[英]Searching an element in a 2D sorted array
I had to write a code (as an exercise) that receives a 2D (square) row wise and col wise sorted array and an element, and return true is the element exists in the array.我必须编写一个代码(作为练习),它接收一个二维(正方形)按行和按列排序的数组和一个元素,并返回 true 是该元素存在于数组中。
The first thing that came to mind when i heard "sorted" is binary search, but than i realized that the last element in each row isn't necessarily smaller than the first one in the next line.当我听到“排序”时,首先想到的是二分查找,但后来我意识到每行中的最后一个元素不一定小于下一行中的第一个元素。
So, i figured out that the best complexity will be O(n), and wrote the following code:所以,我发现最好的复杂度是 O(n),并编写了以下代码:
public static boolean findN(int[][] a, int x) {
if (a.length == 0 || a[0].length == 0 || x > a[a.length - 1][a[0].length - 1] || x < a[0][0]) {
return false;
}
int LastRow = a.length - 1, Lastcol = a[0].length - 1, row = 0, col = 0;
while (row <= LastRow) {
if (a[row][col] == x) {
return true;
} else if (col < Lastcol) {
col++;
} else {
col = 0;
row++;
}
}
return false;
}
array example:
数组示例:
int [] [] arr = {{1,2,7,30}
{2,4,18,50}
{3,6,19,90}
{4,7,20,91}}
I came across a similar problem a few months ago and here is the code I found that works in O(logN + logM) [assuming the array is sorted row-wise as well as column-wise].几个月前我遇到了一个类似的问题,这里是我发现在 O(logN + logM) 中工作的代码[假设数组按行和列排序]。
[...] but than i realized that the last element in each row isn't necessarily smaller than the first one in the next line. [...] 但是我意识到每行中的最后一个元素不一定小于下一行中的第一个元素。 - In this case, you cannot achieve O(logn) complexity.
- 在这种情况下,您无法实现 O(logn) 复杂度。
Simple Binary Search:简单的二分搜索:
static void binarySearch(int mat[][], int i, int j_low, int j_high, int x) {
while (j_low <= j_high) {
int j_mid = (j_low + j_high) / 2;
// Element found
if (mat[i][j_mid] == x) {
System.out.println ( "Found at (" + i + ", " + j_mid +")");
return;
}
else if (mat[i][j_mid] > x)
j_high = j_mid - 1;
else
j_low = j_mid + 1;
}
System.out.println ( "Element no found");
}
Core Logic:核心逻辑:
static void sortedMatrixSearch(int mat[][], int n, int m, int x) {
// Single row matrix
if (n == 1) {
binarySearch(mat, 0, 0, m - 1, x);
return;
}
// Do binary search in middle column.
// Condition to terminate the loop when the
// 2 desired rows are found
int i_low = 0;
int i_high = n - 1;
int j_mid = m / 2;
while ((i_low + 1) < i_high) {
int i_mid = (i_low + i_high) / 2;
// element found
if (mat[i_mid][j_mid] == x) {
System.out.println ( "Found at (" + i_mid +", " + j_mid +")");
return;
}
else if (mat[i_mid][j_mid] > x)
i_high = i_mid;
else
i_low = i_mid;
}
// If element is present on
// the mid of the two rows
if (mat[i_low][j_mid] == x)
System.out.println ( "Found at (" + i_low + "," + j_mid +")");
else if (mat[i_low + 1][j_mid] == x)
System.out.println ( "Found at (" + (i_low + 1) + ", " + j_mid +")");
// Ssearch element on 1st half of 1st row
else if (x <= mat[i_low][j_mid - 1])
binarySearch(mat, i_low, 0, j_mid - 1, x);
// Search element on 2nd half of 1st row
else if (x >= mat[i_low][j_mid + 1] && x <= mat[i_low][m - 1])
binarySearch(mat, i_low, j_mid + 1, m - 1, x);
// Search element on 1st half of 2nd row
else if (x <= mat[i_low + 1][j_mid - 1])
binarySearch(mat, i_low + 1, 0, j_mid - 1, x);
// search element on 2nd half of 2nd row
else
binarySearch(mat, i_low + 1, j_mid + 1, m - 1, x);
}
Driver method:驱动方式:
public static void main (String[] args) {
int n = 4, m = 5, x = 8;
int mat[][] = {{0, 6, 8, 9, 11},
{20, 22, 28, 29, 31},
{36, 38, 50, 61, 63},
{64, 66, 100, 122, 128}};
sortedMatrixSearch(mat, n, m, x);
}
Hope this helps.希望这可以帮助。 Good luck.
祝你好运。
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