數組平衡點

一個序列的平衡點是這樣的，它的左邊的所有的元素的和應該等於右邊的所有的元素的和，比如在下面的序列A：

 

A[0] = -7   A[1] =  1   A[2] = 5
A[3] =  2   A[4] = -4   A[5] = 3
A[6] =  0

 

3是一個平衡點因為:

• A[0] + A[1] + A[2] = A[4] + A[5] + A[6]

6也是一個平衡點因為:

• A[0] + A[1] + A[2] + A[3] + A[4] + A[5] = 0

(零個元素的和是零) 索引7不是平衡點，因為它不是序列A的有效索引。

如果你仍然不是很清楚，那么這里給出了明確的定義：0 ≤ k < n 並且 sum[i=0]^k-1A[i] = sum[i=k+1]^n-1 A[i]。時， 整數k是序列A[0], A[1], ..., A[n−1]$ 的平衡點，這里我們假定零個元素的和為零。

請寫一個函數

int equi(int A[], int N);

返回給定序列的平衡點(任意一個)如果沒有平衡點則返回−1，假設這個序列可達到非常大。

假定:

• N 是 [0..10,000,000] 內的 整數;
• 數組 A 每個元素是取值范圍 [−2,147,483,648..2,147,483,647] 內的 整數 .

復雜度:

• 最壞-情況下，期望的時間復雜度是 O(N);
• 最壞-情況下，期望的空間復雜度是 O(N), 輸入存儲除外 (不計輸入參數所需的存儲空間).

輸入數組中的元素可以修改

C#給出兩個思路一樣只是寫法有點不同的方法：

方法一：

using System;
using System.Collections.Generic;
using System.Linq;
class Solution {
  public int equi ( int[] A ) {
    if (A.Length <= 2)
      return -1;
    long summary = A.Sum();
    long left = 0;

    for (int i = 1; i < A.Length; i++)
    {
       left += A[i - 1];
       if (A[i] == left && summary - left - A[i] == A[i])
            return i;
     }
     return -1;
  }
}

方法二：

using System;
using System.Collections.Generic;
using System.Linq;
class Solution {
  public int equi ( int[] A ) {
    if (A.Length == 0)
                return -1;
     long summary = A.Sum();
            
     long sum_left = 0;
     for (int i = 0; i < A.Length; i++)
     {
          long sum_right = summary - sum_left - A[i];
          if (sum_left == sum_right)
          {
               return i;
           }
           sum_left += A[i];
      }
       return -1;
  }
}

這兩種寫法優劣請大家一起來評判一下。

========================華麗的分割線==========================

測試網站上給出的評判：

方法一：

 

Analysis

 

 

test	time	result
example  Test from the task description	0.080 s.	OK
simple	0.080 s.	OK
extreme_large_numbers  Sequence with extremly large numbers testing arithmetic overflow.	0.070 s.	RUNTIME ERROR  tested program terminated unexpectedly  stdout: Unhandled Exception: System.OverflowException: Number overflow. at System.Linq.Enumerable.<Sum>m__5E (Int32 a, Int32 b) [0x00000] at System.Linq.Enumerable.Sum[Int32,Int32] (IEnumerable`1 source, System.Func`3 selector) [0x00000] at System.Linq.Enumerable.Sum (IEnumerable`1 source) [0x00000] at Solution.equi (System.Int32[] A) [0x00000] at SolutionWrapper.run (System.String input, System.String output) [0x00000] at SolutionWrapper.Main (System.String[] args) [0x00000]
overflow_tests	0.080 s.	RUNTIME ERROR  tested program terminated unexpectedly  stdout: Unhandled Exception: System.OverflowException: Number overflow. at System.Linq.Enumerable.<Sum>m__5E (Int32 a, Int32 b) [0x00000] at System.Linq.Enumerable.Sum[Int32,Int32] (IEnumerable`1 source, System.Func`3 selector) [0x00000] at System.Linq.Enumerable.Sum (IEnumerable`1 source) [0x00000] at Solution.equi (System.Int32[] A) [0x00000] at SolutionWrapper.run (System.String input, System.String output) [0x00000] at SolutionWrapper.Main (System.String[] args) [0x00000]
one_large  one large number at the end of the sequence	0.070 s.	WRONG ANSWER  got -1, but equilibrium point exists, for example on position 0
sum_0  sequence with sum=0	0.070 s.	OK
single  single number	0.070 s.	WRONG ANSWER  got -1, but equilibrium point exists, for example on position 0
empty  Empty array	0.060 s.	OK
combinations_of_two  multiple runs, all combinations of {-1,0,1}^2	0.080 s.	WRONG ANSWER  got -1, but equilibrium point exists, for example on position 0
combinations_of_three  multiple runs, all combinations of {-1,0,1}^3	0.080 s.	WRONG ANSWER  got -1, but equilibrium point exists, for example on position 0
small_pyramid	0.070 s.	WRONG ANSWER  got -1, but equilibrium point exists, for example on position 42
large_long_sequence_of_ones	0.130 s.	WRONG ANSWER  got -1, but equilibrium point exists, for example on position 50000
large_long_sequence_of_minus_ones	0.110 s.	WRONG ANSWER  got -1, but equilibrium point exists, for example on position 50002
medium_pyramid	0.090 s.	WRONG ANSWER  got -1, but equilibrium point exists, for example on position 402
large_pyramid  Large performance test, O(n^2) solutions should fail.	0.160 s.	WRONG ANSWER  got -1, but equilibrium point exists, for example on position 898

方法二：

Analysis

 

Detected time complexity:
O(N)

 

test	time	result
example  Test from the task description	0.100 s.	OK
simple	0.090 s.	OK
extreme_large_numbers  Sequence with extremly large numbers testing arithmetic overflow.	0.070 s.	RUNTIME ERROR  tested program terminated unexpectedly  stdout: Unhandled Exception: System.OverflowException: Number overflow. at System.Linq.Enumerable.<Sum>m__5E (Int32 a, Int32 b) [0x00000] at System.Linq.Enumerable.Sum[Int32,Int32] (IEnumerable`1 source, System.Func`3 selector) [0x00000] at System.Linq.Enumerable.Sum (IEnumerable`1 source) [0x00000] at Solution.equi (System.Int32[] A) [0x00000] at SolutionWrapper.run (System.String input, System.String output) [0x00000] at SolutionWrapper.Main (System.String[] args) [0x00000]
overflow_tests	0.070 s.	RUNTIME ERROR  tested program terminated unexpectedly  stdout: Unhandled Exception: System.OverflowException: Number overflow. at System.Linq.Enumerable.<Sum>m__5E (Int32 a, Int32 b) [0x00000] at System.Linq.Enumerable.Sum[Int32,Int32] (IEnumerable`1 source, System.Func`3 selector) [0x00000] at System.Linq.Enumerable.Sum (IEnumerable`1 source) [0x00000] at Solution.equi (System.Int32[] A) [0x00000] at SolutionWrapper.run (System.String input, System.String output) [0x00000] at SolutionWrapper.Main (System.String[] args) [0x00000]
one_large  one large number at the end of the sequence	0.070 s.	OK
sum_0  sequence with sum=0	0.080 s.	OK
single  single number	0.070 s.	OK
empty  Empty array	0.060 s.	OK
combinations_of_two  multiple runs, all combinations of {-1,0,1}^2	0.070 s.	OK
combinations_of_three  multiple runs, all combinations of {-1,0,1}^3	0.070 s.	OK
small_pyramid	0.070 s.	OK
large_long_sequence_of_ones	0.100 s.	OK
large_long_sequence_of_minus_ones	0.120 s.	OK
medium_pyramid	0.090 s.	OK
large_pyramid  Large performance test, O(n^2) solutions should fail.	0.160 s.	OK