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12 KiB
12 KiB
| title | type |
|---|---|
| Binary Search | docs |
Binary Search
- 二分搜索的经典写法。需要注意的三点：
- 循环退出条件，注意是 low <= high，而不是 low < high。
- mid 的取值，mid := low + (high-low)>>1
- low 和 high 的更新。low = mid + 1，high = mid - 1。
func binarySearchMatrix(nums []int, target int) int {
low, high := 0, len(nums)-1
for low <= high {
mid := low + (high-low)>>1
if nums[mid] == target {
return mid
} else if nums[mid] > target {
high = mid - 1
} else {
low = mid + 1
}
}
return -1
}
- 二分搜索的变种写法。有 4 个基本变种:
- 查找第一个与 target 相等的元素，时间复杂度 O(logn)
- 查找最后一个与 target 相等的元素，时间复杂度 O(logn)
- 查找第一个大于等于 target 的元素，时间复杂度 O(logn)
- 查找最后一个小于等于 target 的元素，时间复杂度 O(logn)
// 二分查找第一个与 target 相等的元素，时间复杂度 O(logn)
func searchFirstEqualElement(nums []int, target int) int {
low, high := 0, len(nums)-1
for low <= high {
mid := low + ((high - low) >> 1)
if nums[mid] > target {
high = mid - 1
} else if nums[mid] < target {
low = mid + 1
} else {
if (mid == 0) || (nums[mid-1] != target) { // 找到第一个与 target 相等的元素
return mid
}
high = mid - 1
}
}
return -1
}
// 二分查找最后一个与 target 相等的元素，时间复杂度 O(logn)
func searchLastEqualElement(nums []int, target int) int {
low, high := 0, len(nums)-1
for low <= high {
mid := low + ((high - low) >> 1)
if nums[mid] > target {
high = mid - 1
} else if nums[mid] < target {
low = mid + 1
} else {
if (mid == len(nums)-1) || (nums[mid+1] != target) { // 找到最后一个与 target 相等的元素
return mid
}
low = mid + 1
}
}
return -1
}
// 二分查找第一个大于等于 target 的元素，时间复杂度 O(logn)
func searchFirstGreaterElement(nums []int, target int) int {
low, high := 0, len(nums)-1
for low <= high {
mid := low + ((high - low) >> 1)
if nums[mid] >= target {
if (mid == 0) || (nums[mid-1] < target) { // 找到第一个大于等于 target 的元素
return mid
}
high = mid - 1
} else {
low = mid + 1
}
}
return -1
}
// 二分查找最后一个小于等于 target 的元素，时间复杂度 O(logn)
func searchLastLessElement(nums []int, target int) int {
low, high := 0, len(nums)-1
for low <= high {
mid := low + ((high - low) >> 1)
if nums[mid] <= target {
if (mid == len(nums)-1) || (nums[mid+1] > target) { // 找到最后一个小于等于 target 的元素
return mid
}
low = mid + 1
} else {
high = mid - 1
}
}
return -1
}
- 在基本有序的数组中用二分搜索。经典解法可以解，变种写法也可以写，常见的题型，在山峰数组中找山峰，在旋转有序数组中找分界点。第 33 题，第 81 题，第 153 题，第 154 题，第 162 题，第 852 题
func peakIndexInMountainArray(A []int) int {
low, high := 0, len(A)-1
for low < high {
mid := low + (high-low)>>1
// 如果 mid 较大，则左侧存在峰值，high = m，如果 mid + 1 较大，则右侧存在峰值，low = mid + 1
if A[mid] > A[mid+1] {
high = mid
} else {
low = mid + 1
}
}
return low
}
- max-min 最大值最小化问题。求在最小满足条件的情况下的最大值。第 410 题，第 875 题，第 1011 题，第 1283 题。
| No. | Title | Solution | Difficulty | TimeComplexity | SpaceComplexity | Favorite | Acceptance |
|---|---|---|---|---|---|---|---|
| 0004 | Median of Two Sorted Arrays | [Go]({{< relref "/ChapterFour/0004.Median-of-Two-Sorted-Arrays.md" >}}) | Hard | 30.8% | |||
| 0029 | Divide Two Integers | [Go]({{< relref "/ChapterFour/0029.Divide-Two-Integers.md" >}}) | Medium | 16.6% | |||
| 0033 | Search in Rotated Sorted Array | [Go]({{< relref "/ChapterFour/0033.Search-in-Rotated-Sorted-Array.md" >}}) | Medium | 35.7% | |||
| 0034 | Find First and Last Position of Element in Sorted Array | [Go]({{< relref "/ChapterFour/0034.Find-First-and-Last-Position-of-Element-in-Sorted-Array.md" >}}) | Medium | 37.1% | |||
| 0035 | Search Insert Position | [Go]({{< relref "/ChapterFour/0035.Search-Insert-Position.md" >}}) | Easy | 42.8% | |||
| 0050 | Pow(x, n) | [Go]({{< relref "/ChapterFour/0050.Powx-n.md" >}}) | Medium | O(log n) | O(1) | 30.8% | |
| 0069 | Sqrt(x) | [Go]({{< relref "/ChapterFour/0069.Sqrtx.md" >}}) | Easy | O(log n) | O(1) | 34.9% | |
| 0074 | Search a 2D Matrix | [Go]({{< relref "/ChapterFour/0074.Search-a-2D-Matrix.md" >}}) | Medium | 37.5% | |||
| 0081 | Search in Rotated Sorted Array II | [Go]({{< relref "/ChapterFour/0081.Search-in-Rotated-Sorted-Array-II.md" >}}) | Medium | 33.5% | |||
| 0153 | Find Minimum in Rotated Sorted Array | [Go]({{< relref "/ChapterFour/0153.Find-Minimum-in-Rotated-Sorted-Array.md" >}}) | Medium | 46.0% | |||
| 0154 | Find Minimum in Rotated Sorted Array II | [Go]({{< relref "/ChapterFour/0154.Find-Minimum-in-Rotated-Sorted-Array-II.md" >}}) | Hard | 41.9% | |||
| 0162 | Find Peak Element | [Go]({{< relref "/ChapterFour/0162.Find-Peak-Element.md" >}}) | Medium | 43.9% | |||
| 0167 | Two Sum II - Input array is sorted | [Go]({{< relref "/ChapterFour/0167.Two-Sum-II---Input-array-is-sorted.md" >}}) | Easy | O(n) | O(1) | 55.4% | |
| 0174 | Dungeon Game | [Go]({{< relref "/ChapterFour/0174.Dungeon-Game.md" >}}) | Hard | 33.2% | |||
| 0209 | Minimum Size Subarray Sum | [Go]({{< relref "/ChapterFour/0209.Minimum-Size-Subarray-Sum.md" >}}) | Medium | O(n) | O(1) | 39.2% | |
| 0222 | Count Complete Tree Nodes | [Go]({{< relref "/ChapterFour/0222.Count-Complete-Tree-Nodes.md" >}}) | Medium | O(n) | O(1) | 48.9% | |
| 0230 | Kth Smallest Element in a BST | [Go]({{< relref "/ChapterFour/0230.Kth-Smallest-Element-in-a-BST.md" >}}) | Medium | O(n) | O(1) | 62.2% | |
| 0240 | Search a 2D Matrix II | [Go]({{< relref "/ChapterFour/0240.Search-a-2D-Matrix-II.md" >}}) | Medium | 44.2% | |||
| 0275 | H-Index II | [Go]({{< relref "/ChapterFour/0275.H-Index-II.md" >}}) | Medium | 36.2% | |||
| 0287 | Find the Duplicate Number | [Go]({{< relref "/ChapterFour/0287.Find-the-Duplicate-Number.md" >}}) | Medium | O(n) | O(1) | ❤️ | 57.2% |
| 0300 | Longest Increasing Subsequence | [Go]({{< relref "/ChapterFour/0300.Longest-Increasing-Subsequence.md" >}}) | Medium | O(n log n) | O(n) | 43.7% | |
| 0315 | Count of Smaller Numbers After Self | [Go]({{< relref "/ChapterFour/0315.Count-of-Smaller-Numbers-After-Self.md" >}}) | Hard | 42.6% | |||
| 0327 | Count of Range Sum | [Go]({{< relref "/ChapterFour/0327.Count-of-Range-Sum.md" >}}) | Hard | 35.9% | |||
| 0349 | Intersection of Two Arrays | [Go]({{< relref "/ChapterFour/0349.Intersection-of-Two-Arrays.md" >}}) | Easy | O(n) | O(n) | 64.5% | |
| 0350 | Intersection of Two Arrays II | [Go]({{< relref "/ChapterFour/0350.Intersection-of-Two-Arrays-II.md" >}}) | Easy | O(n) | O(n) | 51.9% | |
| 0354 | Russian Doll Envelopes | [Go]({{< relref "/ChapterFour/0354.Russian-Doll-Envelopes.md" >}}) | Hard | 36.1% | |||
| 0367 | Valid Perfect Square | [Go]({{< relref "/ChapterFour/0367.Valid-Perfect-Square.md" >}}) | Easy | 42.0% | |||
| 0378 | Kth Smallest Element in a Sorted Matrix | [Go]({{< relref "/ChapterFour/0378.Kth-Smallest-Element-in-a-Sorted-Matrix.md" >}}) | Medium | 55.9% | |||
| 0392 | Is Subsequence | [Go]({{< relref "/ChapterFour/0392.Is-Subsequence.md" >}}) | Easy | O(n) | O(1) | 49.5% | |
| 0410 | Split Array Largest Sum | [Go]({{< relref "/ChapterFour/0410.Split-Array-Largest-Sum.md" >}}) | Hard | 46.1% | |||
| 0436 | Find Right Interval | [Go]({{< relref "/ChapterFour/0436.Find-Right-Interval.md" >}}) | Medium | 48.4% | |||
| 0441 | Arranging Coins | [Go]({{< relref "/ChapterFour/0441.Arranging-Coins.md" >}}) | Easy | 42.3% | |||
| 0454 | 4Sum II | [Go]({{< relref "/ChapterFour/0454.4Sum-II.md" >}}) | Medium | O(n^2) | O(n) | 54.5% | |
| 0475 | Heaters | [Go]({{< relref "/ChapterFour/0475.Heaters.md" >}}) | Medium | 33.6% | |||
| 0483 | Smallest Good Base | [Go]({{< relref "/ChapterFour/0483.Smallest-Good-Base.md" >}}) | Hard | 36.2% | |||
| 0493 | Reverse Pairs | [Go]({{< relref "/ChapterFour/0493.Reverse-Pairs.md" >}}) | Hard | 26.6% | |||
| 0497 | Random Point in Non-overlapping Rectangles | [Go]({{< relref "/ChapterFour/0497.Random-Point-in-Non-overlapping-Rectangles.md" >}}) | Medium | 39.1% | |||
| 0528 | Random Pick with Weight | [Go]({{< relref "/ChapterFour/0528.Random-Pick-with-Weight.md" >}}) | Medium | 44.5% | |||
| 0658 | Find K Closest Elements | [Go]({{< relref "/ChapterFour/0658.Find-K-Closest-Elements.md" >}}) | Medium | 41.8% | |||
| 0668 | Kth Smallest Number in Multiplication Table | [Go]({{< relref "/ChapterFour/0668.Kth-Smallest-Number-in-Multiplication-Table.md" >}}) | Hard | 47.7% | |||
| 0704 | Binary Search | [Go]({{< relref "/ChapterFour/0704.Binary-Search.md" >}}) | Easy | 54.0% | |||
| 0710 | Random Pick with Blacklist | [Go]({{< relref "/ChapterFour/0710.Random-Pick-with-Blacklist.md" >}}) | Hard | O(n) | O(n) | 32.6% | |
| 0718 | Maximum Length of Repeated Subarray | [Go]({{< relref "/ChapterFour/0718.Maximum-Length-of-Repeated-Subarray.md" >}}) | Medium | 50.2% | |||
| 0719 | Find K-th Smallest Pair Distance | [Go]({{< relref "/ChapterFour/0719.Find-K-th-Smallest-Pair-Distance.md" >}}) | Hard | 32.5% | |||
| 0744 | Find Smallest Letter Greater Than Target | [Go]({{< relref "/ChapterFour/0744.Find-Smallest-Letter-Greater-Than-Target.md" >}}) | Easy | 45.6% | |||
| 0778 | Swim in Rising Water | [Go]({{< relref "/ChapterFour/0778.Swim-in-Rising-Water.md" >}}) | Hard | 54.5% | |||
| 0786 | K-th Smallest Prime Fraction | [Go]({{< relref "/ChapterFour/0786.K-th-Smallest-Prime-Fraction.md" >}}) | Hard | 41.9% | |||
| 0793 | Preimage Size of Factorial Zeroes Function | [Go]({{< relref "/ChapterFour/0793.Preimage-Size-of-Factorial-Zeroes-Function.md" >}}) | Hard | 40.7% | |||
| 0852 | Peak Index in a Mountain Array | [Go]({{< relref "/ChapterFour/0852.Peak-Index-in-a-Mountain-Array.md" >}}) | Easy | 71.8% | |||
| 0862 | Shortest Subarray with Sum at Least K | [Go]({{< relref "/ChapterFour/0862.Shortest-Subarray-with-Sum-at-Least-K.md" >}}) | Hard | 25.2% | |||
| 0875 | Koko Eating Bananas | [Go]({{< relref "/ChapterFour/0875.Koko-Eating-Bananas.md" >}}) | Medium | 53.4% | |||
| 0878 | Nth Magical Number | [Go]({{< relref "/ChapterFour/0878.Nth-Magical-Number.md" >}}) | Hard | 28.9% | |||
| 0887 | Super Egg Drop | [Go]({{< relref "/ChapterFour/0887.Super-Egg-Drop.md" >}}) | Hard | 27.0% | |||
| 0911 | Online Election | [Go]({{< relref "/ChapterFour/0911.Online-Election.md" >}}) | Medium | 51.2% | |||
| 0927 | Three Equal Parts | [Go]({{< relref "/ChapterFour/0927.Three-Equal-Parts.md" >}}) | Hard | 34.5% | |||
| 0981 | Time Based Key-Value Store | [Go]({{< relref "/ChapterFour/0981.Time-Based-Key-Value-Store.md" >}}) | Medium | 54.0% | |||
| 1011 | Capacity To Ship Packages Within D Days | [Go]({{< relref "/ChapterFour/1011.Capacity-To-Ship-Packages-Within-D-Days.md" >}}) | Medium | 59.6% | |||
| 1111 | Maximum Nesting Depth of Two Valid Parentheses Strings | [Go]({{< relref "/ChapterFour/1111.Maximum-Nesting-Depth-of-Two-Valid-Parentheses-Strings.md" >}}) | Medium | 72.5% | |||
| 1157 | Online Majority Element In Subarray | [Go]({{< relref "/ChapterFour/1157.Online-Majority-Element-In-Subarray.md" >}}) | Hard | 39.6% | |||
| 1170 | Compare Strings by Frequency of the Smallest Character | [Go]({{< relref "/ChapterFour/1170.Compare-Strings-by-Frequency-of-the-Smallest-Character.md" >}}) | Medium | 59.5% | |||
| 1201 | Ugly Number III | [Go]({{< relref "/ChapterFour/1201.Ugly-Number-III.md" >}}) | Medium | 26.4% | |||
| 1235 | Maximum Profit in Job Scheduling | [Go]({{< relref "/ChapterFour/1235.Maximum-Profit-in-Job-Scheduling.md" >}}) | Hard | 47.0% | |||
| 1283 | Find the Smallest Divisor Given a Threshold | [Go]({{< relref "/ChapterFour/1283.Find-the-Smallest-Divisor-Given-a-Threshold.md" >}}) | Medium | 49.3% | |||
| 1300 | Sum of Mutated Array Closest to Target | [Go]({{< relref "/ChapterFour/1300.Sum-of-Mutated-Array-Closest-to-Target.md" >}}) | Medium | 43.2% | |||
| 1649 | Create Sorted Array through Instructions | [Go]({{< relref "/ChapterFour/1649.Create-Sorted-Array-through-Instructions.md" >}}) | Hard | 36.2% | |||
| 1658 | Minimum Operations to Reduce X to Zero | [Go]({{< relref "/ChapterFour/1658.Minimum-Operations-to-Reduce-X-to-Zero.md" >}}) | Medium | 33.4% | |||
| ------------ | ------------------------------------------------------- | ------- | ---------------- | --------------- | ------------- | ------------- | ------------- |