|
| 1 | +{ |
| 2 | + "cells": [ |
| 3 | + { |
| 4 | + "cell_type": "markdown", |
| 5 | + "id": "floppy-arizona", |
| 6 | + "metadata": {}, |
| 7 | + "source": [ |
| 8 | + "### [绝对差不超过限制的最长连续子数组](https://leetcode-cn.com/problems/longest-continuous-subarray-with-absolute-diff-less-than-or-equal-to-limit/)\n", |
| 9 | + "\n", |
| 10 | + "给你一个整数数组`nums`,和一个表示限制的整数`limit`,请你返回最长连续子数组的长度,该子数组中的任意两个元素之间的绝对差必须小于或者等于`limit`。\n", |
| 11 | + "\n", |
| 12 | + "如果不存在满足条件的子数组,则返回 0 。\n", |
| 13 | + "\n", |
| 14 | + "#### 示例 1:\n", |
| 15 | + "```\n", |
| 16 | + "输入:nums = [8,2,4,7], limit = 4\n", |
| 17 | + "输出:2 \n", |
| 18 | + "解释:所有子数组如下:\n", |
| 19 | + "[8] 最大绝对差 |8-8| = 0 <= 4.\n", |
| 20 | + "[8,2] 最大绝对差 |8-2| = 6 > 4. \n", |
| 21 | + "[8,2,4] 最大绝对差 |8-2| = 6 > 4.\n", |
| 22 | + "[8,2,4,7] 最大绝对差 |8-2| = 6 > 4.\n", |
| 23 | + "[2] 最大绝对差 |2-2| = 0 <= 4.\n", |
| 24 | + "[2,4] 最大绝对差 |2-4| = 2 <= 4.\n", |
| 25 | + "[2,4,7] 最大绝对差 |2-7| = 5 > 4.\n", |
| 26 | + "[4] 最大绝对差 |4-4| = 0 <= 4.\n", |
| 27 | + "[4,7] 最大绝对差 |4-7| = 3 <= 4.\n", |
| 28 | + "[7] 最大绝对差 |7-7| = 0 <= 4. \n", |
| 29 | + "因此,满足题意的最长子数组的长度为 2 。\n", |
| 30 | + "```\n", |
| 31 | + "\n", |
| 32 | + "#### 示例 2:\n", |
| 33 | + "```\n", |
| 34 | + "输入:nums = [10,1,2,4,7,2], limit = 5\n", |
| 35 | + "输出:4 \n", |
| 36 | + "解释:满足题意的最长子数组是 [2,4,7,2],其最大绝对差 |2-7| = 5 <= 5 。\n", |
| 37 | + "```\n", |
| 38 | + "\n", |
| 39 | + "#### 示例 3:\n", |
| 40 | + "```\n", |
| 41 | + "输入:nums = [4,2,2,2,4,4,2,2], limit = 0\n", |
| 42 | + "输出:3\n", |
| 43 | + "```\n", |
| 44 | + "\n", |
| 45 | + "#### 提示:\n", |
| 46 | + "- 1 <= nums.length <= 10^5\n", |
| 47 | + "- 1 <= nums[i] <= 10^9\n", |
| 48 | + "- 0 <= limit <= 10^9" |
| 49 | + ] |
| 50 | + }, |
| 51 | + { |
| 52 | + "cell_type": "code", |
| 53 | + "execution_count": 1, |
| 54 | + "id": "outside-catch", |
| 55 | + "metadata": {}, |
| 56 | + "outputs": [], |
| 57 | + "source": [ |
| 58 | + "from typing import List\n", |
| 59 | + "# 常规解法,超时\n", |
| 60 | + "def longestSubarray(nums: List[int], limit: int) -> int:\n", |
| 61 | + " n, ans = len(nums), 0\n", |
| 62 | + " if n <= 1:\n", |
| 63 | + " return n\n", |
| 64 | + " for i in range(n):\n", |
| 65 | + " ni = nums[i]\n", |
| 66 | + " l, nmin, nmax = 1, ni, ni \n", |
| 67 | + " for j in range(i + 1, n):\n", |
| 68 | + " nj = nums[j]\n", |
| 69 | + " if nmin > nj:\n", |
| 70 | + " nmin = nj\n", |
| 71 | + " if nmax < nj:\n", |
| 72 | + " nmax = nj\n", |
| 73 | + " \n", |
| 74 | + " if nmax - nmin <= limit:\n", |
| 75 | + " ans = max(ans, j - i + 1)\n", |
| 76 | + " return ans" |
| 77 | + ] |
| 78 | + }, |
| 79 | + { |
| 80 | + "cell_type": "code", |
| 81 | + "execution_count": 2, |
| 82 | + "id": "rental-matrix", |
| 83 | + "metadata": {}, |
| 84 | + "outputs": [], |
| 85 | + "source": [ |
| 86 | + "# 超时\n", |
| 87 | + "def longestSubarray(nums: List[int], limit: int) -> int:\n", |
| 88 | + " n, ans = len(nums), 0\n", |
| 89 | + " if n <= 1:\n", |
| 90 | + " return n \n", |
| 91 | + " \n", |
| 92 | + " n0 = nums[0]\n", |
| 93 | + " \n", |
| 94 | + " ans, maxlen, queue = 1, 1, [n0]\n", |
| 95 | + " for i in range(1, n):\n", |
| 96 | + " ni, qmin, qmax = nums[i], min(queue), max(queue)\n", |
| 97 | + "\n", |
| 98 | + " if abs(ni - qmin) <= limit and abs(qmax - ni) <= limit:\n", |
| 99 | + " queue.append(ni)\n", |
| 100 | + " else:\n", |
| 101 | + " ans = max(ans, maxlen)\n", |
| 102 | + " j = len(queue)\n", |
| 103 | + " while abs(ni - queue[j - 1]) <= limit:\n", |
| 104 | + " j -= 1\n", |
| 105 | + " \n", |
| 106 | + " del queue[0:j]\n", |
| 107 | + " queue.append(ni)\n", |
| 108 | + " maxlen = len(queue)\n", |
| 109 | + "\n", |
| 110 | + " ans = max(ans, maxlen)\n", |
| 111 | + " return ans" |
| 112 | + ] |
| 113 | + }, |
| 114 | + { |
| 115 | + "cell_type": "code", |
| 116 | + "execution_count": 3, |
| 117 | + "id": "accompanied-beatles", |
| 118 | + "metadata": {}, |
| 119 | + "outputs": [], |
| 120 | + "source": [ |
| 121 | + "def longestSubarray(nums: List[int], limit: int) -> int:\n", |
| 122 | + " n, ans = len(nums), 0\n", |
| 123 | + " if n <= 1:\n", |
| 124 | + " return n \n", |
| 125 | + " \n", |
| 126 | + " n0 = nums[0]\n", |
| 127 | + " qmax, qmin, ans, start = [n0], [n0], 1, 0\n", |
| 128 | + " \n", |
| 129 | + " for i in range(1, n):\n", |
| 130 | + " ni = nums[i]\n", |
| 131 | + " while qmin and ni < qmin[-1]:\n", |
| 132 | + " qmin.pop()\n", |
| 133 | + " qmin.append(ni)\n", |
| 134 | + " \n", |
| 135 | + " while qmax and ni > qmax[-1]:\n", |
| 136 | + " qmax.pop()\n", |
| 137 | + " qmax.append(ni)\n", |
| 138 | + " \n", |
| 139 | + " while qmax[0] - qmin[0] > limit:\n", |
| 140 | + " if qmin[0] == nums[start]:\n", |
| 141 | + " qmin.pop(0)\n", |
| 142 | + " if qmax[0] == nums[start]:\n", |
| 143 | + " qmax.pop(0)\n", |
| 144 | + " start += 1\n", |
| 145 | + " else:\n", |
| 146 | + " ans = max(ans, i - start + 1)\n", |
| 147 | + " \n", |
| 148 | + " return ans" |
| 149 | + ] |
| 150 | + }, |
| 151 | + { |
| 152 | + "cell_type": "code", |
| 153 | + "execution_count": 4, |
| 154 | + "id": "found-airline", |
| 155 | + "metadata": {}, |
| 156 | + "outputs": [ |
| 157 | + { |
| 158 | + "data": { |
| 159 | + "text/plain": [ |
| 160 | + "5" |
| 161 | + ] |
| 162 | + }, |
| 163 | + "execution_count": 4, |
| 164 | + "metadata": {}, |
| 165 | + "output_type": "execute_result" |
| 166 | + } |
| 167 | + ], |
| 168 | + "source": [ |
| 169 | + "longestSubarray([1,5,6,7,8,10,6,5,6], 4)" |
| 170 | + ] |
| 171 | + }, |
| 172 | + { |
| 173 | + "cell_type": "code", |
| 174 | + "execution_count": 5, |
| 175 | + "id": "square-liverpool", |
| 176 | + "metadata": {}, |
| 177 | + "outputs": [ |
| 178 | + { |
| 179 | + "data": { |
| 180 | + "text/plain": [ |
| 181 | + "2" |
| 182 | + ] |
| 183 | + }, |
| 184 | + "execution_count": 5, |
| 185 | + "metadata": {}, |
| 186 | + "output_type": "execute_result" |
| 187 | + } |
| 188 | + ], |
| 189 | + "source": [ |
| 190 | + "longestSubarray([8,2,4,7], 4)" |
| 191 | + ] |
| 192 | + }, |
| 193 | + { |
| 194 | + "cell_type": "code", |
| 195 | + "execution_count": 6, |
| 196 | + "id": "weird-philippines", |
| 197 | + "metadata": {}, |
| 198 | + "outputs": [ |
| 199 | + { |
| 200 | + "data": { |
| 201 | + "text/plain": [ |
| 202 | + "4" |
| 203 | + ] |
| 204 | + }, |
| 205 | + "execution_count": 6, |
| 206 | + "metadata": {}, |
| 207 | + "output_type": "execute_result" |
| 208 | + } |
| 209 | + ], |
| 210 | + "source": [ |
| 211 | + "longestSubarray([10,1,2,4,7,2], 5)" |
| 212 | + ] |
| 213 | + }, |
| 214 | + { |
| 215 | + "cell_type": "code", |
| 216 | + "execution_count": 7, |
| 217 | + "id": "superior-camel", |
| 218 | + "metadata": {}, |
| 219 | + "outputs": [ |
| 220 | + { |
| 221 | + "data": { |
| 222 | + "text/plain": [ |
| 223 | + "3" |
| 224 | + ] |
| 225 | + }, |
| 226 | + "execution_count": 7, |
| 227 | + "metadata": {}, |
| 228 | + "output_type": "execute_result" |
| 229 | + } |
| 230 | + ], |
| 231 | + "source": [ |
| 232 | + "longestSubarray([4,2,2,2,4,4,2,2], 0)" |
| 233 | + ] |
| 234 | + }, |
| 235 | + { |
| 236 | + "cell_type": "code", |
| 237 | + "execution_count": 8, |
| 238 | + "id": "motivated-graphic", |
| 239 | + "metadata": {}, |
| 240 | + "outputs": [ |
| 241 | + { |
| 242 | + "data": { |
| 243 | + "text/plain": [ |
| 244 | + "6" |
| 245 | + ] |
| 246 | + }, |
| 247 | + "execution_count": 8, |
| 248 | + "metadata": {}, |
| 249 | + "output_type": "execute_result" |
| 250 | + } |
| 251 | + ], |
| 252 | + "source": [ |
| 253 | + "longestSubarray([2, 2, 2, 2, 2, 2], 0)" |
| 254 | + ] |
| 255 | + }, |
| 256 | + { |
| 257 | + "cell_type": "code", |
| 258 | + "execution_count": 9, |
| 259 | + "id": "aerial-smith", |
| 260 | + "metadata": {}, |
| 261 | + "outputs": [ |
| 262 | + { |
| 263 | + "data": { |
| 264 | + "text/plain": [ |
| 265 | + "3" |
| 266 | + ] |
| 267 | + }, |
| 268 | + "execution_count": 9, |
| 269 | + "metadata": {}, |
| 270 | + "output_type": "execute_result" |
| 271 | + } |
| 272 | + ], |
| 273 | + "source": [ |
| 274 | + "longestSubarray([2, 2, 1, 2, 2, 2], 0)" |
| 275 | + ] |
| 276 | + }, |
| 277 | + { |
| 278 | + "cell_type": "code", |
| 279 | + "execution_count": 10, |
| 280 | + "id": "cloudy-explanation", |
| 281 | + "metadata": {}, |
| 282 | + "outputs": [ |
| 283 | + { |
| 284 | + "data": { |
| 285 | + "text/plain": [ |
| 286 | + "25" |
| 287 | + ] |
| 288 | + }, |
| 289 | + "execution_count": 10, |
| 290 | + "metadata": {}, |
| 291 | + "output_type": "execute_result" |
| 292 | + } |
| 293 | + ], |
| 294 | + "source": [ |
| 295 | + "a = [24,12,71,33,5,87,10,11,3,58,2,97,97,36,32,35,15,80,24,45,38,9,22,21,33,68,22,85,35,83,92,38,59,90,42,64,61,15,4,40,50,44,54,25,34,14,33,94,66,27,78,56,3,29,3,51,19,5,93,21,58,91,65,87,55,70,29,81,89,67,58,29,68,84,4,51,87,74,42,85,81,55,8,95,39]\n", |
| 296 | + "longestSubarray(a, 87)" |
| 297 | + ] |
| 298 | + } |
| 299 | + ], |
| 300 | + "metadata": { |
| 301 | + "kernelspec": { |
| 302 | + "display_name": "Python 3", |
| 303 | + "language": "python", |
| 304 | + "name": "python3" |
| 305 | + }, |
| 306 | + "language_info": { |
| 307 | + "codemirror_mode": { |
| 308 | + "name": "ipython", |
| 309 | + "version": 3 |
| 310 | + }, |
| 311 | + "file_extension": ".py", |
| 312 | + "mimetype": "text/x-python", |
| 313 | + "name": "python", |
| 314 | + "nbconvert_exporter": "python", |
| 315 | + "pygments_lexer": "ipython3", |
| 316 | + "version": "3.8.6" |
| 317 | + } |
| 318 | + }, |
| 319 | + "nbformat": 4, |
| 320 | + "nbformat_minor": 5 |
| 321 | +} |
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