LeetCode 329. Longest Increasing Path in a Matrix 在二维数组中寻找最长递增序列

题目：

Given an integer matrix, find the length of the longest increasing path.

From each cell, you can either move to four directions: left, right, up or down. You may NOT move diagonally or move outside of the boundary (i.e. wrap-around is not allowed).

Example 1:

nums = [
  [9,9,4],
  [6,6,8],
  [2,1,1]
]

Return 4
The longest increasing path is [1, 2, 6, 9].

我用的是广搜+动态规划（通俗讲是再创建一个二维数组，存储到子问题的最优解，避免重复搜索）

public class Solution {
    public int longestIncreasingPath(int[][] matrix){
    	if(matrix==null||matrix.length==0||matrix[0].length==0)
    		return 0;
    	int store[][] =new int[matrix.length][matrix[0].length];
    	int result = 0;
    	for(int i=0;i<matrix.length;i++){
    		for(int j=0;j<matrix[0].length;j++){
    			int mid = findAround(i,j,matrix,store,Integer.MAX_VALUE);
    			result = Math.max(result, mid);
    		}
    	}
    	return result;
    }
    

    private static int findAround(int i, int j, int[][] input, int[][] store,int last) {
    	if(i<0||i>=input.length||j<0||j>=input[0].length||input[i][j]>=last)
    		return 0;
    	if(store[i][j]>0)
    		return store[i][j];
    	else{
    		int mid = 0;
    		mid = Math.max(findAround(i+1, j, input, store, input[i][j]),mid);
    		mid = Math.max(findAround(i-1, j, input, store, input[i][j]),mid);
    		mid = Math.max(findAround(i, j+1, input, store, input[i][j]),mid);
    		mid = Math.max(findAround(i, j-1, input, store, input[i][j]),mid);
    		store[i][j] = ++mid;
    		return store[i][j];
    	}
	}

}

改编一下，成为微软的一道面试题，在而矩阵中找最长的连续整数子序列（如:2,3,4,.....）

更改如下：

public static int longestIncreasingPath(int[][] matrix){
    	if(matrix==null||matrix.length==0||matrix[0].length==0)
    		return 0;
    	int store[][] =new int[matrix.length][matrix[0].length];
    	int result = 0;
    	for(int i=0;i<matrix.length;i++){
    		for(int j=0;j<matrix[0].length;j++){
    			int mid = findAround(i,j,matrix,store,matrix[i][j]-1);
    			result = Math.max(result, mid);
    		}
    	}
    	return result;
    }
    

    private static int findAround(int i, int j, int[][] input, int[][] store,int last) {
    	if(i<0||i>=input.length||j<0||j>=input[0].length||input[i][j]!=last+1)
    		return 0;
    	if(store[i][j]>0)
    		return store[i][j];
    	else{
    		int mid = 0;
    		mid = Math.max(findAround(i+1, j, input, store, input[i][j]),mid);
    		mid = Math.max(findAround(i-1, j, input, store, input[i][j]),mid);
    		mid = Math.max(findAround(i, j+1, input, store, input[i][j]),mid);
    		mid = Math.max(findAround(i, j-1, input, store, input[i][j]),mid);
    		store[i][j] = ++mid;
    		return store[i][j];
    	}
	}