时间复杂度与空间复杂度
Published by powerfulyang on Apr 17, 2023
关于算法的时间复杂度与空间复杂度
时间复杂度
- O(1) - 常数时间复杂度:
function constantTime(arr) {
return arr[0];
}
- O(log n) - 对数时间复杂度:
function binarySearch(arr, target) {
let left = 0;
let right = arr.length - 1;
while (left <= right) {
const mid = Math.floor((left + right) / 2);
if (arr[mid] === target) {
return mid;
}
if (arr[mid] < target) {
left = mid + 1;
} else {
right = mid - 1;
}
}
return -1;
}
- O(n) - 线性时间复杂度:
function linearSearch(arr, target) {
for (let i = 0; i < arr.length; i++) {
if (arr[i] === target) {
return i;
}
}
return -1;
}
- O(n * log n) - 线性对数时间复杂度:
function mergeSort(arr) {
if (arr.length <= 1) {
return arr;
}
const mid = Math.floor(arr.length / 2);
const left = mergeSort(arr.slice(0, mid));
const right = mergeSort(arr.slice(mid));
return merge(left, right);
}
function merge(left, right) {
const result = [];
while (left.length && right.length) {
if (left[0] < right[0]) {
result.push(left.shift());
} else {
result.push(right.shift());
}
}
return [...result, ...left, ...right];
}
- O(n^2) - 平方时间复杂度:
function bubbleSort(arr) {
for (let i = 0; i < arr.length; i++) {
for (let j = 0; j < arr.length - i - 1; j++) {
if (arr[j] > arr[j + 1]) {
[arr[j], arr[j + 1]] = [arr[j + 1], arr[j]];
}
}
}
return arr;
}
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)
- O(2^n) - 指数时间复杂度:
function fibonacci(n) {
if (n <= 1) {
return n;
}
return fibonacci(n - 1) + fibonacci(n - 2);
}