Mathematical properties of stack and queue stack of algorithm exercises---

One: The mathematical nature of the stack

When n numbered elements are stacked in a certain order, and can be stacked at any time, the number of numbers ordered by the number of elements n is exactly the sum of the Catalan functions, i.e.

Two: Topic One:

Try to put 1,2,3,4,5,6, six digits into the stack, then there are several ways out of the stack? The use of mathematical properties can be known to have 132

III: Other topics: Judging the legality of the sequence of operations given by the stack

I into the stack o out of the stack, such as ABC into the stack, out of the stack for the CBA, then the given sequence is Iiiooo, indicating 3 first into the stack, and then out of the stack

Now given a sequence (with IO only) to determine whether it is legitimate

Four: Nature

1. Same number of IO

2. Start to middle any position I number is greater than O number

Five: Implementation code

intJudgeCharch[]) {    intInp out; inti; INP= out= i =0;  while(Ch[i]! =' /')    {        if(Ch[i] = ='O')             out++; ElseINP++; if( out>INP)return 0; I++; }    if(INP! = out)        return 0; return 1;}

Mathematical properties of stack and queue stack of algorithm exercises---