Binary Search 二分搜索

经典的二分搜索算法

class Solution {
    public int search(int[] nums, int target) {
        int l = 0, r = nums.length-1;
        while(l <= r) {
            int mid = l + (r - l) / 2;
            if (nums[mid] == target) {
                return mid;
            } else if (nums[mid] > target) {
                r = mid - 1;
            } else {
                l = mid + 1;
            }
        }
        return -1;
    }
}

例题

74. Search a 2D Matrix

在一个有从左到右、从上到下都是sorted的matrix寻找某个数
Input:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 3
Output: true

class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        if (matrix.length == 0 || matrix[0].length == 0) {
            return false;
        }
        int row = matrix.length, col = matrix[0].length;
        int start = 0, end = row * col - 1;
        while (start <= end) {
            int mid = start + (end - start) / 2;
            if (matrix[mid/col][mid%col] == target) {
                return true;
            }
            if (matrix[mid/col][mid%col] > target) {
                end = mid - 1;
            } else {
                start = mid + 1;
            }
        }
        return false;
    }
}

• 把matrix当作一个array来处理

240. Search a 2D Matrix II

一个从左到右递增，从上到下递增的matrix，找target
[
  [1,   4,  7, 11, 15],
  [2,   5,  8, 12, 19],
  [3,   6,  9, 16, 22],
  [10, 13, 14, 17, 24],
  [18, 21, 23, 26, 30]
]
Given target = 5, return true.

Given target = 20, return false.

class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        if (matrix.length == 0 || matrix[0].length == 0) {
            return false;
        }
        int r = 0, c = matrix[0].length - 1;
        while (r < matrix.length && c >= 0) {
            if (matrix[r][c] == target) {
                return true;
            }
            if (matrix[r][c] > target) {
                c--;
            } else {
                r++;
            }
        }
        return false;
    }
}

image.png

33. Search in Rotated Sorted Array

一个升序的数列有某个点分开并且更换前后两部分的顺序，找到目标数值
Input: nums = [4,5,6,7,0,1,2], target = 0
Output: 4

class Solution {
    public int search(int[] nums, int target) {
        if (nums.length == 0) {
            return -1;
        }
        int start = 0, end = nums.length - 1;
        while (start <= end) {
            int mid = start + (end - start) / 2;
            if (nums[mid] == target) {
                return mid;
            } 
            // left part if sorted
            if (nums[start] <= nums[mid]) {
                if (target < nums[start] || target > nums[mid]) {
                    start = mid + 1;
                } else {
                    end = mid - 1;
                }
            } else {
                // right part is sorted
                if (target < nums[mid] || target > nums[end]) {
                    end = mid - 1;
                } else {
                    start = mid + 1;
                }
            } 
        }
        return -1;
    }
}

• int mid = start + (end - start) / 2;
• if (nums[start] <= nums[mid])means left part is sorted; else , the right part is sorted

81. Search in Rotated Sorted Array II

class Solution {
    public boolean search(int[] nums, int target) {
        if (nums.length == 0) {
            return false;
        }
        int start = 0, end = nums.length-1;
        while (start <= end) {
            int mid = start + (end - start) / 2;
            if (nums[mid] == target) {
                return true;
            }
            // left part is sorted
            if (nums[start] < nums[mid]) {
                if (target < nums[start] || target > nums[mid]) {
                    start = mid + 1;
                } else {
                    end = mid - 1;
                }
            } else if (nums[start] > nums[mid]) {
                // right part is sorted
                if (target < nums[mid] || target > nums[end]) {
                    end = mid - 1;
                } else {
                    start = mid + 1;
                }
            } else {
                start++;
            }
        }
        return false;
    }
}

• if (nums[start] < nums[mid]) means left part is sorted
• else if (nums[start] > nums[mid]) means right part is sorted
• else if (nums[start] == nums[mid])since mid != target, so start != mid, then can increase start