LeetCode.419 Arithmetic Slices
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题目:
A sequence of number is called arithmetic if it consists of at least three elements and if the difference between any two consecutive elements is the same.
For example, these are arithmetic sequence:
1, 3, 5, 7, 97, 7, 7, 73, -1, -5, -9
The following sequence is not arithmetic.
1, 1, 2, 5, 7
A zero-indexed array A consisting of N numbers is given. A slice of that array is any pair of integers (P, Q) such that 0 <= P < Q < N.
A slice (P, Q) of array A is called arithmetic if the sequence:
A[P], A[p + 1], ..., A[Q - 1], A[Q] is arithmetic. In particular, this means that P + 1 < Q.
The function should return the number of arithmetic slices in the array A.
Example:
A = [1, 2, 3, 4]return: 3, for 3 arithmetic slices in A: [1, 2, 3], [2, 3, 4] and [1, 2, 3, 4] itself.分析1(原创-易理解):
class Solution { public int numberOfArithmeticSlices(int[] A) { //给定数组,找出其中符合规则的算数子序列(至少三个元素,其中每两个元素之间相差的相同(可以为0,即全部为相同的)),将其切分满足条件的子序列,子序列长度最少3。 //思路:先将大的序列找出来。然后分别从大序列中查找小的序列找出其中规律。例如【1,2,3,4,5,6】 长度为3的:6-(3-1)=4 长度为4:6-(4-1)=3 长度为5:6-(5-1)=2 长度为6 6-(6-1)=1 //结果就是:4+3+2+1=10 //注意:序列串要么递增,要么递减。例如 1,2,3,4,5 或者 3,-1,-5,-9 if(A.length<3) return 0; List<List<Integer>> list=new ArrayList<>(); //求数组中的大序列 int interval=Integer.MAX_VALUE; //默认递增 boolean flag=true; //i的更新在下面for循环中动态更新 for(int i=0;i<A.length-2;){ List<Integer> subList=new ArrayList<>(); subList.add(A[i]); for(int j=i+1;j<A.length;j++){ if(subList.size()==1&&j-i==1){ subList.add(A[j]); interval=A[j]-A[j-1]; }else if(A[j]-A[j-1]==interval){ subList.add(A[j]); //不断更新i的值 i=j; }else if(A[j]-A[j-1]!=interval){ //不相等了,断层 i=j-1; interval=Integer.MAX_VALUE; //跳出 break; } } if(subList.size()>=3){ list.add(subList); } } //求大序列中的子序列 int count = 0; for (List<Integer> in : list) { for (int i = in.size(); i >= 3; i--) { count += in.size() - (i - 1); } } return count; }}
分析2(参考答案):
class Solution { public int numberOfArithmeticSlices(int[] A) { //给定数组,找出其中符合规则的算数子序列(至少三个元素,其中每两个元素之间相差的相同(可以为0,即全部为相同的)),将其切分满足条件的子序列,子序列长度最少3。 //思路:先将大的序列找出来。然后分别从大序列中查找小的序列找出其中规律。例如【1,2,3,4,5,6】 长度为3的:6-(3-1)=4 长度为4:6-(4-1)=3 长度为5:6-(5-1)=2 长度为6 6-(6-1)=1 //结果就是:4+3+2+1=10 //注意:序列串要么递增,要么递减。例如 1,2,3,4,5 或者 3,-1,-5,-9 if(A.length==0||A==null) return 0; int count=0; int cur=0; for(int i=2;i<A.length;i++){ if(A[i]-A[i-1]==A[i-1]-A[i-2]){ cur++; count+=cur; }else{ //将cur置为0 cur=0; } } return count; }}
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