目录
1. 二分查找-I
1.1 题目描述
1.2 解题思路
方法:二分法(推荐使用)
2. 二维数组中的查找
2.1 题目描述
2.2 解题思路
方法一:二分查找(推荐使用)
3. 寻找峰值
3.1 题目描述
3.2 解题思路
方法一:二分查找(推荐使用)
4. 数组中的逆序对
4.1 题目描述
4.2 解题思路
方法一:归并排序(推荐使用)
方法二:树状数组(扩展思路)
5. 旋转数组的最小数字
5.1 题目描述
5.2 解题思路
方法一:二分法(推荐使用)
方法二:遍历查找(扩展思路)
6. 比较版本号
6.1 题目描述
6.2 解题思路
方法一:双指针遍历截取(推荐使用)
方法二:分割截取(思路扩展)
7. 寻找文件副本
7.1 题目描述
7.2 解题思路
方法一:哈希表
方法二:原地交换
8. 统计目标成绩的出现次数
8.1 题目描述
8.2 解题思路
方法一:二分查找
9. 点名
9.1 题目描述
9.2 解题思路
方法一:二分查找
10. 招式拆解 II
10.1 题目描述
10.2 解题思路
方法一:哈希表
方法二:有序哈希表
11. 搜索插入位置
11.1 题目描述
11.2 解题思路
方法一:二分查找
12. 搜索二维矩阵
12.1 题目描述
12.2 解题思路
方法一:两次二分查找
方法二:一次二分查找
13. 在排序数组中查找元素的第一个和最后一个位置
13.1 题目描述
13.2 解题思路
方法一:二分查找
14. 搜索旋转排序数组
14.1 题目描述
14.2 解题思路
方法一:二分查找
15. 寻找旋转排序数组中的最小值
15.1 题目描述
15.2 解题思路
方法一:二分查找
16. 寻找两个正序数组的中位数
16.1 题目描述
16.2 解题思路
方法一:二分查找
方法二:划分数组
17. 猜数字大小
17.1 题目描述
17.2 解题思路
方法一:二分查找
18. 咒语和药水的成功对数
18.1 题目描述
18.2 解题思路
方法一:二分查找
方法二:双指针
19. 爱吃香蕉的珂珂
19.1 题目描述
19.2 解题思路
方法一:二分查找
1. 二分查找-I
1.1 题目描述
1.2 解题思路
方法:二分法(推荐使用)
Java实现代码:
import java.util.*;
public class Solution {public int search (int[] nums, int target) {int l = 0;int r = nums.length - 1;//从数组首尾开始,直到二者相遇while(l <= r){ //每次检查中点的值int m = (l + r) / 2; if(nums[m] == target)return m;//进入左的区间if(nums[m] > target) r = m - 1;//进入右区间else l = m + 1;}//未找到return -1; }
}
2. 二维数组中的查找
2.1 题目描述
2.2 解题思路
方法一:二分查找(推荐使用)
Java实现代码:
public class Solution {public boolean Find(int target, int [][] array) {//优先判断特殊if(array.length == 0) return false;int n = array.length;if(array[0].length == 0) return false;int m = array[0].length;//从最左下角的元素开始往左或往上for(int i = n - 1, j = 0; i >= 0 && j < m; ){ //元素较大,往上走if(array[i][j] > target) i--;//元素较小,往右走else if(array[i][j] < target) j++;elsereturn true;}return false;}
}
3. 寻找峰值
3.1 题目描述
3.2 解题思路
方法一:二分查找(推荐使用)
Java实现代码:
import java.util.*;
public class Solution {public int findPeakElement (int[] nums) {int left = 0;int right = nums.length - 1;//二分法while(left < right){ int mid = (left + right) / 2;//右边是往下,不一定有坡峰if(nums[mid] > nums[mid + 1])right = mid;//右边是往上,一定能找到波峰elseleft = mid + 1;}//其中一个波峰return right; }
}
4. 数组中的逆序对
4.1 题目描述
4.2 解题思路
方法一:归并排序(推荐使用)
Java实现代码:
public class Solution {public int mod = 1000000007;public int mergeSort(int left, int right, int [] data, int [] temp){//停止划分if(left >= right) return 0;//取中间int mid = (left + right) / 2; //左右划分合并int res = mergeSort(left, mid, data, temp) + mergeSort(mid + 1, right, data, temp); //防止溢出res %= mod; int i = left, j = mid + 1;for(int k = left; k <= right; k++)temp[k] = data[k];for(int k = left; k <= right; k++){if(i == mid + 1)data[k] = temp[j++];else if(j == right + 1 || temp[i] <= temp[j])data[k] = temp[i++];//左边比右边大,答案增加else{ data[k] = temp[j++];// 统计逆序对res += mid - i + 1; }}return res % mod;}public int InversePairs(int [] array) {int n = array.length;int[] res = new int[n];return mergeSort(0, n - 1, array, res);}
}
方法二:树状数组(扩展思路)
import java.util.*;
class BIT {private int[] tree;private int n;//初始化树状数组的大小public BIT(int m) { this.n = m;this.tree = new int[m + 1];}//使数组呈现2、4、8、16这种树状public int lowbit(int x) { return x & (-x);}//查询序列1到x的前缀和public int query(int x) { int res = 0;while(x != 0){res += tree[x];x -= lowbit(x);}return res;}//序列x位置的数加1public void update(int x) { while(x <= n){tree[x]++;x += lowbit(x);}}
}public class Solution {public int mod = 1000000007;public int InversePairs(int [] array) {int n = array.length;int[] temp = new int[n];System.arraycopy(array, 0, temp, 0, n);//排序得到一份有序的数组Arrays.sort(temp); //二分法重新映射,将数字变成其在有序数组中的位置for (int i = 0; i < n; ++i) //二分法查找在其在有序数组中的位置array[i] = Arrays.binarySearch(temp, array[i]) + 1;//建立大小为n的树状数组BIT bit = new BIT(n); int res = 0;//统计逆序对for(int i = 0; i < n; i++){ //前缀和做差res = (res + bit.query(n) - bit.query(array[i])) % mod;bit.update(array[i]);}return res;}
}
5. 旋转数组的最小数字
5.1 题目描述
5.2 解题思路
方法一:二分法(推荐使用)
Java实现代码:
import java.util.ArrayList;
public class Solution {public int minNumberInRotateArray(int [] array) {int left = 0;int right = array.length - 1;while(left < right){int mid = (left + right) / 2;//最小的数字在mid右边if(array[mid] > array[right]) left = mid + 1;//无法判断,一个一个试else if(array[mid] == array[right]) right--;//最小数字要么是mid要么在mid左边else right = mid;}return array[left];}
}
方法二:遍历查找(扩展思路)
import java.util.*;
public class Solution {public int minNumberInRotateArray(int [] array) {//数组一定有元素int res = array[0]; //遍历数组for(int i = 1; i < array.length; i++) //每次维护最小值res = Math.min(res, array[i]); return res;}
}
6. 比较版本号
6.1 题目描述
6.2 解题思路
方法一:双指针遍历截取(推荐使用)
Java实现代码:
import java.util.*;
public class Solution {public int compare (String version1, String version2) {int n1 = version1.length();int n2 = version2.length();int i = 0, j = 0;//直到某个字符串结束while(i < n1 || j < n2){long num1 = 0;//从下一个点前截取数字while(i < n1 && version1.charAt(i) != '.'){ num1 = num1 * 10 + (version1.charAt(i) - '0');i++;}//跳过点i++; long num2 = 0;//从下一个点前截取数字while(j < n2 && version2.charAt(j) != '.'){ num2 = num2 * 10 + (version2.charAt(j) - '0');j++;}//跳过点j++; //比较数字大小if(num1 > num2) return 1;if(num1 < num2)return -1;}//版本号相同return 0; }
}
方法二:分割截取(思路扩展)
import java.util.*;
public class Solution {public int compare (String version1, String version2) {//按照.划分String[] nums1 = version1.split("\\."); String[] nums2 = version2.split("\\.");for(int i = 0; i < nums1.length || i < nums2.length; i++){//较短的版本号后续都取0String str1 = i < nums1.length ? nums1[i] : "0"; String str2 = i < nums2.length ? nums2[i] : "0";long num1 = 0;//字符串转数字for(int j = 0; j < str1.length(); j++) num1 = num1 * 10 + (str1.charAt(j) - '0');long num2 = 0;for(int j = 0; j < str2.length(); j++)num2 = num2 * 10 + (str2.charAt(j) - '0');//比较数字大小if(num1 > num2) return 1;if(num1 < num2)return -1;}//版本相同return 0;}
}
7. 寻找文件副本
7.1 题目描述
7.2 解题思路
方法一:哈希表
class Solution {public int findRepeatDocument(int[] documents) {Set<Integer> hmap = new HashSet<>();for(int doc : documents) {if(hmap.contains(doc)) return doc;hmap.add(doc);}return -1;}}
方法二:原地交换
class Solution {public int findRepeatDocument(int[] documents) {int i = 0;while(i < documents.length) {if(documents[i] == i) {i++;continue;}if(documents[documents[i]] == documents[i]) return documents[i];int tmp = documents[i];documents[i] = documents[tmp];documents[tmp] = tmp;}return -1;}}
8. 统计目标成绩的出现次数
8.1 题目描述
8.2 解题思路
方法一:二分查找
class Solution {public int countTarget(int[] scores, int target) {int leftIdx = binarySearch(scores, target, true);int rightIdx = binarySearch(scores, target, false) - 1;if (leftIdx <= rightIdx && rightIdx < scores.length && scores[leftIdx] == target && scores[rightIdx] == target) {return rightIdx - leftIdx + 1;} return 0;}public int binarySearch(int[] nums, int target, boolean lower) {int left = 0, right = nums.length - 1, ans = nums.length;while (left <= right) {int mid = (left + right) / 2;if (nums[mid] > target || (lower && nums[mid] >= target)) {right = mid - 1;ans = mid;} else {left = mid + 1;}}return ans;}
}
9. 点名
9.1 题目描述
9.2 解题思路
方法一:二分查找
class Solution {public int takeAttendance(int[] records) {int i = 0, j = records.length - 1;while(i <= j) {int m = (i + j) / 2;if(records[m] == m) i = m + 1;else j = m - 1;}return i;}}
10. 招式拆解 II
10.1 题目描述
10.2 解题思路
方法一:哈希表
class Solution {public char dismantlingAction(String arr) {HashMap<Character, Boolean> hmap = new HashMap<>();char[] sc = arr.toCharArray();for(char c : sc)hmap.put(c, !hmap.containsKey(c));for(char c : sc)if(hmap.get(c)) return c;return ' ';}}
方法二:有序哈希表
class Solution {public char dismantlingAction(String arr) {Map<Character, Boolean> hmap = new LinkedHashMap<>();char[] sc = arr.toCharArray();for(char c : sc)hmap.put(c, !hmap.containsKey(c));for(Map.Entry<Character, Boolean> d : hmap.entrySet()){if(d.getValue()) return d.getKey();}return ' ';}}
11. 搜索插入位置
11.1 题目描述
11.2 解题思路
方法一:二分查找
class Solution {public int searchInsert(int[] nums, int target) {int n = nums.length;int left = 0, right = n - 1, ans = n;while (left <= right) {int mid = ((right - left) >> 1) + left;if (target <= nums[mid]) {ans = mid;right = mid - 1;} else {left = mid + 1;}}return ans;}
}
12. 搜索二维矩阵
12.1 题目描述
12.2 解题思路
方法一:两次二分查找
class Solution {public boolean searchMatrix(int[][] matrix, int target) {int rowIndex = binarySearchFirstColumn(matrix, target);if (rowIndex < 0) {return false;}return binarySearchRow(matrix[rowIndex], target);}public int binarySearchFirstColumn(int[][] matrix, int target) {int low = -1, high = matrix.length - 1;while (low < high) {int mid = (high - low + 1) / 2 + low;if (matrix[mid][0] <= target) {low = mid;} else {high = mid - 1;}}return low;}public boolean binarySearchRow(int[] row, int target) {int low = 0, high = row.length - 1;while (low <= high) {int mid = (high - low) / 2 + low;if (row[mid] == target) {return true;} else if (row[mid] > target) {high = mid - 1;} else {low = mid + 1;}}return false;}
}
方法二:一次二分查找
class Solution {public boolean searchMatrix(int[][] matrix, int target) {int m = matrix.length, n = matrix[0].length;int low = 0, high = m * n - 1;while (low <= high) {int mid = (high - low) / 2 + low;int x = matrix[mid / n][mid % n];if (x < target) {low = mid + 1;} else if (x > target) {high = mid - 1;} else {return true;}}return false;}
}
13. 在排序数组中查找元素的第一个和最后一个位置
13.1 题目描述
13.2 解题思路
方法一:二分查找
class Solution {public int[] searchRange(int[] nums, int target) {int leftIdx = binarySearch(nums, target, true);int rightIdx = binarySearch(nums, target, false) - 1;if (leftIdx <= rightIdx && rightIdx < nums.length && nums[leftIdx] == target && nums[rightIdx] == target) {return new int[]{leftIdx, rightIdx};} return new int[]{-1, -1};}public int binarySearch(int[] nums, int target, boolean lower) {int left = 0, right = nums.length - 1, ans = nums.length;while (left <= right) {int mid = (left + right) / 2;if (nums[mid] > target || (lower && nums[mid] >= target)) {right = mid - 1;ans = mid;} else {left = mid + 1;}}return ans;}
}
14. 搜索旋转排序数组
14.1 题目描述
14.2 解题思路
方法一:二分查找
class Solution {public int search(int[] nums, int target) {int n = nums.length;if (n == 0) {return -1;}if (n == 1) {return nums[0] == target ? 0 : -1;}int l = 0, r = n - 1;while (l <= r) {int mid = (l + r) / 2;if (nums[mid] == target) {return mid;}if (nums[0] <= nums[mid]) {if (nums[0] <= target && target < nums[mid]) {r = mid - 1;} else {l = mid + 1;}} else {if (nums[mid] < target && target <= nums[n - 1]) {l = mid + 1;} else {r = mid - 1;}}}return -1;}
}
15. 寻找旋转排序数组中的最小值
15.1 题目描述
15.2 解题思路
方法一:二分查找
class Solution {public int findMin(int[] nums) {int low = 0;int high = nums.length - 1;while (low < high) {int pivot = low + (high - low) / 2;if (nums[pivot] < nums[high]) {high = pivot;} else {low = pivot + 1;}}return nums[low];}
}
16. 寻找两个正序数组的中位数
16.1 题目描述
16.2 解题思路
方法一:二分查找
class Solution {public double findMedianSortedArrays(int[] nums1, int[] nums2) {int length1 = nums1.length, length2 = nums2.length;int totalLength = length1 + length2;if (totalLength % 2 == 1) {int midIndex = totalLength / 2;double median = getKthElement(nums1, nums2, midIndex + 1);return median;} else {int midIndex1 = totalLength / 2 - 1, midIndex2 = totalLength / 2;double median = (getKthElement(nums1, nums2, midIndex1 + 1) + getKthElement(nums1, nums2, midIndex2 + 1)) / 2.0;return median;}}public int getKthElement(int[] nums1, int[] nums2, int k) {/* 主要思路:要找到第 k (k>1) 小的元素,那么就取 pivot1 = nums1[k/2-1] 和 pivot2 = nums2[k/2-1] 进行比较* 这里的 "/" 表示整除* nums1 中小于等于 pivot1 的元素有 nums1[0 .. k/2-2] 共计 k/2-1 个* nums2 中小于等于 pivot2 的元素有 nums2[0 .. k/2-2] 共计 k/2-1 个* 取 pivot = min(pivot1, pivot2),两个数组中小于等于 pivot 的元素共计不会超过 (k/2-1) + (k/2-1) <= k-2 个* 这样 pivot 本身最大也只能是第 k-1 小的元素* 如果 pivot = pivot1,那么 nums1[0 .. k/2-1] 都不可能是第 k 小的元素。把这些元素全部 "删除",剩下的作为新的 nums1 数组* 如果 pivot = pivot2,那么 nums2[0 .. k/2-1] 都不可能是第 k 小的元素。把这些元素全部 "删除",剩下的作为新的 nums2 数组* 由于我们 "删除" 了一些元素(这些元素都比第 k 小的元素要小),因此需要修改 k 的值,减去删除的数的个数*/int length1 = nums1.length, length2 = nums2.length;int index1 = 0, index2 = 0;int kthElement = 0;while (true) {// 边界情况if (index1 == length1) {return nums2[index2 + k - 1];}if (index2 == length2) {return nums1[index1 + k - 1];}if (k == 1) {return Math.min(nums1[index1], nums2[index2]);}// 正常情况int half = k / 2;int newIndex1 = Math.min(index1 + half, length1) - 1;int newIndex2 = Math.min(index2 + half, length2) - 1;int pivot1 = nums1[newIndex1], pivot2 = nums2[newIndex2];if (pivot1 <= pivot2) {k -= (newIndex1 - index1 + 1);index1 = newIndex1 + 1;} else {k -= (newIndex2 - index2 + 1);index2 = newIndex2 + 1;}}}
}
方法二:划分数组
class Solution {public double findMedianSortedArrays(int[] nums1, int[] nums2) {if (nums1.length > nums2.length) {return findMedianSortedArrays(nums2, nums1);}int m = nums1.length;int n = nums2.length;int left = 0, right = m;// median1:前一部分的最大值// median2:后一部分的最小值int median1 = 0, median2 = 0;while (left <= right) {// 前一部分包含 nums1[0 .. i-1] 和 nums2[0 .. j-1]// 后一部分包含 nums1[i .. m-1] 和 nums2[j .. n-1]int i = (left + right) / 2;int j = (m + n + 1) / 2 - i;// nums_im1, nums_i, nums_jm1, nums_j 分别表示 nums1[i-1], nums1[i], nums2[j-1], nums2[j]int nums_im1 = (i == 0 ? Integer.MIN_VALUE : nums1[i - 1]);int nums_i = (i == m ? Integer.MAX_VALUE : nums1[i]);int nums_jm1 = (j == 0 ? Integer.MIN_VALUE : nums2[j - 1]);int nums_j = (j == n ? Integer.MAX_VALUE : nums2[j]);if (nums_im1 <= nums_j) {median1 = Math.max(nums_im1, nums_jm1);median2 = Math.min(nums_i, nums_j);left = i + 1;} else {right = i - 1;}}return (m + n) % 2 == 0 ? (median1 + median2) / 2.0 : median1;}
}
17. 猜数字大小
17.1 题目描述
17.2 解题思路
方法一:二分查找
public class Solution extends GuessGame {public int guessNumber(int n) {int left = 1, right = n;while (left < right) { // 循环直至区间左右端点相同int mid = left + (right - left) / 2; // 防止计算时溢出if (guess(mid) <= 0) {right = mid; // 答案在区间 [left, mid] 中} else {left = mid + 1; // 答案在区间 [mid+1, right] 中}}// 此时有 left == right,区间缩为一个点,即为答案return left;}
}
18. 咒语和药水的成功对数
18.1 题目描述
18.2 解题思路
方法一:二分查找
class Solution {public int[] successfulPairs(int[] spells, int[] potions, long success) {Arrays.sort(potions);int n = spells.length, m = potions.length;int[] res = new int[n];for (int i = 0; i < n; i++) {long t = (success + spells[i] - 1) / spells[i] - 1;res[i] = m - binarySearch(potions, 0, m - 1, t);}return res;}public int binarySearch(int[] arr, int lo, int hi, long target) {int res = hi + 1;while (lo <= hi) {int mid = lo + (hi - lo) / 2;if (arr[mid] > target) {res = mid;hi = mid - 1;} else {lo = mid + 1;}}return res;}
}
方法二:双指针
class Solution {public int[] successfulPairs(int[] spells, int[] potions, long success) {int n = spells.length, m = potions.length;int[] res = new int[n];int[][] idx = new int[n][2];for (int i = 0; i < n; ++i) {idx[i][0] = spells[i];idx[i][1] = i;}Arrays.sort(potions);for (int i = 0, j = m - 1; i < j; ++i, --j) {int temp = potions[i];potions[i] = potions[j];potions[j] = temp;}Arrays.sort(idx, (a, b) -> a[0] - b[0]);for (int i = 0, j = 0; i < n; ++i) {int p = idx[i][1];int v = idx[i][0];while (j < m && (long) potions[j] * v >= success) {++j;}res[p] = j;}return res;}
}
19. 爱吃香蕉的珂珂
19.1 题目描述
19.2 解题思路
方法一:二分查找
class Solution {public int minEatingSpeed(int[] piles, int h) {int low = 1;int high = 0;for (int pile : piles) {high = Math.max(high, pile);}int k = high;while (low < high) {int speed = (high - low) / 2 + low;long time = getTime(piles, speed);if (time <= h) {k = speed;high = speed;} else {low = speed + 1;}}return k;}public long getTime(int[] piles, int speed) {long time = 0;for (int pile : piles) {int curTime = (pile + speed - 1) / speed;time += curTime;}return time;}
}