/
Problem238_productOfArrayExceptSelf.java
159 lines (129 loc) · 4.92 KB
/
Problem238_productOfArrayExceptSelf.java
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
package com.longluo.top100;
import java.util.Arrays;
/**
* 238. 除自身以外数组的乘积
* <p>
* 给你一个整数数组 nums，返回 数组 answer ，其中 answer[i] 等于 nums 中除 nums[i] 之外其余各元素的乘积 。
* 题目数据 保证 数组 nums之中任意元素的全部前缀元素和后缀的乘积都在 32 位 整数范围内。
* <p>
* 请不要使用除法，且在 O(n) 时间复杂度内完成此题。
* <p>
* 示例 1:
* 输入: nums = [1,2,3,4]
* 输出: [24,12,8,6]
* <p>
* 示例 2:
* 输入: nums = [-1,1,0,-3,3]
* 输出: [0,0,9,0,0]
* <p>
* 提示：
* 2 <= nums.length <= 10^5
* -30 <= nums[i] <= 30
* 保证 数组 nums之中任意元素的全部前缀元素和后缀的乘积都在 32 位 整数范围内
* <p>
* 进阶：你可以在 O(1) 的额外空间复杂度内完成这个题目吗？（ 出于对空间复杂度分析的目的，输出数组不被视为额外空间。）
* <p>
* https://leetcode.com/problems/product-of-array-except-self/
*/
public class Problem238_productOfArrayExceptSelf {
// BF time: O(n^2) space: O(1)
// TimeOut
public static int[] productExceptSelf_bf(int[] nums) {
int len = nums.length;
int[] ans = new int[len];
for (int i = 0; i < len; i++) {
int product = 1;
for (int j = 0; j < i; j++) {
product *= nums[j];
}
for (int j = i + 1; j < len; j++) {
product *= nums[j];
}
ans[i] = product;
}
return ans;
}
// Prefix time: O(3 * n) = O(n) space: O(n)
public static int[] productExceptSelf_prefix(int[] nums) {
int len = nums.length;
int[] left = new int[len + 1];
int[] right = new int[len + 1];
left[0] = 1;
// Left[i] = nums[0] * nums[1] ... nums[i]
for (int i = 0; i < len; i++) {
left[i + 1] = nums[i] * left[i];
}
right[len] = 1;
// right[i] = nums[len - 1] * nums[len - 2] ... nums[i]
for (int i = len - 1; i >= 0; i--) {
right[i] = nums[i] * right[i + 1];
}
int[] ans = new int[len];
for (int i = 0; i < len; i++) {
ans[i] = left[i] * right[i + 1];
}
return ans;
}
// Prefix Opt time: O(n) space: O(n)
public static int[] productExceptSelf_prefix_opt(int[] nums) {
int len = nums.length;
int[] ans = new int[len];
int[] left = new int[len];
int[] right = new int[len];
left[0] = 1;
// Left[i] = nums[0] * nums[1] ... nums[i - 1]
for (int i = 1; i < len; i++) {
left[i] = nums[i - 1] * left[i - 1];
}
right[len - 1] = 1;
// right[i] = nums[len - 1] * nums[len - 2] ... nums[i + 1]
for (int i = len - 2; i >= 0; i--) {
right[i] = nums[i + 1] * right[i + 1];
}
for (int i = 0; i < len; i++) {
ans[i] = left[i] * right[i];
}
return ans;
}
// Prefix time: O(2n) space: O(1)
public static int[] productExceptSelf(int[] nums) {
int len = nums.length;
int[] ans = new int[len];
ans[0] = 1;
// ans[i] = nums[0] * nums[1] ... nums[i - 1]
for (int i = 1; i < len; i++) {
ans[i] = nums[i - 1] * ans[i - 1];
}
int right = 1;
for (int i = len - 1; i >= 0; i--) {
ans[i] = ans[i] * right;
right *= nums[i];
}
return ans;
}
// Prefix Opt time: O(n) space: O(1)
public static int[] productExceptSelf_Opt(int[] nums) {
int len = nums.length;
int[] ans = new int[len];
Arrays.fill(ans, 1);
int left = 1;
int right = 1;
for (int i = 0; i < len; i++) {
ans[i] = ans[i] * left;
ans[len - i - 1] = ans[len - i - 1] * right;
left = left * nums[i];
right = right * nums[len - i - 1];
}
return ans;
}
public static void main(String[] args) {
System.out.println("[24,12,8,6] ?= " + Arrays.toString(productExceptSelf_bf(new int[]{1, 2, 3, 4})));
System.out.println("[0,0,9,0,0] ?= " + Arrays.toString(productExceptSelf_bf(new int[]{-1, 1, 0, -3, 3})));
System.out.println("[12,16,24,48,24] ?= " + Arrays.toString(productExceptSelf_prefix(new int[]{4, 3, 2, 1, 2})));
System.out.println("[24,12,8,6] ?= " + Arrays.toString(productExceptSelf_prefix(new int[]{1, 2, 3, 4})));
System.out.println("[0,0,9,0,0] ?= " + Arrays.toString(productExceptSelf_prefix(new int[]{-1, 1, 0, -3, 3})));
System.out.println("[0,0,9,0,0] ?= " + Arrays.toString(productExceptSelf_prefix_opt(new int[]{-1, 1, 0, -3, 3})));
System.out.println("[24,12,8,6] ?= " + Arrays.toString(productExceptSelf(new int[]{1, 2, 3, 4})));
System.out.println("[24,12,8,6] ?= " + Arrays.toString(productExceptSelf_Opt(new int[]{1, 2, 3, 4})));
}
}