|
| 1 | +{ |
| 2 | + "cells": [ |
| 3 | + { |
| 4 | + "cell_type": "code", |
| 5 | + "execution_count": 2, |
| 6 | + "metadata": {}, |
| 7 | + "outputs": [], |
| 8 | + "source": [ |
| 9 | + "from typing import List" |
| 10 | + ] |
| 11 | + }, |
| 12 | + { |
| 13 | + "cell_type": "code", |
| 14 | + "execution_count": 7, |
| 15 | + "metadata": {}, |
| 16 | + "outputs": [], |
| 17 | + "source": [ |
| 18 | + "class Solution:\n", |
| 19 | + " def findValueOfPartition(self, nums: List[int]) -> int:\n", |
| 20 | + " #nums = set(nums)\n", |
| 21 | + " nums = sorted(nums)\n", |
| 22 | + " length = len(nums)\n", |
| 23 | + " min_ = float('inf')\n", |
| 24 | + " for i in range(length-1):\n", |
| 25 | + " min_ = min(min_, abs(nums[i] - nums[i+1]))\n", |
| 26 | + " return min_" |
| 27 | + ] |
| 28 | + }, |
| 29 | + { |
| 30 | + "cell_type": "code", |
| 31 | + "execution_count": 8, |
| 32 | + "metadata": {}, |
| 33 | + "outputs": [ |
| 34 | + { |
| 35 | + "data": { |
| 36 | + "text/plain": [ |
| 37 | + "0" |
| 38 | + ] |
| 39 | + }, |
| 40 | + "execution_count": 8, |
| 41 | + "metadata": {}, |
| 42 | + "output_type": "execute_result" |
| 43 | + } |
| 44 | + ], |
| 45 | + "source": [ |
| 46 | + "nums = [1,3,2,4]\n", |
| 47 | + "nums = [100,1,10]\n", |
| 48 | + "nums = [2,2,2,2,2,3,4,5,5,6,7,7,5,4,1212,1435,876543,65432,2345,76543]\n", |
| 49 | + "nums = [84,11,100,100,75]\n", |
| 50 | + "Solution().findValueOfPartition(nums)" |
| 51 | + ] |
| 52 | + }, |
| 53 | + { |
| 54 | + "cell_type": "code", |
| 55 | + "execution_count": null, |
| 56 | + "metadata": {}, |
| 57 | + "outputs": [], |
| 58 | + "source": [] |
| 59 | + }, |
| 60 | + { |
| 61 | + "cell_type": "code", |
| 62 | + "execution_count": 67, |
| 63 | + "metadata": {}, |
| 64 | + "outputs": [], |
| 65 | + "source": [ |
| 66 | + "class Solution:\n", |
| 67 | + " def specialPerm(self, nums: List[int]) -> int:\n", |
| 68 | + " \n", |
| 69 | + " def backtrack(curr_num, used):\n", |
| 70 | + " if used == (1 << len(nums)) - 1: return 1\n", |
| 71 | + "\n", |
| 72 | + " if (curr_num, used) in memo: return memo[(curr_num, used)]\n", |
| 73 | + "\n", |
| 74 | + " count = 0\n", |
| 75 | + " for i in range(len(nums)):\n", |
| 76 | + " if (not used & (1 << i)) and (nums[i] % curr_num == 0 or curr_num % nums[i] == 0):\n", |
| 77 | + " count += backtrack(nums[i], used | (1 << i))\n", |
| 78 | + "\n", |
| 79 | + " memo[(curr_num, used)] = count\n", |
| 80 | + " return count\n", |
| 81 | + "\n", |
| 82 | + " MOD = int(1e9) + 7\n", |
| 83 | + " nums.sort()\n", |
| 84 | + " memo = {}\n", |
| 85 | + "\n", |
| 86 | + " total_permutations = 0\n", |
| 87 | + " for i in range(len(nums)):\n", |
| 88 | + " total_permutations += backtrack(nums[i], 1 << i)\n", |
| 89 | + " total_permutations %= MOD\n", |
| 90 | + "\n", |
| 91 | + " return total_permutations" |
| 92 | + ] |
| 93 | + }, |
| 94 | + { |
| 95 | + "cell_type": "code", |
| 96 | + "execution_count": 68, |
| 97 | + "metadata": {}, |
| 98 | + "outputs": [ |
| 99 | + { |
| 100 | + "data": { |
| 101 | + "text/plain": [ |
| 102 | + "0" |
| 103 | + ] |
| 104 | + }, |
| 105 | + "execution_count": 68, |
| 106 | + "metadata": {}, |
| 107 | + "output_type": "execute_result" |
| 108 | + } |
| 109 | + ], |
| 110 | + "source": [ |
| 111 | + "#nums = [1,4,3]\n", |
| 112 | + "#nums = [2,3,6,7,8,9]\n", |
| 113 | + "Solution().specialPerm(nums)" |
| 114 | + ] |
| 115 | + }, |
| 116 | + { |
| 117 | + "cell_type": "code", |
| 118 | + "execution_count": 88, |
| 119 | + "metadata": {}, |
| 120 | + "outputs": [], |
| 121 | + "source": [ |
| 122 | + "class Solution:\n", |
| 123 | + " def distanceTraveled(self, mainTank: int, additionalTank: int) -> int:\n", |
| 124 | + " \n", |
| 125 | + " mileage = 10\n", |
| 126 | + " total_fuel = 0\n", |
| 127 | + " covered = 0\n", |
| 128 | + " while mainTank>=1:\n", |
| 129 | + " if mainTank >= 5:\n", |
| 130 | + " total_fuel +=5\n", |
| 131 | + " mainTank -=5\n", |
| 132 | + " covered = 5\n", |
| 133 | + " else:\n", |
| 134 | + " total_fuel += mainTank\n", |
| 135 | + " covered = mainTank\n", |
| 136 | + " mainTank = 0\n", |
| 137 | + " if covered == 5 and additionalTank>=1:\n", |
| 138 | + " additionalTank-=1\n", |
| 139 | + " covered = 0\n", |
| 140 | + " mainTank +=1\n", |
| 141 | + " \n", |
| 142 | + " return total_fuel*mileage" |
| 143 | + ] |
| 144 | + }, |
| 145 | + { |
| 146 | + "cell_type": "code", |
| 147 | + "execution_count": 89, |
| 148 | + "metadata": {}, |
| 149 | + "outputs": [ |
| 150 | + { |
| 151 | + "data": { |
| 152 | + "text/plain": [ |
| 153 | + "60" |
| 154 | + ] |
| 155 | + }, |
| 156 | + "execution_count": 89, |
| 157 | + "metadata": {}, |
| 158 | + "output_type": "execute_result" |
| 159 | + } |
| 160 | + ], |
| 161 | + "source": [ |
| 162 | + "mainTank = 5; additionalTank = 10\n", |
| 163 | + "#mainTank = 1; additionalTank = 2\n", |
| 164 | + "mainTank = 5; additionalTank = 1\n", |
| 165 | + "Solution().distanceTraveled(mainTank, additionalTank)" |
| 166 | + ] |
| 167 | + }, |
| 168 | + { |
| 169 | + "cell_type": "code", |
| 170 | + "execution_count": null, |
| 171 | + "metadata": {}, |
| 172 | + "outputs": [], |
| 173 | + "source": [] |
| 174 | + }, |
| 175 | + { |
| 176 | + "cell_type": "code", |
| 177 | + "execution_count": 165, |
| 178 | + "metadata": {}, |
| 179 | + "outputs": [], |
| 180 | + "source": [ |
| 181 | + "from functools import cache\n", |
| 182 | + "\n", |
| 183 | + "class Solution:\n", |
| 184 | + " def paintWalls(self, cost: List[int], time: List[int]) -> int:\n", |
| 185 | + " \n", |
| 186 | + " n=len(cost)\n", |
| 187 | + " \n", |
| 188 | + " @cache\n", |
| 189 | + " def dp(idx,t):\n", |
| 190 | + " if idx==n: return 0 if t>=0 else sys.maxsize\n", |
| 191 | + " #this index painted by paid painter\n", |
| 192 | + " ans=cost[idx] + dp(idx+1, min(n+1, t+time[idx]))\n", |
| 193 | + " #free painter\n", |
| 194 | + " ans = min(ans, dp(idx+1, t-1))\n", |
| 195 | + " return ans\n", |
| 196 | + " return dp(0,0)" |
| 197 | + ] |
| 198 | + }, |
| 199 | + { |
| 200 | + "cell_type": "code", |
| 201 | + "execution_count": 166, |
| 202 | + "metadata": {}, |
| 203 | + "outputs": [ |
| 204 | + { |
| 205 | + "data": { |
| 206 | + "text/plain": [ |
| 207 | + "55" |
| 208 | + ] |
| 209 | + }, |
| 210 | + "execution_count": 166, |
| 211 | + "metadata": {}, |
| 212 | + "output_type": "execute_result" |
| 213 | + } |
| 214 | + ], |
| 215 | + "source": [ |
| 216 | + "cost = [1,2,3,2]; time = [1,2,3,2]\n", |
| 217 | + "cost = [2,3,4,2]; time = [1,1,1,1]\n", |
| 218 | + "cost = [26,53,10,24,25,20,63,51]; time = [1,1,1,1,2,2,2,1]\n", |
| 219 | + "Solution().paintWalls(cost, time)" |
| 220 | + ] |
| 221 | + }, |
| 222 | + { |
| 223 | + "cell_type": "code", |
| 224 | + "execution_count": 158, |
| 225 | + "metadata": {}, |
| 226 | + "outputs": [], |
| 227 | + "source": [ |
| 228 | + "from typing import List\n", |
| 229 | + "\n", |
| 230 | + "class Solution:\n", |
| 231 | + " def paintWalls(self, cost: List[int], time: List[int]) -> int:\n", |
| 232 | + " n = len(cost)\n", |
| 233 | + "\n", |
| 234 | + " # Sort the walls based on cost in ascending order\n", |
| 235 | + " sorted_pairs = sorted(zip(cost, time))\n", |
| 236 | + "\n", |
| 237 | + " dp = [float('inf')] * (n + 1)\n", |
| 238 | + " dp[0] = 0\n", |
| 239 | + "\n", |
| 240 | + " for i in range(1, n + 1):\n", |
| 241 | + " curr_cost, curr_time = sorted_pairs[i - 1]\n", |
| 242 | + " for j in range(i, 0, -1):\n", |
| 243 | + " if curr_cost >= dp[j - 1]:\n", |
| 244 | + " dp[j] = min(dp[j], dp[j - 1] + curr_time)\n", |
| 245 | + "\n", |
| 246 | + " return dp[n]\n" |
| 247 | + ] |
| 248 | + }, |
| 249 | + { |
| 250 | + "cell_type": "code", |
| 251 | + "execution_count": 113, |
| 252 | + "metadata": {}, |
| 253 | + "outputs": [ |
| 254 | + { |
| 255 | + "data": { |
| 256 | + "text/plain": [ |
| 257 | + "[1, 2, 1, 2, 1, 1, 1, 2]" |
| 258 | + ] |
| 259 | + }, |
| 260 | + "execution_count": 113, |
| 261 | + "metadata": {}, |
| 262 | + "output_type": "execute_result" |
| 263 | + } |
| 264 | + ], |
| 265 | + "source": [ |
| 266 | + "[j for i,j in sorted(zip(cost, time))]\n", |
| 267 | + "# cost = [10, 20, 24, 25, 26, 51, 53, 63], time = [1, 2, 1, 2, 1, 1, 1, 2]" |
| 268 | + ] |
| 269 | + }, |
| 270 | + { |
| 271 | + "cell_type": "code", |
| 272 | + "execution_count": 109, |
| 273 | + "metadata": {}, |
| 274 | + "outputs": [ |
| 275 | + { |
| 276 | + "name": "stdout", |
| 277 | + "output_type": "stream", |
| 278 | + "text": [ |
| 279 | + "11\n" |
| 280 | + ] |
| 281 | + } |
| 282 | + ], |
| 283 | + "source": [ |
| 284 | + "def minCost(cost, time):\n", |
| 285 | + " n = len(cost)\n", |
| 286 | + "\n", |
| 287 | + " # Initialize the dynamic programming arrays\n", |
| 288 | + " dp = [float('inf')] * (n + 1)\n", |
| 289 | + " dp_free = [float('inf')] * (n + 1)\n", |
| 290 | + " dp[0] = 0\n", |
| 291 | + " dp_free[0] = 0\n", |
| 292 | + "\n", |
| 293 | + " for i in range(1, n + 1):\n", |
| 294 | + " # Calculate the cost when the paid painter is used\n", |
| 295 | + " dp[i] = min(dp[i], dp[i - 1] + cost[i - 1])\n", |
| 296 | + "\n", |
| 297 | + " # Calculate the cost when the free painter is used\n", |
| 298 | + " dp_free[i] = min(dp_free[i], dp[i - 1], dp_free[i - 1]) + time[i - 1]\n", |
| 299 | + "\n", |
| 300 | + " return min(dp[n], dp_free[n])\n", |
| 301 | + "\n", |
| 302 | + "cost = [26, 53, 10, 24, 25, 20, 63, 51]\n", |
| 303 | + "time = [1, 1, 1, 1, 2, 2, 2, 1]\n", |
| 304 | + "result = minCost(cost, time)\n", |
| 305 | + "print(result)\n" |
| 306 | + ] |
| 307 | + }, |
| 308 | + { |
| 309 | + "cell_type": "code", |
| 310 | + "execution_count": 96, |
| 311 | + "metadata": {}, |
| 312 | + "outputs": [ |
| 313 | + { |
| 314 | + "name": "stdout", |
| 315 | + "output_type": "stream", |
| 316 | + "text": [ |
| 317 | + "[83, 83, 97, 71, 71, 86, 92, 85, 8, 1, 52, 55, 11, 79, 56, 3, 13, 95, 76, 8, 56, 7, 94, 77, 41, 43, 83, 54, 93, 14, 57, 101, 2, 33, 85, 40, 21, 57, 30, 27, 48, 4, 78, 104, 57, 78, 100, 40, 9, 3]\n" |
| 318 | + ] |
| 319 | + } |
| 320 | + ], |
| 321 | + "source": [ |
| 322 | + "# 1 <= cost.length <= 500\n", |
| 323 | + "# cost.length == time.length\n", |
| 324 | + "# 1 <= cost[i] <= 106\n", |
| 325 | + "# 1 <= time[i] <= 500\n", |
| 326 | + "\n", |
| 327 | + "print([random.randrange(1,106) for i in range(50)])" |
| 328 | + ] |
| 329 | + }, |
| 330 | + { |
| 331 | + "cell_type": "code", |
| 332 | + "execution_count": 97, |
| 333 | + "metadata": {}, |
| 334 | + "outputs": [ |
| 335 | + { |
| 336 | + "name": "stdout", |
| 337 | + "output_type": "stream", |
| 338 | + "text": [ |
| 339 | + "[475, 229, 141, 89, 101, 226, 14, 220, 51, 394, 149, 395, 335, 37, 111, 177, 266, 246, 22, 422, 298, 151, 381, 399, 193, 304, 136, 296, 84, 175, 424, 47, 90, 235, 471, 428, 38, 137, 137, 240, 192, 424, 408, 303, 450, 407, 168, 419, 494, 45]\n" |
| 340 | + ] |
| 341 | + } |
| 342 | + ], |
| 343 | + "source": [ |
| 344 | + "print([random.randrange(1,500) for i in range(50)])" |
| 345 | + ] |
| 346 | + } |
| 347 | + ], |
| 348 | + "metadata": { |
| 349 | + "kernelspec": { |
| 350 | + "display_name": "base", |
| 351 | + "language": "python", |
| 352 | + "name": "python3" |
| 353 | + }, |
| 354 | + "language_info": { |
| 355 | + "codemirror_mode": { |
| 356 | + "name": "ipython", |
| 357 | + "version": 3 |
| 358 | + }, |
| 359 | + "file_extension": ".py", |
| 360 | + "mimetype": "text/x-python", |
| 361 | + "name": "python", |
| 362 | + "nbconvert_exporter": "python", |
| 363 | + "pygments_lexer": "ipython3", |
| 364 | + "version": "3.9.13" |
| 365 | + }, |
| 366 | + "orig_nbformat": 4 |
| 367 | + }, |
| 368 | + "nbformat": 4, |
| 369 | + "nbformat_minor": 2 |
| 370 | +} |
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