时间复杂度与空间复杂度

时间复杂度

  1. O(1) - 常数时间复杂度:
js
1function constantTime(arr) {
2  return arr[0];
3}
  1. O(log n) - 对数时间复杂度:
js
1function binarySearch(arr, target) {
2  let left = 0;
3  let right = arr.length - 1;
4
5  while (left <= right) {
6    const mid = Math.floor((left + right) / 2);
7
8    if (arr[mid] === target) {
9      return mid;
10    }
11
12    if (arr[mid] < target) {
13      left = mid + 1;
14    } else {
15      right = mid - 1;
16    }
17  }
18
19  return -1;
20}
  1. O(n) - 线性时间复杂度:
js
1function linearSearch(arr, target) {
2  for (let i = 0; i < arr.length; i++) {
3    if (arr[i] === target) {
4      return i;
5    }
6  }
7
8  return -1;
9}
  1. O(n * log n) - 线性对数时间复杂度:
js
1function mergeSort(arr) {
2  if (arr.length <= 1) {
3    return arr;
4  }
5
6  const mid = Math.floor(arr.length / 2);
7  const left = mergeSort(arr.slice(0, mid));
8  const right = mergeSort(arr.slice(mid));
9
10  return merge(left, right);
11}
12
13function merge(left, right) {
14  const result = [];
15
16  while (left.length && right.length) {
17    if (left[0] < right[0]) {
18      result.push(left.shift());
19    } else {
20      result.push(right.shift());
21    }
22  }
23
24  return [...result, ...left, ...right];
25}
  1. O(n^2) - 平方时间复杂度:
js
1function bubbleSort(arr) {
2  for (let i = 0; i < arr.length; i++) {
3    for (let j = 0; j < arr.length - i - 1; j++) {
4      if (arr[j] > arr[j + 1]) {
5        [arr[j], arr[j + 1]] = [arr[j + 1], arr[j]];
6      }
7    }
8  }
9
10  return arr;
11}

这个复杂度可以视为等差数列的和,从 1 到 (n-1)。在渐进意义上,O(n*(n-1)/2) 仍然等于 O(n^2)

  1. O(2^n) - 指数时间复杂度:
js
1function fibonacci(n) {
2  if (n <= 1) {
3    return n;
4  }
5
6  return fibonacci(n - 1) + fibonacci(n - 2);
7}