1335. 工作计划的最低难度

你需要制定一份 d 天的工作计划表。工作之间存在依赖，要想执行第 i 项工作，你必须完成全部 j 项工作（ 0 <= j < i）。

你每天 至少 需要完成一项任务。工作计划的总难度是这 d 天每一天的难度之和，而一天的工作难度是当天应该完成工作的最大难度。

给你一个整数数组 jobDifficulty 和一个整数 d，分别代表工作难度和需要计划的天数。第 i 项工作的难度是 jobDifficulty[i]。

返回整个工作计划的 最小难度 。如果无法制定工作计划，则返回 -1 。

来源：力扣（LeetCode）
链接：https://leetcode.cn/problems/minimum-difficulty-of-a-job-schedule
著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

动态规划

import java.util.Arrays;

class Solution {

    public int minDifficulty(int[] jobDifficulty, int d) {
        int n = jobDifficulty.length;
        if (d > n) {
            return -1;
        }
        int[][] dp = new int[n][d];
        int INF = Integer.MAX_VALUE - 1000;
        dp[0][0] = jobDifficulty[0];
        int max = jobDifficulty[0];
        for (int i = 1; i < n; i++) {
            max = Math.max(max, jobDifficulty[i]);
            dp[i][0] = max;
            for (int j = 1; j <= Math.min(d - 1, i); j++) {
                int regionMax = 0;
                dp[i][j] = INF;
                for (int k = i; k >= j; k--) {
                    regionMax = Math.max(regionMax, jobDifficulty[k]);
                    dp[i][j] = Math.min(dp[i][j], dp[k - 1][j - 1] + regionMax);
                }
            }
        }
        return dp[n - 1][d - 1];
    }

    public int minDifficulty(int[] jobDifficulty, int d) {
        int n = jobDifficulty.length;
        if (n < d) {
            return -1;
        }
        int INF = Integer.MAX_VALUE - 1000;
        int[][] dp = new int[d][n];
        for (int i = 0; i < d; ++i) {
            Arrays.fill(dp[i], INF);
        }
        int max = 0;
        for (int i = 0; i < n; ++i) {
            max = Math.max(max, jobDifficulty[i]);
            dp[0][i] = max;
        }
        for (int i = 1; i < d; ++i) {
            for (int j = i; j < n; ++j) {
                int regionMax = 0;
                for (int k = j; k >= i; --k) {
                    regionMax = Math.max(regionMax, jobDifficulty[k]);
                    dp[i][j] = Math.min(dp[i][j], regionMax + dp[i - 1][k - 1]);
                }
            }
        }
        return dp[d - 1][n - 1];
    }

    public int minDifficulty(int[] jobDifficulty, int d) {
        int n = jobDifficulty.length;
        if (n < d) {
            return -1;
        }
        int INF = Integer.MAX_VALUE - 1000;
        int[] dp = new int[n];
        Arrays.fill(dp, INF);
        int max = 0;
        for (int i = 0; i < n; ++i) {
            max = Math.max(max, jobDifficulty[i]);
            dp[i] = max;
        }
        for (int i = 1; i < d; ++i) {
            int[] helper = new int[n];
            for (int j = i; j < n; ++j) {
                int regionMax = 0;
                helper[j] = INF;
                for (int k = j; k >= i; --k) {
                    regionMax = Math.max(regionMax, jobDifficulty[k]);
                    helper[j] = Math.min(helper[j], regionMax + dp[k - 1]);
                }
            }
            System.arraycopy(helper, 0, dp, 0, n);
        }
        return dp[n - 1];
    }
}

单调栈

import java.util.Stack;

class Solution {
    public int minDifficulty(int[] jobDifficulty, int d) {
        int n = jobDifficulty.length;
        if (n < d) {
            return -1;
        }
        int[][] dp = new int[d][n];
        int INF = Integer.MAX_VALUE - 1000;
        int max = 0;
        for (int i = 0; i < n; i++) {
            max = Math.max(max, jobDifficulty[i]);
            dp[0][i] = max;
        }
        for (int i = 1; i < d; i++) {
            Stack<int[]> stack = new Stack<>();
            for (int j = i; j < n; j++) {
                int min = dp[i - 1][j - 1];
                while (!stack.isEmpty() && jobDifficulty[stack.peek()[0]] <= jobDifficulty[j]) {
                    min = Math.min(min, stack.pop()[1]);
                }
                dp[i][j] = min + jobDifficulty[j];
                if (!stack.isEmpty()) {
                    dp[i][j] = Math.min(dp[i][stack.peek()[0]], dp[i][j]);
                }
                stack.push(new int[]{j, min});
            }
        }
        return dp[d - 1][n - 1];
    }
}