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The following is a dynamic programming implementation (with Python 3) which uses a matrix to keep track of the optimal solutions to sub-problems, and returns the minimum number of coins, or "Infinity" if there is no way to make change with the coins given. A second matrix may be used to obtain the set of coins for the optimal solution.
In a uniformly-random instance of the stable marriage problem with n men and n women, the average number of stable matchings is asymptotically . [6] In a stable marriage instance chosen to maximize the number of different stable matchings, this number is an exponential function of n . [ 7 ]
Hence, the number of steps is O(log m), where m is the number of edges. This is bounded by ( ()). A worst-case graph, in which the average number of steps is ( ()), is a graph made of n/2 connected components, each with 2 nodes. The degree of all nodes is 1, so each node is selected with probability 1/2, and with probability 1/4 both ...
Integer overflow can be demonstrated through an odometer overflowing, a mechanical version of the phenomenon. All digits are set to the maximum 9 and the next increment of the white digit causes a cascade of carry-over additions setting all digits to 0, but there is no higher digit (1,000,000s digit) to change to a 1, so the counter resets to zero.
In the maximum resource bin packing problem, [51] the goal is to maximize the number of bins used, such that, for some ordering of the bins, no item in a later bin fits in an earlier bin. In a dual problem, the number of bins is fixed, and the goal is to minimize the total number or the total size of items placed into the bins, such that no ...
The clique number ω(G) is the number of vertices in a maximum clique of G. [1] Several closely related clique-finding problems have been studied. [14] In the maximum clique problem, the input is an undirected graph, and the output is a maximum clique in the graph. If there are multiple maximum cliques, one of them may be chosen arbitrarily. [14]
The number of moves required by this solution is 2 n − 1. If the objective is to maximize the number of moves (without cycling) then the dynamic programming functional equation is slightly more complicated and 3 n − 1 moves are required. [13]
The problem is to select the maximum number of activities that can be performed by a single person or machine, assuming that a person can only work on a single activity at a time. The activity selection problem is also known as the Interval scheduling maximization problem (ISMP) , which is a special type of the more general Interval Scheduling ...