LeetCode---Arithmetic Slices、Partition Equal Subset Sum

413. Arithmetic Slices

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, 9
7, 7, 7, 7
3, -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.

等差数列划分

如果一个数列至少有三个元素，并且任意两个相邻元素之差相同，则称该数列为等差数列。

思路：用DP来做，定义一个一维dp数组，其中dp[i]表示，到i位置为止的Arithmetic Slices的个数，那么我们从第三个数字开始遍历，如果当前数字和之前两个数字构成Arithmetic Slices，那么我们更新dp[i]为dp[i-1]+1
dp[i]=dp[i-1]+1可以理解为，当A[i]可以和A[i-1]以及A[i-2]构成Arithmetic Slices的时候，那么能和A[i-1]构成Arithmetic Slices的元素必定能和A[i]构成算数切片，所以有个dp[i-1]，除此之外，当前这个最新元素还可以和它前面的两个元素构成Arithmetic Slices，而它前面的两个元素在dp[i-1]的时候只有两个元素，无法构成Arithmetic Slices，故+1。然后res累加上dp[i]的值即可

class Solution(object):
    def numberOfArithmeticSlices(self, A):
        """
        :type A: List[int]
        :rtype: int
        """
        l=len(A)
        if l<3:
            return 0
        dp=[0]*l
        result=0
        for i in range(2,l):
            if 2*A[i-1]==A[i-2]+A[i]:
                dp[i]=dp[i-1]+1
            result+=dp[i]
        return result

416. Partition Equal Subset Sum

Given a non-empty array containing only positive integers, find if the array can be partitioned into two subsets such that the sum of elements in both subsets is equal.

Note:

1. Each of the array element will not exceed 100.
2. The array size will not exceed 200.

 

Example 1:

Input: [1, 5, 11, 5]

Output: true

Explanation: The array can be partitioned as [1, 5, 5] and [11].

Example 2:

Input: [1, 2, 3, 5]

Output: false

Explanation: The array cannot be partitioned into equal sum subsets.

class Solution(object):
    def canPartition(self, nums):
        """
        :type nums: List[int]
        :rtype: bool
        """
        lens=len(nums)
        if lens==1:
            return False
        t=sum(nums)
        if t%2==1:
            return False
        tar=t//2
        dp=[[0]*(tar+1) for _ in range(lens+1)]
        for i in range(1,lens+1):
            for j in range(1,tar+1):
                if j