【C++前缀和】2731. 移动机器人|1922

本文涉及的基础知识点

C++算法：前缀和、前缀乘积、前缀异或的原理、源码及测试用例包括课程视频

LeetCode2731. 移动机器人

有一些机器人分布在一条无限长的数轴上，他们初始坐标用一个下标从 0 开始的整数数组 nums 表示。当你给机器人下达命令时，它们以每秒钟一单位的速度开始移动。
给你一个字符串 s ，每个字符按顺序分别表示每个机器人移动的方向。‘L’ 表示机器人往左或者数轴的负方向移动，‘R’ 表示机器人往右或者数轴的正方向移动。
当两个机器人相撞时，它们开始沿着原本相反的方向移动。
请你返回指令重复执行 d 秒后，所有机器人之间两两距离之和。由于答案可能很大，请你将答案对 109 + 7 取余后返回。
注意：
对于坐标在 i 和 j 的两个机器人，(i,j) 和 (j,i) 视为相同的坐标对。也就是说，机器人视为无差别的。
当机器人相撞时，它们立即改变它们的前进方向，这个过程不消耗任何时间。
当两个机器人在同一时刻占据相同的位置时，就会相撞。
例如，如果一个机器人位于位置 0 并往右移动，另一个机器人位于位置 2 并往左移动，下一秒，它们都将占据位置 1，并改变方向。再下一秒钟后，第一个机器人位于位置 0 并往左移动，而另一个机器人位于位置 2 并往右移动。
例如，如果一个机器人位于位置 0 并往右移动，另一个机器人位于位置 1 并往左移动，下一秒，第一个机器人位于位置 0 并往左行驶，而另一个机器人位于位置 1 并往右移动。
示例 1：
输入：nums = [-2,0,2], s = “RLL”, d = 3
输出：8
解释：
1 秒后，机器人的位置为 [-1,-1,1] 。现在下标为 0 的机器人开始往左移动，下标为 1 的机器人开始往右移动。
2 秒后，机器人的位置为 [-2,0,0] 。现在下标为 1 的机器人开始往左移动，下标为 2 的机器人开始往右移动。
3 秒后，机器人的位置为 [-3,-1,1] 。
下标为 0 和 1 的机器人之间距离为 abs(-3 - (-1)) = 2 。
下标为 0 和 2 的机器人之间的距离为 abs(-3 - 1) = 4 。
下标为 1 和 2 的机器人之间的距离为 abs(-1 - 1) = 2 。
所有机器人对之间的总距离为 2 + 4 + 2 = 8 。
示例 2：
输入：nums = [1,0], s = “RL”, d = 2
输出：5
解释：
1 秒后，机器人的位置为 [2,-1] 。
2 秒后，机器人的位置为 [3,-2] 。
两个机器人的距离为 abs(-2 - 3) = 5 。
提示：
2 <= nums.length <= 10⁵
-2 * 10⁹ <= nums[i] <= 2 * 10⁹
0 <= d <= 10⁹
nums.length == s.length
s 只包含 ‘L’ 和 ‘R’ 。
nums[i] 互不相同。

C++前缀和

AB碰撞和不碰撞效果一样。AB碰撞后，A和B互换 $\iff$ 所有机器人运动方向不变。
long long型数组pos,pos[i]记录d秒后，第i个机器人位置。若干s[i]等于L，则pos[i]=nums[i]- d；否则，pos[i] = nums[i]+d。
对pos排序。
long long型数组dis, dis[i]记录第i个机器人距离所有它左边机器人之和。

i是0	i>0
dis[i] = 0	dis[i] = dis[i-1] + (pos[i]-pos[i-1])*i

代码

核心代码

class Solution {
		public:
			int sumDistance(vector<int>& nums, string s, int d) {
				vector<long long> pos;
				const int N = nums.size();
				for (int i = 0; i < N;i++) {
					if ('L' == s[i]) {
						pos.emplace_back(nums[i] - (long long)d);
					}
					else {
						pos.emplace_back(nums[i] + (long long)d);
					}
				}
				sort(pos.begin(), pos.end());
				vector<long long> dis(N);				
				for (int i = 1; i < N; i++) {
					dis[i] = dis[i - 1] + (pos[i] - pos[i - 1]) * i;
                    dis[i] %=  (int)(1e9+7);
				}
				long long ret = accumulate(dis.begin(), dis.end(), 0LL);
				return ret % (int)(1e9+7);
			}
		};

单元测试

vector<int> nums;
		string s;
		int d;
		TEST_METHOD(TestMethod1)
		{
			nums = { 2000000000,-2000000000 }, s = "RL", d = 1000000000;
			auto res = Solution().sumDistance(nums, s, d);
			AssertEx(999999965, res);
		}
		TEST_METHOD(TestMethod11)
		{
			nums = { -2, 0, 2 }, s = "RLL", d = 3;
			auto res = Solution().sumDistance(nums, s, d);
			AssertEx(8, res);
		}
		TEST_METHOD(TestMethod12)
		{
			nums = { 1,0 }, s = "RL", d = 2;
			auto res = Solution().sumDistance(nums, s, d);
			AssertEx(5, res);
		}
		TEST_METHOD(TestMethod13)
		{
			nums = { 10421,535686,-577310,-553499,-446384,-214024,433375,482991,-134992,488334,-538986,-495046,235593,469077,-175854,-258011,105550,-33819,-262675,-527552,-572600,295456,-570995,-272723,-226772,-805,429160,-351177,-463359,-35635,-42218,532797,328108,397721,-519551,-382316,374672,-149682,-551360,-429581,577121,-262244,-240933,-472284,-311647,575937,-515348,571070,431488,508682,-581561,528184,294618,458063,-480161,520654,506387,45202,-532471,504453,62212,-86197,-351839,-355186,-197206,236586,-241362,-113048,-294682,-142178,539933,-167605,-183969,4042,-253632,-387325,-266191,-369563,-82026,-111758,-285366,392160,-440295,-336066,165370,-257198,-21327,-349883,161336,420300,151952,-538676,-526180,492660,-187458,-75064,-499415,12995,-199088,-203047,319206,507945,87339,-69057,546163,97641,-49327,-251455,172750,-408543,-511831,-135448,162504,320036,400270,394198,-78558,536092,-539557,545814,-310633,216965,109096,-211067,439355,-332107,-104653,546759,245372,-483196,550737,-540599,-258516,-364869,-345323,437309,92676,-59957,-227323,-441134,-148657,-300253,-116205,55479,-459449,-269787,-304272,-256586,-570802,497174,513753,-230465,50327,-172955,-550822,-475817,587138,-153441,-387182,-553339,560009,65247,444673,135420,-509690,492398,198089,-129229,-546313,493402,-429792,-290510,-253252,-293591,235755,-372590,126760,491670,363788,281735,527688,-262211,-387086,218518,372942,430089,-85166,-136439,-442631,444942,222378,-382502,483845,211997,-160464,539794,299625,21495,303000,50598,363647,-169734,507160,-239002,38905,-380255,-421730,398512,497697,-195994,-359741,200484,120892,244454,-584256,-273069,-163032,-478946,-441271,-382870,-154119,-275001,22798,245623,-399550,287023,76378,-169737,546609,220057,-307094,-364841,499324,-159330,-568679,465161,-221706,579306,79993,138311,-419992,486358,-81176,-16117,258250,-419364,-231481,227683,-207085,351215,580870,-293665,-555527,141857,189480,-68788,-546102,-14871,-554917,447765,-478627,78241,-174224,326800,573073,-26316,-61998,-418186,59570,322281,-18540,543431,-490520,-211079,-593702,-168196,280596,-365957,380525,86350,-398705,-80021,-68042,-455482,-326453,161828,441446,-513844,305710,347467,-484546,-451888,433152,505827,442371,-111490,474818,129197,232666,493296,-566406,-273795,-334127,594412,-405121,589993,-559967,196306,17649,114052,-192167,118413,-520174,9095,72997,-72327,192948,-337742,-171602,-97266,-464709,-160740,140213,-299483,522012,307883,399166,229470,-406582,-168788,591476,-232937,-306744,416391,-194439,241535,360093,154576,269829,156728,-241586,-163873,-84086,168965,136489,257752,351340,51964,-317544,29576,-273908,-452286,428847,-333711,-558388,-215598,104658,324973,-121800,-518718,-238016,475075,-140504,357590,119459,84831,133621,-197236,-217846,-181933,-483140,58375,383558,232105,-175795,-580121,-501145,129886,271616,-103045,-339857,47161,-557374,-401535,-535796,248529,-188638,91766,456064,-87809,-403877,156909,-276961,460881,89217,154442,-76425,32038,-381836,-335586,326399,-362485,-357178,-537569,-275730,-570632,-589394,-97176,418366,503319,167716,-214835,519746,595712,-414845,384612,-114654,-95411,150576,144676,-377374,472251,63285,154117,-84932,334399,413746,-47127,-22361,-553407,-526034,9624,36756,388852,-452388,106364,439729,579180,492276,34799,334241,-114782,381049,-450353,335365,-131514,556661,-362147,-386226,418799,-144668,-275345,115318,134563,-42432,18623,-211442,-518693,-126957,-352327,-573198,593733,-377303,403255,-491208,453333,514995,250277,-576142,464818,-343631,-362597,260797,-318935,61494,226302,-554440,136885,-402182,-462896,139167,-265132,-67914,-336666,-534159,-490950,-337600,-95504,207026,-91921,74887,5457,-381568,-99837,-497088,-293348,4609,281644,-308310,55378,317985,174232,-49098,574370,357005,-227748,201844,81284,471257,188629,-348594,-294110,42526,75635,-29806,-108748,-477927,-190381,206736,-89130,144579,7742,445984,-51715,582270,65443,-474534,-450300,-584597,11965,-443980,122479,197067,171684,-94662,409242,-204539,117235,-35341,-238544,-495931,479765,573233,482142,237933,-396344,539422,439392,-65002,553778,-483116,381807,142362,437692,-214768,-118291,-64387,-388124,238859,34644,-312891,584207,57772,-61654,152487,-426099,-471821,-40319,-79806,463536,512696,177623,-69736,-84054,-473591,317920,-426926,-495351,465778,-241357,-289633,441161,362187,102256,102931,-397589,-114568,266556,558474,164613,-219023,45935,5949,-57197,-535702,99969,-34121,-568937,-31773,-556003,-417630,247361,-437020,-476065,590294,349583,-360608,448647,455933,282533,426527,-515754,223269,513916,361165,-525785,-192643,426738,-69872,-360710,376086,-111926,-288619,-49688,-145979,-414745,-345609,311806,203814,-271386,-421091,147989,-440359,-460888,445283,-368640,-785,368093,68593,-457706,489169,172661,402639,-39431,517806,587950,-21729,-128341,-190247,-65219,304435,-8825,412081,367536,-311987,514562,-205558,-88492,-405252,453706,-381828,-372600,205494,-78442,309605,437175,-288136,382223,331811,137563,89594,-285988,484839,281643,139912,-229210,427092,462609,29199,415077,-354605,33426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},
				 s = "RRLRLRRLRRLRLLRLRLLRRLLLLRLRLRLLLRLLLLRRLLLLRRRLRLRRLRLRRRLRLRRLLLLLLLLRLRRRLRRRLRRLLRRRLRLRLLRRLRLRLLLLLLRRLLRRLRLLRLRRLLLLLRRLRLRRLRRRLLLRRLRRLRLRLRRRRRLRLRLRLRLRRRLRLRLRLRLRLLLRLLLLRRLRRRRLRRRLRRLRLLRRRLLLLRRLLRLRLLRLLRRRRRRRLLRRLRLLLRLRRLRLLRLRLRLLLLRRLLLRRRRRRRLRRRRRLRLLLRRRRLRLLLRLRRRLRLRLLRRRRRRLLRRRRRRRRRLRRRLLRLRRLRRRLLLLRLRRLRRLLRRRRLLRRLRLLRLRRLLRRLRRRLRRLLLLLRRRLRLRLLRLLLLRRLRRRLLLLRLRRLLRLRLLLRRRRLRRRLRRLLRRLLLRLRRLRLLLLLRLLRRRLLRRRRRRRRLLRLLRLLLRRRRRLLRLLRRRRLRRRRLRRLLLRLRRRLLLLLLRRLRLLLLRRLLRRRLLLLLLLLRLLRRRLRLLRLLLRRRLLLLLLLRLRLRLRRLLLRLLLRLLLRLRLLRLLRLLRRRRRRRLRLLLLRRRLLRRLRRRRLLLRRRLLRLRRLRLRLLRRLLLRLRLLRLLLLRLLRRRRRLLRLLLRLRLLLLLRLLLLRLLRLRRRRLLLRLRRRRRRRRRLRLLRLRRLLRRLRRRRLLLLLRRLRRLRRRLRRLRRRRLLLRLRLLLLLRLLRRLRLLLLRLLRLLRRRRRLRRLRLLLRLRRRLRL", d = 248;
			auto res = Solution().sumDistance(nums, s, d);
			AssertEx(920311702, res);
		}

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如果程序是一条龙，那算法就是他的是睛
失败+反思=成功成功+反思=成功