idx ) : NEW_LINE |
If idx is equal to N or A + B is equal to 0 | if ( idx == len ( vec ) or A + B == 0 ) : NEW_LINE INDENT return 0 NEW_LINE DEDENT |
Stores the count of 0 's in arr[idx] | zero = count0 ( vec [ idx ] ) NEW_LINE |
Stores the count of 1 's in arr[idx] | one = len ( vec [ idx ] ) - zero NEW_LINE |
Stores the length of the subset if arr [ i ] is included | inc = 0 NEW_LINE |
If zero is less than or equal to A and one is less than or equal to B | if ( zero <= A and one <= B ) : NEW_LINE INDENT inc = 1 + solve ( vec , A - zero , B - one , idx + 1 ) NEW_LINE DEDENT |
Stores the length of the subset if arr [ i ] is excluded | exc = solve ( vec , A , B , idx + 1 ) NEW_LINE |
Returns max of inc and exc | return max ( inc , exc ) NEW_LINE |
Function to find the length of the longest subset from an array of strings with at most A 0 ' s ▁ and ▁ B ▁ 1' s | def MaxSubsetlength ( arr , A , B ) : NEW_LINE |
Return | return solve ( arr , A , B , 0 ) NEW_LINE |
Driver Code | if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT arr = [ "1" , "0" , "10" ] NEW_LINE A = 1 NEW_LINE B = 1 NEW_LINE print ( MaxSubsetlength ( arr , A , B ) ) NEW_LINE DEDENT |
Function to check if the string s consists of a single distinct character or not | def isUnique ( s ) : NEW_LINE INDENT return True if len ( set ( s ) ) == 1 else False NEW_LINE DEDENT |
Function to calculate the maximum score possible by removing substrings | def maxScore ( s , a ) : NEW_LINE INDENT n = len ( s ) NEW_LINE DEDENT |
If string is empty | if n == 0 : NEW_LINE INDENT return 0 NEW_LINE DEDENT |
If length of string is 1 | if n == 1 : NEW_LINE INDENT return a [ 0 ] NEW_LINE DEDENT |
Store the maximum result | mx = - 1 NEW_LINE |
Try to remove all substrings that satisfy the condition and check for resultant string after removal | for i in range ( n ) : NEW_LINE INDENT for j in range ( i , n ) : NEW_LINE DEDENT |
Store the substring { s [ i ] , . . , s [ j ] } | sub = s [ i : j + 1 ] NEW_LINE |
Check if the substring contains only a single distinct character | if isUnique ( sub ) : NEW_LINE INDENT mx = max ( mx , a [ len ( sub ) - 1 ] + maxScore ( s [ : i ] + s [ j + 1 : ] , a ) ) NEW_LINE DEDENT |
Return the maximum score | return mx NEW_LINE |
Driver Code | if __name__ == " _ _ main _ _ " : NEW_LINE INDENT s = "011" NEW_LINE a = [ 1 , 3 , 1 ] NEW_LINE print ( maxScore ( s , a ) ) NEW_LINE DEDENT |
Initialize a dictionary to store the precomputed results | dp = dict ( ) NEW_LINE |
Function to calculate the maximum score possible by removing substrings | def maxScore ( s , a ) : NEW_LINE |
If s is present in dp [ ] array | if s in dp : NEW_LINE INDENT return dp [ s ] NEW_LINE DEDENT |
Base Cases : | n = len ( s ) NEW_LINE |
If length of string is 0 | if n == 0 : NEW_LINE INDENT return 0 NEW_LINE DEDENT |
If length of string is 1 | if n == 1 : NEW_LINE INDENT return a [ 0 ] NEW_LINE DEDENT |
Put head pointer at start | head = 0 NEW_LINE |
Initialize the max variable | mx = - 1 NEW_LINE |
Generate the substrings using two pointers | while head < n : NEW_LINE INDENT tail = head NEW_LINE while tail < n : NEW_LINE DEDENT |
If s [ head ] and s [ tail ] are different | if s [ tail ] != s [ head ] : NEW_LINE |
Move head to tail and break | head = tail NEW_LINE break NEW_LINE |
Store the substring | sub = s [ head : tail + 1 ] NEW_LINE |
Update the maximum | mx = max ( mx , a [ len ( sub ) - 1 ] + maxScore ( s [ : head ] + s [ tail + 1 : ] , a ) ) NEW_LINE |
Move the tail | tail += 1 NEW_LINE if tail == n : NEW_LINE break NEW_LINE |
Store the score | dp [ s ] = mx NEW_LINE return mx NEW_LINE |
Driver Code | if __name__ == " _ _ main _ _ " : NEW_LINE INDENT s = " abb " NEW_LINE a = [ 1 , 3 , 1 ] NEW_LINE print ( maxScore ( s , a ) ) NEW_LINE DEDENT |
Dimensions of the DP table | size = 100 NEW_LINE |
Stores the dp states | ans = [ [ 0 for i in range ( size ) ] for j in range ( size ) ] NEW_LINE |
Function to recursively count the number of unique outcomes possible by performing S flips on N coins | def numberOfUniqueOutcomes ( n , s ) : NEW_LINE |
Base Case | if ( s < n ) : NEW_LINE INDENT ans [ n ] [ s ] = 0 ; NEW_LINE DEDENT elif ( n == 1 or n == s ) : NEW_LINE INDENT ans [ n ] [ s ] = 1 ; NEW_LINE DEDENT |
If the count for the current state is not calculated , then calculate it recursively | elif ( ans [ n ] [ s ] == 0 ) : NEW_LINE INDENT ans [ n ] [ s ] = ( numberOfUniqueOutcomes ( n - 1 , s - 1 ) + numberOfUniqueOutcomes ( n - 1 , s - 2 ) ) NEW_LINE DEDENT |
Otherwise return the already calculated value | return ans [ n ] [ s ] ; NEW_LINE |
Driver Code | N = 5 NEW_LINE S = 8 NEW_LINE print ( numberOfUniqueOutcomes ( N , S ) ) NEW_LINE |
Function to print the minimum number of character removals required to remove X as a subsequence from the string str | def printMinimumRemovals ( s , X ) : NEW_LINE |
Length of the string str | N = len ( s ) NEW_LINE |
Length of the string X | M = len ( X ) NEW_LINE |
Stores the dp states | dp = [ [ 0 for x in range ( M ) ] for y in range ( N ) ] NEW_LINE |
Fill first row of dp [ ] [ ] | for j in range ( M ) : NEW_LINE |
If X [ j ] matches with str [ 0 ] | if ( s [ 0 ] == X [ j ] ) : NEW_LINE INDENT dp [ 0 ] [ j ] = 1 NEW_LINE DEDENT for i in range ( 1 , N ) : NEW_LINE for j in range ( M ) : NEW_LINE |
If s [ i ] is equal to X [ j ] | if ( s [ i ] == X [ j ] ) : NEW_LINE |
Update state after removing str [ i [ | dp [ i ] [ j ] = dp [ i - 1 ] [ j ] + 1 NEW_LINE |
Update state after keeping str [ i ] | if ( j != 0 ) : NEW_LINE INDENT dp [ i ] [ j ] = min ( dp [ i ] [ j ] , dp [ i - 1 ] [ j - 1 ] ) NEW_LINE DEDENT |
If str [ i ] is not equal to X [ j ] | else : NEW_LINE INDENT dp [ i ] [ j ] = dp [ i - 1 ] [ j ] NEW_LINE DEDENT |
Print the minimum number of characters removals | print ( dp [ N - 1 ] [ M - 1 ] ) NEW_LINE |
Driver Code | if __name__ == " _ _ main _ _ " : NEW_LINE |
Input | s = " btagd " NEW_LINE X = " bad " NEW_LINE |
Function call to get minimum number of character removals | printMinimumRemovals ( s , X ) NEW_LINE |
Dp table for memoization | dp = [ - 1 for i in range ( 100000 ) ] NEW_LINE |
Function to count the number of ways to N - th station | def findWays ( x ) : NEW_LINE |
Base Cases | if ( x < 0 ) : NEW_LINE INDENT return 0 NEW_LINE DEDENT if ( x == 0 ) : NEW_LINE INDENT return 1 NEW_LINE DEDENT if ( x == 1 ) : NEW_LINE INDENT return 2 NEW_LINE DEDENT if ( x == 2 ) : NEW_LINE INDENT return 4 NEW_LINE DEDENT |
If current state is already evaluated | if ( dp [ x ] != - 1 ) : NEW_LINE INDENT return dp [ x ] NEW_LINE DEDENT |
Count ways in which train 1 can be chosen | count = findWays ( x - 1 ) NEW_LINE |
Count ways in which train 2 can be chosen | count += findWays ( x - 2 ) NEW_LINE |
Count ways in which train 3 can be chosen | count += findWays ( x - 3 ) NEW_LINE |
Store the current state | dp [ x ] = count NEW_LINE |
Return the number of ways | return dp [ x ] NEW_LINE |
Driver Code | if __name__ == ' _ _ main _ _ ' : NEW_LINE |
Given Input | n = 4 NEW_LINE |
Function call to count the number of ways to reach the n - th station | print ( findWays ( n ) ) NEW_LINE |
Python3 program for the above approach | from bisect import bisect_left , bisect_right NEW_LINE import sys NEW_LINE |
Function to find the maximum possible sum of arectangle which is less than K | def maxSubarraySum ( sum , k , row ) : NEW_LINE INDENT curSum , curMax = 0 , - sys . maxsize - 1 NEW_LINE DEDENT |
Stores the values ( cum_sum - K ) | sumSet = { } NEW_LINE |
Insert 0 into the set sumSet | sumSet [ 0 ] = 1 NEW_LINE |
Traverse over the rows | for r in range ( row ) : NEW_LINE |
Get cumulative sum from [ 0 to i ] | curSum += sum [ r ] NEW_LINE |
Search for upperbound of ( cSum - K ) in the hashmap | arr = list ( sumSet . keys ( ) ) NEW_LINE it = bisect_left ( arr , curSum - k ) NEW_LINE |
If upper_bound of ( cSum - K ) exists , then update max sum | if ( it != len ( arr ) ) : NEW_LINE INDENT curMax = max ( curMax , curSum - it ) NEW_LINE DEDENT |
Insert cummulative value in the hashmap | sumSet [ curSum ] = 1 NEW_LINE |
Return the maximum sum which is less than K | return curMax NEW_LINE |
Function to find the maximum sum of rectangle such that its sum is no larger than K | def maxSumSubmatrix ( matrix , k ) : NEW_LINE |
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