g1601_1700.s1643_kth_smallest_instructions.Solution Maven / Gradle / Ivy

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package g1601_1700.s1643_kth_smallest_instructions;

// #Hard #Array #Dynamic_Programming #Math #Combinatorics
// #2022_04_21_Time_1_ms_(100.00%)_Space_43.3_MB_(20.97%)

/**
 * 1643 - Kth Smallest Instructions\.
 *
 * Hard
 *
 * Bob is standing at cell `(0, 0)`, and he wants to reach `destination`: `(row, column)`. He can only travel **right** and **down**. You are going to help Bob by providing **instructions** for him to reach `destination`.
 *
 * The **instructions** are represented as a string, where each character is either:
 *
 * *   `'H'`, meaning move horizontally (go **right** ), or
 * *   `'V'`, meaning move vertically (go **down** ).
 *
 * Multiple **instructions** will lead Bob to `destination`. For example, if `destination` is `(2, 3)`, both `"HHHVV"` and `"HVHVH"` are valid **instructions**.
 *
 * However, Bob is very picky. Bob has a lucky number `k`, and he wants the k^th **lexicographically smallest instructions** that will lead him to `destination`. `k` is **1-indexed**.
 *
 * Given an integer array `destination` and an integer `k`, return _the_ k^th _**lexicographically smallest instructions** that will take Bob to_ `destination`.
 *
 * **Example 1:**
 *
 * ![](https://assets.leetcode.com/uploads/2020/10/12/ex1.png)
 *
 * **Input:** destination = [2,3], k = 1
 *
 * **Output:** "HHHVV"
 *
 * **Explanation:** All the instructions that reach (2, 3) in lexicographic order are as follows: ["HHHVV", "HHVHV", "HHVVH", "HVHHV", "HVHVH", "HVVHH", "VHHHV", "VHHVH", "VHVHH", "VVHHH"].
 *
 * **Example 2:**
 *
 * **![](https://assets.leetcode.com/uploads/2020/10/12/ex2.png)**
 *
 * **Input:** destination = [2,3], k = 2
 *
 * **Output:** "HHVHV"
 *
 * **Example 3:**
 *
 * **![](https://assets.leetcode.com/uploads/2020/10/12/ex3.png)**
 *
 * **Input:** destination = [2,3], k = 3
 *
 * **Output:** "HHVVH"
 *
 * **Constraints:**
 *
 * *   `destination.length == 2`
 * *   `1 <= row, column <= 15`
 * *   `1 <= k <= nCr(row + column, row)`, where `nCr(a, b)` denotes `a` choose `b`.
**/
@SuppressWarnings("java:S135")
public class Solution {
    public String kthSmallestPath(int[] destination, int k) {
        StringBuilder sb = new StringBuilder();
        int v = destination[0];
        int n = v + destination[1];
        while (true) {
            int range = choose(--n, v);
            if (k <= range) {
                sb.append('H');
            } else {
                sb.append('V');
                v--;
                k -= range;
            }
            if (v == 0) {
                for (int i = 1; i <= n; i++) {
                    sb.append('H');
                }
                break;
            } else if (v == n) {
                for (int i = 1; i <= v; i++) {
                    sb.append('V');
                }
                break;
            }
        }

        return sb.toString();
    }

    private int choose(int n, int k) {
        if (n - k < k) {
            k = n - k;
        }
        int answer = 1;
        for (int i = 1; i <= k; i++) {
            answer = answer * (n + 1 - i) / i;
        }
        return answer;
    }
}