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Java-based LeetCode algorithm problem solutions, regularly updated
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package g2701_2800.s2731_movement_of_robots;

// #Medium #Array #Sorting #Prefix_Sum #Brainteaser
// #2023_09_22_Time_9_ms_(100.00%)_Space_54.7_MB_(63.56%)

import java.util.Arrays;

/**
 * 2731 - Movement of Robots\.
 *
 * Medium
 *
 * Some robots are standing on an infinite number line with their initial coordinates given by a **0-indexed** integer array `nums` and will start moving once given the command to move. The robots will move a unit distance each second.
 *
 * You are given a string `s` denoting the direction in which robots will move on command. `'L'` means the robot will move towards the left side or negative side of the number line, whereas `'R'` means the robot will move towards the right side or positive side of the number line.
 *
 * If two robots collide, they will start moving in opposite directions.
 *
 * Return _the sum of distances between all the pairs of robots_ `d` _seconds after the command._ Since the sum can be very large, return it modulo 10⁹ + 7.
 *
 * **Note:**
 *
 * *   For two robots at the index `i` and `j`, pair `(i,j)` and pair `(j,i)` are considered the same pair.
 * *   When robots collide, they **instantly change** their directions without wasting any time.
 * *   Collision happens when two robots share the same place in a moment.
 *     *   For example, if a robot is positioned in 0 going to the right and another is positioned in 2 going to the left, the next second they'll be both in 1 and they will change direction and the next second the first one will be in 0, heading left, and another will be in 2, heading right.
 *     *   For example, if a robot is positioned in 0 going to the right and another is positioned in 1 going to the left, the next second the first one will be in 0, heading left, and another will be in 1, heading right.
 *
 * **Example 1:**
 *
 * **Input:** nums = [-2,0,2], s = "RLL", d = 3
 *
 * **Output:** 8
 *
 * **Explanation:**
 *
 * After 1 second, the positions are [-1,-1,1]. Now, the robot at index 0 will move left, and the robot at index 1 will move right.
 *
 * After 2 seconds, the positions are [-2,0,0]. Now, the robot at index 1 will move left, and the robot at index 2 will move right.
 *
 * After 3 seconds, the positions are [-3,-1,1].
 *
 * The distance between the robot at index 0 and 1 is abs(-3 - (-1)) = 2.
 *
 * The distance between the robot at index 0 and 2 is abs(-3 - 1) = 4.
 *
 * The distance between the robot at index 1 and 2 is abs(-1 - 1) = 2.
 *
 * The sum of the pairs of all distances = 2 + 4 + 2 = 8.
 *
 * **Example 2:**
 *
 * **Input:** nums = [1,0], s = "RL", d = 2
 *
 * **Output:** 5
 *
 * **Explanation:**
 *
 * After 1 second, the positions are [2,-1].
 *
 * After 2 seconds, the positions are [3,-2].
 *
 * The distance between the two robots is abs(-2 - 3) = 5.
 *
 * **Constraints:**
 *
 * *   2 <= nums.length <= 10⁵
 * *   -2 * 10⁹ <= nums[i] <= 2 * 10⁹
 * *   0 <= d <= 10⁹
 * *   `nums.length == s.length`
 * *   `s` consists of 'L' and 'R' only
 * *   `nums[i]` will be unique.
**/
public class Solution {
    public int sumDistance(int[] nums, String s, int d) {
        int n = nums.length;
        int mod = (int) (1e9 + 7);
        for (int i = 0; i < n; i++) {
            nums[i] += (s.charAt(i) == 'R') ? d : -d;
        }
        Arrays.sort(nums);
        long res = 0;
        for (int i = 0; i < n; i++) {
            res = (res + (1L + i + i - n) * nums[i]) % mod;
        }
        return (int) ((res + mod) % mod);
    }
}