_656.java

package com.fishercoder.solutions;

import java.util.*;

/**
 * 656. Coin Path
 *
 * Given an array A (index starts at 1) consisting of N integers: A1, A2, ..., AN and an integer B.
 * The integer B denotes that from any place (suppose the index is i) in the array A,
 * you can jump to any one of the place in the array A indexed i+1, i+2, …, i+B if this place can be jumped to.
 * Also, if you step on the index i, you have to pay Ai coins. If Ai is -1, it means you can’t jump to the place indexed i in the array.
 * Now, you start from the place indexed 1 in the array A,
 * and your aim is to reach the place indexed N using the minimum coins.
 * You need to return the path of indexes (starting from 1 to N) in the array you should take to get to the place indexed N using minimum coins.
 * If there are multiple paths with the same cost, return the lexicographically smallest such path.
 * If it's not possible to reach the place indexed N then you need to return an empty array.

 Example 1:
 Input: [1,2,4,-1,2], 2
 Output: [1,3,5]

 Example 2:
 Input: [1,2,4,-1,2], 1
 Output: []

 Note:
 Path Pa1, Pa2, ..., Pan is lexicographically smaller than Pb1, Pb2, ..., Pbm,
 if and only if at the first i where Pai and Pbi differ, Pai < Pbi; when no such i exists, then n < m.
 A1 >= 0. A2, ..., AN (if exist) will in the range of [-1, 100].
 Length of A is in the range of [1, 1000].
 B is in the range of [1, 100].
 */

public class _656 {

    /**
     * Time: O(n*B)
     * Reference: https://leetcode.com/articles/coin-path/#approach-3-using-dynamic-programming-accepted
     */
    public List<Integer> cheapestJump(int[] A, int B) {
        int[] next = new int[A.length];
        long[] dp = new long[A.length];
        Arrays.fill(next, -1);
        List<Integer> res = new ArrayList();
        for (int i = A.length - 2; i >= 0; i--) {
            long min_cost = Integer.MAX_VALUE;
            for (int j = i + 1; j <= i + B && j < A.length; j++) {
                if (A[j] >= 0) {
                    long cost = A[i] + dp[j];
                    if (cost < min_cost) {
                        min_cost = cost;
                        next[i] = j;
                    }
                }
            }
            dp[i] = min_cost;
        }
        int i;
        for (i = 0; i < A.length && next[i] > 0; i = next[i]) {
            res.add(i + 1);
        }
        if (i == A.length - 1 && A[i] >= 0) {
            res.add(A.length);
        } else {
            return new ArrayList<>();
        }
        return res;
    }
}