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| 1 | +#!/usr/bin/env python3 |
| 2 | +""" |
| 3 | +CREATED AT: 2022εΉ΄11ζ07ζ₯ |
| 4 | + |
| 5 | +URL: https://leetcode.com/problems/minimum-total-distance-traveled/ |
| 6 | + |
| 7 | +GITHUB: https://github.com/Jiezhi/myleetcode |
| 8 | + |
| 9 | +FileName: 2463-MinimumTotalDistanceTraveled |
| 10 | + |
| 11 | +Difficulty: Hard |
| 12 | + |
| 13 | +Desc: |
| 14 | + |
| 15 | +Tag: |
| 16 | + |
| 17 | +See: |
| 18 | + |
| 19 | +""" |
| 20 | +from tool import * |
| 21 | + |
| 22 | + |
| 23 | +class Solution: |
| 24 | + def minimumTotalDistance(self, robot: List[int], factory: List[List[int]]) -> int: |
| 25 | + """ |
| 26 | + Ref: https://leetcode.cn/problems/minimum-total-distance-traveled/discuss/2783305/Python-DP-Solution |
| 27 | + Runtime: 2908 ms, faster than 50.00% |
| 28 | + Memory Usage: 445.2 MB, less than 100.00% |
| 29 | + 1 <= robot.length, factory.length <= 100 |
| 30 | + factory[j].length == 2 |
| 31 | + -10^9 <= robot[i], positionj <= 10^9 |
| 32 | + 0 <= limitj <= robot.length |
| 33 | + The input will be generated such that it is always possible to repair every robot. |
| 34 | + """ |
| 35 | + |
| 36 | + robot.sort() |
| 37 | + factory.sort() |
| 38 | + |
| 39 | + @cache |
| 40 | + def dp(i, j, k) -> int: |
| 41 | + if i == len(robot): |
| 42 | + return 0 |
| 43 | + if j == len(factory): |
| 44 | + return math.inf |
| 45 | + return min(dp(i, j + 1, 0), |
| 46 | + dp(i + 1, j, k + 1) + abs(robot[i] - factory[j][0]) if factory[j][1] > k else math.inf) |
| 47 | + |
| 48 | + return dp(0, 0, 0) |
| 49 | + |
| 50 | + def minimumTotalDistance2(self, robot: List[int], factory: List[List[int]]) -> int: |
| 51 | + """ |
| 52 | + 1 <= robot.length, factory.length <= 100 |
| 53 | + factory[j].length == 2 |
| 54 | + -10^9 <= robot[i], positionj <= 10^9 |
| 55 | + 0 <= limitj <= robot.length |
| 56 | + The input will be generated such that it is always possible to repair every robot. |
| 57 | + """ |
| 58 | + cnt = Counter() |
| 59 | + for p, l in factory: |
| 60 | + if l > 0: |
| 61 | + cnt[p] = l |
| 62 | + rob = [] |
| 63 | + for r in robot: |
| 64 | + if cnt[r] > 0: |
| 65 | + cnt[r] -= 1 |
| 66 | + else: |
| 67 | + rob.append(r) |
| 68 | + |
| 69 | + dq = collections.deque([(rob, cnt, 0)]) |
| 70 | + ret = math.inf |
| 71 | + while dq: |
| 72 | + rob, cnt, step = dq.popleft() |
| 73 | + if not rob: |
| 74 | + ret = min(ret, step) |
| 75 | + continue |
| 76 | + rob_copy = rob.copy() |
| 77 | + r = rob_copy.pop() |
| 78 | + for fp in cnt.keys(): |
| 79 | + cnt_copy = cnt.copy() |
| 80 | + if cnt_copy[fp] == 1: |
| 81 | + del cnt_copy[fp] |
| 82 | + else: |
| 83 | + cnt_copy[fp] -= 1 |
| 84 | + dq.append((rob_copy, cnt_copy, step + abs(fp - r))) |
| 85 | + return ret |
| 86 | + |
| 87 | + |
| 88 | +def test(): |
| 89 | + assert Solution().minimumTotalDistance( |
| 90 | + [670355988, 403625544, 886437985, 224430896, 126139936, -477101480, -868159607, -293937930], |
| 91 | + [[333473422, 7], [912209329, 7], [468372740, 7], [-765827269, 4], [155827122, 4], [635462096, 2], |
| 92 | + [-300275936, 2], [-115627659, 0]]) == 509199280 |
| 93 | + assert Solution().minimumTotalDistance(robot=[0, 4, 6], factory=[[2, 2], [6, 2]]) == 4 |
| 94 | + assert Solution().minimumTotalDistance(robot=[1, -1], factory=[[-2, 1], [2, 1]]) == 2 |
| 95 | + |
| 96 | + |
| 97 | +if __name__ == '__main__': |
| 98 | + test() |
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