Backtracking Algorithm (aka Heuristic Algorithm)
In order to find a solution to the problem, first select a certain possible situation for testing. In the process of testing, once the assumption of the original choice is found to be wrong, it will take a step back and re-select, continue to test forward, and so on until the get a solution or prove no solution.
Example: Generate lottery number combination.
Suppose there is a lottery, each bet consists of 7 numbers 1-29, and these 7 numbers cannot be the same, write a program to generate all combinations of numbers.
Java code description:
public class Test {
public static int MAXN = 7; //Set the number of digits for each group of lottery tickets
public static int NUM = 29; //Set the numbers that make up the lottery ticket
public static int[] num = new int[NUM];
public static int[] lottery = new int[MAXN];
public static void main(String[] args) {
int i,j;
for(i=0;i<NUM;i++){ //Set the lottery numbers
num[i] = i+1;
}
for(j=0;j<MAXN;j++){
lottery[j] = 0;
}
combine(NUM,MAXN);
}
public static void combine(int n,int m){
int i,j;
for(i=n;i>=m;i--){
lottery[m-1] = num[i-1]; //save a digit
if(m>1){
combine(i-1,m-1);
}else{ //If m=1, output a bet number
for(j = MAXN -1;j>=0;j--){
System.out.print(lottery[j]+" ");
}
System.out.println();
}
}
}
}
operation result:
After the above program is finished, all possible points will be listed. This scenario can also be achieved by exhaustiveness.