Leetcode: 456. 132 Pattern

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最新推荐文章于 2022-11-30 22:05:20 发布

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分类专栏： Leetcode Stack

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本文探讨了在一系列整数中查找是否存在132模式的问题，即子序列ai, aj, ak满足i < j < k且ai < ak < aj。提出了两种算法解决方案：暴力法和堆栈法，详细解释了每种方法的实现过程和关键步骤。

Question:

Given a sequence of n integers a1, a2, …, an, a 132 pattern is a subsequence ai, aj, ak such that i < j < k and ai < ak < aj. Design an algorithm that takes a list of n numbers as input and checks whether there is a 132 pattern in the list.

Solution1: Brute Force

class Solution {
    public boolean find132pattern(int[] nums) {
    	if (nums.length < 3) {
            return false;
        }
        int min_i = Integer.MAX_VALUE;
        for (int j = 0; j < nums.length - 1; j++) {
        	min_i = Math.min(min_i, nums[j]);
        	for (int k = j + 1; k < nums.length; k++) {
        		if (nums[j] > nums[k] && min < nums[k]) {
        			return true;
        		}
        	}
        }
        return false;
    }
}

Note1:

Iterate the numbers in the array and take each element as the largest one (nums[j]), since the smallest one (nums[i]) can only be ahead of nums[j], so we can also fixed it. For each num[j], loop through all the element behind it to find the one in the middle (nums[k]).

Solution2(Stack):

class Solution {
    public boolean find132pattern(int[] nums) {
    	if (nums.length < 3) {
            return false;
        }
        int[] minArray = new int[nums.length];
        int min_i = Integer.MAX_VALUE;
        Stack<Integer> stack = new Stack<>();
        for (int j = 0; j < nums.length; j++) {
        	min_i = Math.min(min_i, nums[j]);
        	minArray[j] = min_i;
        }
        for (int k = nums.length - 1; k >= 1; k--) {
        	if ( nums[k] > minArray[k] && (stack.isEmpty() || stack.peek() > nums[k])) {
        		stack.push(nums[k]);
        	}
        	else if (!stack.isEmpty() && nums[k] > minArray[k] && stack.peek() < nums[k] {
        		if (stack.peek() > minArray[k]) {
        			return true;
        		} else {
        			stack.pop();
        		}
        	}
        }
        return false;
    }
}