我們可以用2*1的小矩形橫着或者豎着去覆蓋更大的矩形。請問用n個2*1的小矩形無重疊地覆蓋一個2*n的大矩形,總共有多少種方法?
分析:
解題思路:歸納法(列舉出n=1,2,3,4,5 總結規律)
得到:
f(1)=1
f(2)=2
f(3)=3
f(4)=5
f(5)=8
即:n>2時,f(n)=f(n-1) + f(n-2)
代碼1:使用遞歸
public class Solution {
public int RectCover(int target) {
if(target == 1){
return 1;
}else if(target == 2){
return 2;
}else{
return RectCover(target - 1) + RectCover(target - 2);
}
}
public static void main(String[] args) {
Solution s = new Solution();
System.out.println(s.RectCover(5));
}
}
代碼2
public class Solution1 {
public int RectCover(int target) {
int one = 1;
int two = 2;
if(target == 1){
return 1;
}
if(target == 2){
return 2;
}
int result = 0;
for(int i = 3;i <= target;i++){
result = one + two;
one = two;
two = result;
}
return result;
}
public static void main(String[] args) {
Solution1 s = new Solution1();
System.out.println(s.RectCover(5));
}
}