我正在尝试通过将备忘录应用于递归解决方案来使用Javascript解决LeetCode的longest palindromic subsequence问题.这是递归解决方案longestPalindromicSubsequence.js：

function longestPalindromicSubsequence(string, start = 0, end = string.length) {
  if (end < start) { return 0; }
  if (start === end) { return 1; }
  if (string[start] === string[end]) {
    return 2 + longestPalindromicSubsequence(string, start + 1, end - 1);
  }
  return Math.max(
    longestPalindromicSubsequence(string, start + 1, end),
    longestPalindromicSubsequence(string, start, end - 1),
  );
}

module.exports = longestPalindromicSubsequence;

这是一些关于Jest的测试用例,longestPalindromicSubsequence.test.js：

const longestPalindromicSubsequence = require('./longestPalindromicSubsequence');

describe('longest palindromic subsequence', () => {
  test('works for aab', () => {
    expect(longestPalindromicSubsequence('aab')).toBe(2);
  });

  test('works for long string', () => {
    expect(longestPalindromicSubsequence(`${'a'.repeat(50)}bcdef`)).toBe(50);
  });
});

这行得通,但是由于递归调用数量呈指数增长,因此速度很慢.例如,对于长度为〜50的字符串,它需要9秒：

$jest longestPalindromicSubsequence.test.js
 PASS  ./longestPalindromicSubsequence.test.js (9.6s)
  longest palindromic subsequence
    ✓ works for aab (3ms)
    ✓ works for long string (9315ms)

Test Suites: 1 passed, 1 total
Tests:       2 passed, 2 total
Snapshots:   0 total
Time:        10.039s
Ran all test suites matching /longestPalindromicSubsequence.test.js/i.

为了提高性能,我尝试在更新的模块longestPalindromicSubsequence2.js中使用_.memoize：

const _ = require('lodash');

const longestPalindromicSubsequence = _.memoize(
  (string, start = 0, end = string.length) => {
    if (end < start) { return 0; }
    if (start === end) { return 1; }
    if (string[start] === string[end]) {
      return 2 + longestPalindromicSubsequence(string, start + 1, end - 1);
    }
    return Math.max(
      longestPalindromicSubsequence(string, start + 1, end),
      longestPalindromicSubsequence(string, start, end - 1),
    );
  },
  (string, start, end) => [string, start, end], // resolver function
);

module.exports = longestPalindromicSubsequence;

但是,当我尝试使用此模块运行测试时,出现“ Javascript堆内存不足”错误：

$jest longestPalindromicSubsequence.test.js

 RUNS  ./longestPalindromicSubsequence.test.js

<--- Last few GCs --->
at[89308:0x104801e00]    15800 ms: Mark-sweep 1379.2 (1401.3) -> 1379.2 (1401.3) MB, 1720.4 / 0.0 ms  (+ 0.0 ms in 5 steps since start of marking, biggest step 0.0 ms, walltime since start of marking 1735 ms) (average mu = 0.128, current mu = 0.057) allocat[89308:0x104801e00]    17606 ms: Mark-sweep 1390.0 (1412.3) -> 1390.0 (1412.3) MB, 1711.7 / 0.0 ms  (+ 0.0 ms in 4 steps since start of marking, biggest step 0.0 ms, walltime since start of marking 1764 ms) (average mu = 0.091, current mu = 0.052) allocat

<--- JS stacktrace --->

==== JS stack trace =========================================

    0: ExitFrame [pc: 0x20b000bdc01d]
Security context: 0x1c189571e549 <JSObject>
    1: /* anonymous */ [0x1c18f7682201] [/Users/kurtpeek/GoogleDrive/LeetCode/longestPalindromicSubsequence2.js:~14] [pc=0x20b0015cd091](this=0x1c18d38893a1 <JSGlobal Object>,string=0x1c18f7682271 <String[55]: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabcdef>,start=45,end=45)
    2: memoized [0x1c18f7682309] [/Users/kurtpeek/GoogleDrive/LeetCode/node_...

FATAL ERROR: Ineffective mark-compacts near heap limit Allocation failed - JavaScript heap out of memory
 1: 0x100037733 node::Abort() [/usr/local/bin/node]
 2: 0x1000378d6 node::FatalTryCatch::~FatalTryCatch() [/usr/local/bin/node]
 3: 0x10018e57b v8::Utils::ReportOOMFailure(v8::internal::Isolate*, char const*, bool) [/usr/local/bin/node]
 4: 0x10018e51c v8::internal::V8::FatalProcessOutOfMemory(v8::internal::Isolate*, char const*, bool) [/usr/local/bin/node]
 5: 0x1004682ee v8::internal::Heap::UpdateSurvivalStatistics(int) [/usr/local/bin/node]
 6: 0x100469ed7 v8::internal::Heap::CheckIneffectiveMarkCompact(unsigned long, double) [/usr/local/bin/node]
 7: 0x1004675cb v8::internal::Heap::PerformGarbageCollection(v8::internal::GarbageCollector, v8::GCCallbackFlags) [/usr/local/bin/node]
 8: 0x1004663e6 v8::internal::Heap::CollectGarbage(v8::internal::AllocationSpace, v8::internal::GarbageCollectionReason, v8::GCCallbackFlags) [/usr/local/bin/node]
 9: 0x10046eafc v8::internal::Heap::AllocateRawWithLigthRetry(int, v8::internal::AllocationSpace, v8::internal::AllocationAlignment) [/usr/local/bin/node]
10: 0x10046eb48 v8::internal::Heap::AllocateRawWithRetryOrFail(int, v8::internal::AllocationSpace, v8::internal::AllocationAlignment) [/usr/local/bin/node]
11: 0x10044eb7a v8::internal::Factory::NewFillerObject(int, bool, v8::internal::AllocationSpace) [/usr/local/bin/node]
12: 0x100634916 v8::internal::Runtime_AllocateInTargetSpace(int, v8::internal::Object**, v8::internal::Isolate*) [/usr/local/bin/node]
13: 0x20b000bdc01d 
Abort trap: 6

据我从Node.js heap out of memory的了解,Node的标准内存使用为1.7GB,我认为这已经足够了.有任何想法为何备忘录版本不起作用以及如何修复它？

解决方法:

我设法通过将解析器功能从(string,start,end)=>更改为解决此问题. [string,start,end] to(字符串,开始,结束)=>字符串开始结束：

const _ = require('lodash');

const longestPalindromicSubsequence = _.memoize(
  (string, start = 0, end = string.length) => {
    if (end < start) { return 0; }
    if (start === end) { return 1; }
    if (string[start] === string[end]) {
      return 2 + longestPalindromicSubsequence(string, start + 1, end - 1);
    }
    return Math.max(
      longestPalindromicSubsequence(string, start + 1, end),
      longestPalindromicSubsequence(string, start, end - 1),
    );
  },
  (string, start, end) => string + start + end, // resolver function
);

module.exports = longestPalindromicSubsequence;

现在,“长字符串”测试只需3毫秒：

$jest longestPalindromicSubsequence.test.js
 PASS  ./longestPalindromicSubsequence.test.js
  longest palindromic subsequence
    ✓ works for aab (3ms)
    ✓ works for long string (3ms)

Test Suites: 1 passed, 1 total
Tests:       2 passed, 2 total
Snapshots:   0 total
Time:        1.004s, estimated 10s
Ran all test suites matching /longestPalindromicSubsequence.test.js/i.

看起来使用字符串作为缓存的键要比使用数组的存储效率高得多-也许是因为字符串在Javascript中是不可变的？欢迎对此改进做出任何解释.