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Lesson4_2.java
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49 lines (36 loc) · 1.22 KB
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class Result {
public long wheatNum = 0;
public long wheatTotalNum = 0;
}
public class Lesson4_2 {
/**
* @Description: 使用函数的递归（嵌套）调用，进行归纳法证明
* @param k-放到第几格，result-保存当前格子的麦粒数和麦粒总数
* @return boolean-放到第k格时是否成立
*/
public static boolean prove(int k, Result result) {
// 证明n = 1时，命题是否成立
if (k == 1) {
if ((Math.pow(2, 1) - 1) == 1) {
result.wheatNum = 1;
result.wheatTotalNum = 1;
return true;
} else return false;
}
// 如果n = (k-1)时命题成立，证明n = k时命题是否成立
else {
boolean proveOfPreviousOne = prove(k - 1, result);
result.wheatNum *= 2;
result.wheatTotalNum += result.wheatNum;
boolean proveOfCurrentOne = false;
if (result.wheatTotalNum == (Math.pow(2, k) - 1)) proveOfCurrentOne = true;
if (proveOfPreviousOne && proveOfCurrentOne) return true;
else return false;
}
}
public static void main(String[] args) {
int grid = 63;
Result result = new Result();
System.out.println(Lesson4_2.prove(grid, result));
}
}