Example 10 where the optimality principle does not hold

The principle of optimality refers to the fact that "the optimal decision sequence of the multi-stage decision-making process has the property that for a certain state caused by the previous decision, the decision sequence of the subsequent stages must constitute the optimal strategy, regardless of the initial state and the initial decision", and this optimality principle is the basis of dynamic programming. Therefore, the optimality principle is true, and there is no example where the optimality principle does not exist.

This important principle is conceptually easy to understand and means that if the optimal route from to (as shown in the figure below) is given, then the route from any point on the optimal route must be the optimal route from to.

If the route arc ab + arc b c is the optimal route to, then the optimality principle shows that arc b c must be the optimal route from to, which can be proved by the counterproof method.

If there is another route, the arc bic is the optimal route that has less cost than the arc bc. Then the optimal route along the arc AB+ arc BIC has a lower cost than the arc AB+arc B C. But this conclusion happens to contradict the assumption that the route arc ab + arc b c is the optimal route (i.e., the least costly) to which it is to, and this contradiction shows that there is no less expensive route than from to along arc b c.

In other words, the route arc AB+arc B C is the optimal route to which it is reached.

Your mistake lies in absolutizing the theory of probability, indeed, when n is big enough, it is n 2 times a day to lose and win, but the regularity of this probability is an approximation, not absolute equality, you should remember that when you are learning probability, the example of the coin given in the book, the positive and negative trees given in the book are close to equal, still 100 times there are 49 positive and 51 negative and still 10000 times 4980 times positive and 5020 times negative all show that the probability of positive and negative is 1 2, 1 2 This ratio is an approximation, A limit, and from time to time it is said that the actual still coin must be half open.

Your question is the same, although the ideal probability of everyone winning is N times a day, but for a certain day, A wins and B wins, which is still a reflection of this ideal probability, but in absolute terms, it is definitely B who wins on this day. Therefore, the two discussions are not contradictory.

Multi-segment diagram problem: The path and change path are multiplied and negative numbers are allowed.

Multi-segment diagram problem: There are negative paths, and the absolute value of the sum of the path weights is required to be minimized.

The optimal strategy as the whole process has the property that regardless of the past state and decision, the remaining decisions of the ridge rise must constitute the optimal sub-strategy for the state formed by the previous decision. That is, any of the rear sub-strategies of an optimal strategy is always optimal.

This is Sakura dynamic planning.

The principle of optimality of the laughing state.

This is an example of DP introductory question, the number pyramid

If you don't understand, you can ask, hope!

It depends on whether your objective function is the largest or the smallest, the maximum is that the test number must be less than or equal to 0, and the smallest test number is greater than or equal to 0

(1) Theoretical basis of the principle of material recycling: the significance of material recycling: it can avoid environmental pollution and its impact on the stability and development of the system.

2) Theoretical basis of the principle of species diversity: the stability of the resistance of the ecosystem Significance: The degree of biodiversity can improve the stability of the resistance of the system and improve the productivity of the system.

3) Theoretical basis of the principle of coordination and equilibrium: the coordination and equilibrium of organisms and the environment significance: the number of organisms does not exceed the carrying capacity of the environment, which can avoid the imbalance and destruction of the system.

4) Theoretical basis of the principle of holism: the significance of the social-economic-natural composite system: the unity and coordination of various relationships to ensure the balance and stability of the system.

5) Principles of Systematics and EngineeringTheoretical basis: The structure of the system determines the functional principle:

Distributed is superior to centralized and ring meaning: improve and optimize the structure of the system to improve the function bTheoretical basis:

The principle of system integrity: the whole is greater than the part Significance: Maintain the high productivity of the system.

<> columns and columns are separated by large distances, and rows are separated by rows, the optimal result of clustering into three classes should be one for each column, and the intra-class variance is minimal.

However, if the initial points are selected as the middle three points, the clustering result becomes a category for each behavior, which is obviously the local optimum, not the global optimum.

PS: From someone else's literature.