[Solved] Algorithm Homework8- Find Root

Find the root for the equation:Where x is a real number in [0,1] (i.e., 0 ≤ x ≤ 1)InputInput consists of a single test case. The test case consists of 6 integers in a single line: a, b, c, d, e and f (where 0 ≤ a, c ≤20, −20 ≤ b, d, e ≤ 0, and -10^9 ≤ f ≤ 10^9).OutputThe output should be a single line containing the value x of the root for the above equation, correct up to 4 decimal places(there should be exactly 4 digits after the decimal point), or the string ‘No solution’, whichever is applicable.You can assume that there will be only one root in [0,1] if it exists.Example 1Input:0 0 0 0 1 -1Output:1.0000Example 2Input:0 0 0 0 1 0Output:0.0000Example 3Input:1 0 0 0 0 1Output:No solutionPage 1/1Kou SortKou just finished her first algorithm class and designed a new sorting algorithm: given an array of N distinct numbers, thealgorithm sorts them in ascending order by performing the minimum number of swaps required. A swap is an exchange oftwo adjacent elements in the array.For example, if the array is [9, 1, 0, 5, 4], the smallest number of required swaps to produce the array [0, 1, 4, 5, 9] is 6.0: [9, 1, 0, 5, 4] (original array)1: [1, 9, 0, 5, 4] (swap 1)2: [1, 0, 9, 5, 4]3: [1, 0, 5, 9, 5]4: [1, 0, 5, 4, 9]5: [0, 1, 5, 4, 5]6: [0, 1, 4, 5, 9] (swap 6)(Note that there may be other sequences of swaps that lead to the minimum number of swaps.)Now Kou wants to determine if her algorithm always performs as she claims it does. Given an array of N distinct integers,your task is to figure out the minimum number of swaps required to sort it. Kou will then make sure that her algorithmperforms exactly that number of swaps.InputThe first line of the input contains a single integer N (1 <= N <= 500,000), the size of that array. The following N linesrepresent the content of the input array. Each of these N lines contains a single integer between 0 and 999,999,999. It isguaranteed that the array contains no duplicates.OutputYou should print one line containing a single integer: the minimum number of swaps required to sort the given array.Example 1Input:591054Output:6Example 2Input:3123Output:0Page 1/1Load BalanceYou are an operator of a super computing center and in control of M nodes. One day, a research institute from LightKingdom submitted N computational tasks. Given the computational power needed for each task, you are to distribute thetasks among the available nodes. Restriction: every node can process up to two tasks. You also want to distribute theworkload as evenly as possible, i.e. minimize the following imbalance valuewhere Avg is average load per node and Loadiis the load of the i-th node.InputThe first line of the input contains two integers M (1 <= M <= 5) and N (1 <= N <= 2M), indicating the number of nodes youcontrol and the number of tasks, respectively.The second line contains N integers, each of which represents the computational power required for a task. Numbers onthese line are between 1 and 1000.OutputPrint one line IMBALANCE = I where I is the minimum imbalance value rounded to 5 decimal places.Example 1Input:2 36 3 8Output:IMBALANCE = 1.00000Example 2Input:3 551 19 27 14 33Output:IMBALANCE = 6.00000Example 3Input:5 91 2 3 5 7 11 13 17 19Output:IMBALANCE = 11.60000Page 1/1Nucleic AcidsFor a string S of length N, we can define inversion as follows: If for an integer pair (i,j), we have 0 ≤ i < j < N, and S[i]>S[j],then (i,j) is a inversion for S.Define a function Count(S), which returns the number of distinct inversions in S.For example, Count(“ABC”) = 0 since “ABC” is sorted, and Count(“DAABEC”) = 5, since D is greater than four letters to itsright and E is greater than one letter to its right.You are responsible for cataloging a sequence of nucleic acid strings, which are strings containing only the four letters A, C,G, and T. The Count(S) is a measure of “unsortedness” for S. You want to catalog them in order of “unsortedness”, from“most sorted” to “least sorted”. All the strings are of the same length.InputThe first line contains 2 integers: a positvie n (0 < n ≤ 50) giving the length of all strings, and a positive integer m (0 < m ≤100) giving the number of strings, These are followed by m lines, each containing a string of length n.OutputOutput m lines, the list of input strings, arranged from “most sorted” to “least sorted”. If two or more strings are equallysorted, list them in the same order they are in the input file.Example 1Input:6 3GATCAGACCCTTAAAAAAOutput:ACCCTTAAAAAAGATCAGPage 1/1Party FeeSaya just graduated from her high school! She and her classmates rented a ballroom and held a party to celebrate theirgraduation. They realized that the room fee was not split evenly since some of them did not bring enough money. Aftergoing home, they decided to re-split the fee. However, the payment app they use only allows transfers between friends. Asa kind person, you want to help them out.You will be given information about how much money each of them owes or is owed and whom the friends are. Your task isto figure out if it is possible for them to redistribute the party fee evenly.InputThe first line of the input contains two integers N (2 <= N <= 10,000) and M (0 <= M <= 50,000), representing the number ofstudents and the number of friendships, respectively.Each of the following N lines contains a single integer d (-10,000 <= d <= 10,000), indicating how much that student owes (ifd > 0) or is owed (if d < 0). The student had already paid the right amount of the party fee if d is 0. It is guaranteed that sumof all d’s is 0.The following M lines describe friendships. Each of these M lines contains two integers a and b (0 <= a < b < N), meaningthat the a-th and the b-th student are friends. Note that a friendship may appear more than once and it is also possible thatsomeone is friends with themselves.OutputYou should print one line containing POSSIBLE or IMPOSSIBLE , indicating if it is possible for them to redistribute theparty fee only by sending money to their friends.Example 1Input:5 3100-75-25-42420 11 23 4Output:POSSIBLEExample 2Input:4 21520-10-250 21 3Output:IMPOSSIBL