Initial knowledge algorithm

Algorithm one: Recursion

One: Concept

The core is to use the existing information to deduce the new things by using the known condition, gradually recursion by the specific relation and finally getting the result.

II: Classification

Of course, there are two kinds of recursion, "push forward" and "reverse push"

Push: Results from the condition.

Inverse push: The conditions are introduced from the results.

Three: examples

<1> examples of shun-push

The university should know the famous "Fibonacci" series, that is, the problem of breeding rabbits, the topic I will probably say.

If 1 pairs of rabbits can have 1 pairs of rabbits a month, and each pair of rabbits in its 3rd month after birth can have 1 pairs of rabbits, if starting from 1 pairs of newborn rabbits, 1 years later can

How many rabbits are bred?

Idea: Actually this question we can divide the rabbit into "January big Rabbit", "February Big Rabbit", "March Big Rabbit".

① initial: A pair of January-size rabbits with a total of 1 pairs.

② First Month: January The Big Rabbit became the February Big Rabbit, the total is still 1 pairs.

③ Second Month: February The Big Rabbit became the March Big Rabbit, bred a pair of small rabbits, the total is 2 pairs.

④ Third Month: March the big Rabbit TMD had a pair of rabbits, last month the Big Rabbit became February Big Rabbit, the total is 3 pairs.

......                    ......

F0=1

F1=1

F2=f0+f1

F3=f1+f2

......

Fn=fn-2+fn-1

You see, is not the embodiment of the "recursive" core idea, the code is very simple.

1             int month = 12;

3             int[] fab = new Int[month];

5             fab[0] = 1;

7             Fab[1] = 1;

9             //Launch results from known conditions
Ten for             (int i = 2; i < month; i++)
Each             {
                 Fab[i] = fab[i-1] + fab[i-2];
-             }

             (int i = 0; i < month; i++)
+             {
                 Console.WriteLine ("{0} months Rabbit: {1}", I, fab[i]);
(+             }

<2> examples of Inverse push

This is a question about saving money, a rich second generation to his son's four years of college life to save a sum, rich generation can only take 3k per month as the next month's living expenses, the use of the whole deposit 0 to take the way,

Annual interest rate at 1.71%, ask rich second generation need to deposit how much money.

Train of thought: This topic is we know the result, need to reverse push condition, 48th month rich three generations to even this belt to take the 3k a take away, then

The 47th month Deposit shall be: (Deposit of the 48th month +3000)/(1+0.0171/12 (month));

The 46th month deposit shall be: (Deposit of the 47th month +3000)/(1+0.0171/12 (month));

.....                    .....

The 1th month deposit shall be: (Deposit of the 2nd month +3000)/(1+0.0171/12 (month));

1   //Bank Withdraw Money question
2             double[] month = new double[49];

4///The             last one months of the linked interest is 3000
5             month[48] = 3000;

7             Double rate = 0.0171;

9             //Reverse push
Ten for             (int i = i--; i > 0;)
Each             {
                 Month[i] = (month[i + 1] + month[48])/(1 + RATE/12);
-             }

             (int i = i--; i > 0;)
+             {
                 Console.WriteLine ("{0} month end Benli total: {1}", I, month[i]);
(+             }

Initial knowledge algorithm