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Add Binary Search in 2D Array (TheAlgorithms#3240)
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@Shashwat79802
Shashwat79802 authored Sep 3, 2022
1 parent 9e37775 commit 6cfb628
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74 changes: 74 additions & 0 deletions src/main/java/com/thealgorithms/searches/BinarySearch2dArray.java
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package com.thealgorithms.searches;
/*
To apply this method, the provided array must be strictly sorted. In this method, two pointers, one at 0th row
& the other at the last row are taken & the searching is done on the basis of the middle element of the middle column.
If that element is equal to target, its coordinates are returned, else if it is smaller than the target, the rows above
that element are ignored (because the elements above it will also be smaller than the target), else that element is
greater than the target, then the rows below it are ignored.
*/
public class BinarySearch2dArray
{
static int[] BinarySearch(int[][] arr, int target){

int rowCount = arr.length, colCount = arr[0].length;

if (rowCount == 1){
return binarySearch(arr, target, 0, 0, colCount);
}

int startRow = 0, endRow = rowCount - 1, midCol = colCount/2;

while (startRow < endRow - 1){

int midRow = startRow + (endRow - startRow) / 2; //getting the index of middle row

if (arr[midRow][midCol] == target){
return new int[] {midRow, midCol};
}
else if (arr[midRow][midCol] < target)
startRow = midRow;
else
endRow = midRow;
}
/*
if the above search fails to find the target element, these conditions will be used to find the target
element, which further uses the binary search algorithm in the places which were left unexplored.
*/
if (arr[startRow][midCol] == target)
return new int[] {startRow, midCol};

if (arr[endRow][midCol] == target)
return new int[] {endRow, midCol};

if (target <= arr[startRow][midCol-1])
return binarySearch(arr, target, startRow, 0, midCol-1);

if (target >= arr[startRow][midCol+1] && target <= arr[startRow][colCount-1])
return binarySearch(arr,target, startRow, midCol+1, colCount-1);

if (target <= arr[endRow][midCol-1])
return binarySearch(arr, target, endRow, 0, midCol-1);

else
return binarySearch(arr,target, endRow, midCol+1, colCount-1);
}

static int[] binarySearch(int[][] arr, int target, int row, int colStart, int colEnd){

while (colStart <= colEnd){

int midIndex = colStart + (colEnd - colStart) / 2;

if (arr[row][midIndex] == target)
return new int[] {row, midIndex};

else if (arr[row][midIndex] < target)
colStart = midIndex + 1;
else
colEnd = midIndex - 1;
}

return new int[] {-1, -1};
}
}

117 changes: 117 additions & 0 deletions src/test/java/com/thealgorithms/searches/BinarySearch2dArrayTest.java
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package com.thealgorithms.searches;

import org.junit.jupiter.api.Test;

import java.util.*;

import static org.junit.jupiter.api.Assertions.assertEquals;

public class BinarySearch2dArrayTest {

@Test
// valid test case
public void BinarySearch2dArrayTestMiddle() {
int[][] arr = { {1, 2, 3, 4},
{5, 6, 7, 8},
{9,10,11,12}};
int target = 6;

int[] ans = BinarySearch2dArray.BinarySearch(arr, target);
int[] expected = {1,1};
System.out.println(Arrays.toString(ans));
assertEquals(1, ans[0]);
assertEquals(1, ans[1]);
}

@Test
// valid test case
public void BinarySearch2dArrayTestMiddleSide() {
int[][] arr = { {1, 2, 3, 4},
{5, 6, 7, 8},
{9,10,11,12}};
int target = 8;

int[] ans = BinarySearch2dArray.BinarySearch(arr, target);
int[] expected = {1,3};
System.out.println(Arrays.toString(ans));
assertEquals(1, ans[0]);
assertEquals(3, ans[1]);
}

@Test
// valid test case
public void BinarySearch2dArrayTestUpper() {
int[][] arr = { {1, 2, 3, 4},
{5, 6, 7, 8},
{9,10,11,12}};
int target = 2;

int[] ans = BinarySearch2dArray.BinarySearch(arr, target);
int[] expected = {0,1};
System.out.println(Arrays.toString(ans));
assertEquals(0, ans[0]);
assertEquals(1, ans[1]);
}

@Test
// valid test case
public void BinarySearch2dArrayTestUpperSide() {
int[][] arr = { {1, 2, 3, 4},
{5, 6, 7, 8},
{9,10,11,12}};
int target = 1;

int[] ans = BinarySearch2dArray.BinarySearch(arr, target);
int[] expected = {0,0};
System.out.println(Arrays.toString(ans));
assertEquals(0, ans[0]);
assertEquals(0, ans[1]);
}

@Test
// valid test case
public void BinarySearch2dArrayTestLower() {
int[][] arr = { {1, 2, 3, 4},
{5, 6, 7, 8},
{9,10,11,12}};
int target = 10;

int[] ans = BinarySearch2dArray.BinarySearch(arr, target);
int[] expected = {2,1};
System.out.println(Arrays.toString(ans));
assertEquals(2, ans[0]);
assertEquals(1, ans[1]);
}

@Test
// valid test case
public void BinarySearch2dArrayTestLowerSide() {
int[][] arr = { {1, 2, 3, 4},
{5, 6, 7, 8},
{9,10,11,12}};
int target = 11;

int[] ans = BinarySearch2dArray.BinarySearch(arr, target);
int[] expected = {2,2};
System.out.println(Arrays.toString(ans));
assertEquals(2, ans[0]);
assertEquals(2, ans[1]);
}

@Test
// valid test case
public void BinarySearch2dArrayTestNotFound() {
int[][] arr = { {1, 2, 3, 4},
{5, 6, 7, 8},
{9,10,11,12}};
int target = 101;

int[] ans = BinarySearch2dArray.BinarySearch(arr, target);
int[] expected = {-1,-1};
System.out.println(Arrays.toString(ans));
assertEquals(-1, ans[0]);
assertEquals(-1, ans[1]);
}

}

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