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g2101_2200.s2140_solving_questions_with_brainpower.Solution Maven / Gradle / Ivy

package g2101_2200.s2140_solving_questions_with_brainpower;

// #Medium #Array #Dynamic_Programming #2022_06_05_Time_5_ms_(98.77%)_Space_92.6_MB_(94.67%)

/**
 * 2140 - Solving Questions With Brainpower\.
 *
 * Medium
 *
 * You are given a **0-indexed** 2D integer array `questions` where questions[i] = [pointsi, brainpoweri].
 *
 * The array describes the questions of an exam, where you have to process the questions **in order** (i.e., starting from question `0`) and make a decision whether to **solve** or **skip** each question. Solving question `i` will **earn** you pointsi points but you will be **unable** to solve each of the next brainpoweri questions. If you skip question `i`, you get to make the decision on the next question.
 *
 * *   For example, given `questions = \[\[3, 2], [4, 3], [4, 4], [2, 5]]`:
 *     *   If question `0` is solved, you will earn `3` points but you will be unable to solve questions `1` and `2`.
 *     *   If instead, question `0` is skipped and question `1` is solved, you will earn `4` points but you will be unable to solve questions `2` and `3`.
 *
 * Return _the **maximum** points you can earn for the exam_.
 *
 * **Example 1:**
 *
 * **Input:** questions = \[\[3,2],[4,3],[4,4],[2,5]]
 *
 * **Output:** 5
 *
 * **Explanation:** The maximum points can be earned by solving questions 0 and 3. 
 *
 * - Solve question 0: Earn 3 points, will be unable to solve the next 2 questions 
 *
 * - Unable to solve questions 1 and 2 
 *
 * - Solve question 3: Earn 2 points 
 *   
 * Total points earned: 3 + 2 = 5. There is no other way to earn 5 or more points.
 *
 * **Example 2:**
 *
 * **Input:** questions = \[\[1,1],[2,2],[3,3],[4,4],[5,5]]
 *
 * **Output:** 7
 *
 * **Explanation:** The maximum points can be earned by solving questions 1 and 4. 
 *
 * - Skip question 0 
 *
 * - Solve question 1: Earn 2 points, will be unable to solve the next 2 questions 
 *
 * - Unable to solve questions 2 and 3 
 *
 * - Solve question 4: Earn 5 points 
 *   
 * Total points earned: 2 + 5 = 7. There is no other way to earn 7 or more points.
 *
 * **Constraints:**
 *
 * *   1 <= questions.length <= 105
 * *   `questions[i].length == 2`
 * *   1 <= pointsi, brainpoweri <= 105
**/
public class Solution {
    public long mostPoints(int[][] questions) {
        int n = questions.length;
        long[] memo = new long[n];
        memo[n - 1] = questions[n - 1][0];
        for (int i = n - 2; i >= 0; i--) {
            if (i + questions[i][1] + 1 < n) {
                memo[i] = Math.max(memo[i + 1], questions[i][0] + memo[i + questions[i][1] + 1]);
            } else {
                memo[i] = Math.max(memo[i + 1], questions[i][0]);
            }
        }
        return memo[0];
    }
}