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Monotonic Stack 单调栈

基本流程

一般会用到 Deque 的以下四个方法:

  • deque.isEmpty():如果 deque 不包含任何元素,则返回 true,否则返回 false。因为要栈顶元素在满足要求的时候要弹出,所以需要进行空栈判断。有些场景,可能栈一定不会空的时候,就不需要该方法进行空栈判断。

  • deque.push(e):将元素 e 入栈。

  • deque.pop():将栈顶元素弹出,并返回当前弹出的栈顶元素。

  • deque.peek():获取栈顶元素,不弹出。

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// 定义一个单调栈
Deque<Integer> stack = new LinkedList<>();
// 第一个元素,直接添加
stack.push(0); // 这里存的是数组下标
for (int i = 1; i < nums.length; i++) {
    // 单调递增栈这里就是大于,即 nums[i] > nums[deque.peek()]
    if (nums[i] < nums[stack.peek()]) {
        stack.push(i);
    } else if (nums[i] == nums[stack.peek()]) {
        stack.push(i);
        // 此处除了入栈,在有些场景下,还有可能有其他操作
        // ..............
    } else {
        // 循环比较,直到遇到当前元素小于栈顶的元素情况,跳出循环
        // 单调递增栈,这里是小于,即nums[i] < nums[deque.peek()]
        while (!stack.isEmpty() && nums[i] > nums[stack.peek()]) {
            //主要逻辑
            // ............
            // ............
            // 弹出栈顶元素
            stack.pop();
        }
        stack.push(i);
    }
}

可能你会问:什么时候用单调栈?

需要给当前的元素,找右边/左边第一个比它大/小的位置。

记住这两句话:

  • 单调递增栈,利用波谷剔除栈中的波峰,留下波谷;

  • 单调递减栈,利用波峰剔除栈中的波谷,留下波峰。

经典题目

  1. 42. 接雨水 — 这个单调栈,在中间过程加了一些操作,有意思。

  2. 84. 柱状图中最大的矩形

  3. [0085-maximal-rectangle]

  4. 155. Min Stack — 这个辅助栈也可以认为是一种单调栈。

  5. [0255-verify-preorder-sequence-in-binary-search-tree]

  6. 316. 去除重复字母

  7. [0321-create-maximum-number]

  8. 402. Remove K Digits

  9. [0456-132-pattern]

  10. 496. Next Greater Element I

  11. 503. Next Greater Element II

  12. 581. Shortest Unsorted Continuous Subarray

  13. 654. Maximum Binary Tree

  14. 739. Daily Temperatures

  15. 768. Max Chunks To Make Sorted II

  16. [0769-max-chunks-to-make-sorted]

  17. [0853-car-fleet]

  18. [0901-online-stock-span]

  19. [0907-sum-of-subarray-minimums]

  20. [0962-maximum-width-ramp]

  21. [0975-odd-even-jump]

  22. [1008-construct-binary-search-tree-from-preorder-traversal]

  23. [1019-next-greater-node-in-linked-list]

  24. [1063-number-of-valid-subarrays]

  25. 1081. 不同字符的最小子序列

  26. [1124-longest-well-performing-interval]

  27. [1130-minimum-cost-tree-from-leaf-values]

  28. [1475-final-prices-with-a-special-discount-in-a-shop]

  29. [1504-count-submatrices-with-all-ones]

  30. [1526-minimum-number-of-increments-on-subarrays-to-form-a-target-array]

  31. [1574-shortest-subarray-to-be-removed-to-make-array-sorted]

  32. [1673-find-the-most-competitive-subsequence]

  33. [1762-buildings-with-an-ocean-view]

  34. [1776-car-fleet-ii]

  35. [1793-maximum-score-of-a-good-subarray]

  36. [1856-maximum-subarray-min-product]

  37. [1944-number-of-visible-people-in-a-queue]

  38. [1950-maximum-of-minimum-values-in-all-subarrays]

  39. [1996-the-number-of-weak-characters-in-the-game]

  40. [2030-smallest-k-length-subsequence-with-occurrences-of-a-letter]

  41. [2104-sum-of-subarray-ranges]

  42. [2281-sum-of-total-strength-of-wizards]

  43. [2282-number-of-people-that-can-be-seen-in-a-grid]

  44. [2289-steps-to-make-array-non-decreasing]

  45. [2297-jump-game-viii]

  46. [2334-subarray-with-elements-greater-than-varying-threshold]

  47. [2345-finding-the-number-of-visible-mountains]

  48. [2355-maximum-number-of-books-you-can-take]

  49. [2454-next-greater-element-iv]

  50. [2487-remove-nodes-from-linked-list]

  51. [2617-minimum-number-of-visited-cells-in-a-grid]

  52. [2736-maximum-sum-queries]

  53. [2818-apply-operations-to-maximize-score]

  54. [2832-maximal-range-that-each-element-is-maximum-in-it]

  55. [2863-maximum-length-of-semi-decreasing-subarrays]

  56. [2865-beautiful-towers-i]

  57. [2866-beautiful-towers-ii]

  58. [2940-find-building-where-alice-and-bob-can-meet]

  59. [2945-find-maximum-non-decreasing-array-length]

  60. [3113-find-the-number-of-subarrays-where-boundary-elements-are-maximum]

  61. [3205-maximum-array-hopping-score-i]

  62. [3221-maximum-array-hopping-score-ii]

  63. [3229-minimum-operations-to-make-array-equal-to-target]

  64. [3359-find-sorted-submatrices-with-maximum-element-at-most-k]

  65. [3420-count-non-decreasing-subarrays-after-k-operations]

  66. [3430-maximum-and-minimum-sums-of-at-most-size-k-subarrays]