enumeration algorithm

enumeration (exhaustive) method

 

The essence of the enumeration method is to search for the correct solution from all the candidate answers. The use of this algorithm needs to meet two conditions:

(1): The number of candidate answers can be predetermined;

(2): The range of candidate answers must have a definite set before solving.

 

Example 1: Fill in the numbers game.

 

 Java code description:

public static void main(String[] args) {

		int multi = 1;
		int result = 0;
		int i1, i2, i3, i4, i5;
		for (i1 = 1; i1 <= 9; i1++) {
			for (i2 = 0; i2 <= 9; i2++) {
				for (i3 = 0; i3 <= 9; i3++) {
					for (i4 = 0; i4 <= 9; i4++) {
						for (i5 = 0; i5 <= 9; i5++) {
							multi = i1 * 10000 + i2 * 1000 + i3 * 100 + i4 * 10 + i5;
							result = i5 * 100000 + i5 * 10000 + i5 * 1000 + i5 * 100 + i5 * 10 + i5;
							if (multi * i1 == result) {
								System.out.println(i1 + " " + i2 + " " + i3 + " " + i4 + " " + i5);
								System.out.println("        " + i1);
								System.out.println("-----------------");
								System.out.println(i5 + " " + i5 + " " + i5 + " " + i5 + " " + i5);
								break;
							}
						}
					}
				}
			}
		}

	}

 

 operation result:


 

Example 2: Fill operator:

 

Java code description:

	private static void tysf() {
		int[] i = new int[5];// Array i is used to represent 4 operators
		int j; // loop variable
		int sign; // sign when accumulating
		int result = 0; // save the result value of the expression
		int count = 0; // counter, count the eligible schemes
		int[] num = new int[6]; // save operand
		float left, right; // save intermediate results
		char[] oper = { ' ', '+', '-', '*', '/' }; // operator
		System.out.println("Please enter five numbers");
		Scanner sc = new Scanner(System.in);
		for (int ii = 1; ii <num.length; ii ++) {
			num[ii] = sc.nextInt();
		}
		System.out.println("Please enter the result");
		result = sc.nextInt();
		// for (i[0] = 1; i[0] < 4; i[0]++) { //fill operator in loop 4, 1 means +, 2 means -, 3 means *, 4 means /
		// if ((i[0] < 4) || (num[1] != 0)) { //If the operator is /, the second operand cannot be 0
		for (i[1] = 1; i[1] <= 4; i[1]++) {
			if ((i[1] < 4) || (num[2] != 0)) {
				for (i[2] = 1; i[2] <= 4; i[2]++) {
					if ((i[2] < 4) || (num[3] != 0)) {
						for (i[3] = 1; i[3] <= 4; i[3]++) {
							if ((i[3] < 4) || (num[4] != 0)) {
								for (i[4] = 1; i[4] <= 4; i[4]++) {
									if ((i[4] < 4) || (num[5] != 0)) {
										left = 0;
										right = num[1];
										sign = 1;
										for (j = 1; j <= 4; j++) {
											switch (oper[i[j]]) {
											case '+':
												left = left + sign * right;
												sign = 1;
												right = num[j + 1];
												break;
											case '-':
												left = left + sign * right;
												sign = -1; // subtraction by sign=-1
												right = num[j + 1];
												break;
											case '*':
												right = right * num[j + 1]; // implement multiplication
												break;
											case '/':
												right = right / num[j + 1]; // implement division
												break;
											}
										}
										if (left + sign * right == result) {
											count++;
											System.out.print(count + "  ");
											for (j = 1; j <= 4; j++) {
												System.out.print(num[j] + "" + oper[i[j]]);
											}
											System.out.println("=" + result);
										}
									}
								}
							}
						}
					}
				}
			}
		}
		if (count == 0) {
			System.out.println("No matches");
		}
	}

 operation result: