题目:
Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties:
- Integers in each row are sorted from left to right.
- The first integer of each row is greater than the last integer of the previous row.
For example,
Consider the following matrix:
[
[1, 3, 5, 7],
[10, 11, 16, 20],
[23, 30, 34, 50]
]
Given target = 3
, return true
.
思路:
分两步,(1)先二分搜索的元素定位到行:当目标小于第一列某个元素时,向前面的行中去搜索;当目标大于第一列某个元素分两种情况 a、大于该元素所在行的最后一个元素时,往后面的行中去搜索,b、小于等于该元素所在行的最后一个元素,则可以定位到该元素所在的行。(2)在定位好的行中二分搜索
注意,在第一步查找所在行时,while(l<r)而不是whilel<=r;当target>nums[middle]时,还需要判断一下target和该行末的值,从而确定是否需要l=middle+1。
/**
* @param {number[][]} matrix
* @param {number} target
* @return {boolean}
*/
var searchMatrix = function(matrix, target) {
var m=matrix.length,n=matrix[0].length; var L=0,R=m-1,middle=0;
while(L<R){
middle=L+Math.floor((R-L)/2);
if(target<matrix[middle][0]){
R=middle-1;
}else if(target>matrix[middle][0]){
if(target>matrix[middle][n-1]){
L=middle+1;
}else{
L=middle;
break;
}
}else{
return true;
}
} var row=L;
var l=0,r=n-1,middle=0;
while(l<=r){
middle=l+Math.floor((r-l)/2);
if(matrix[row][middle]>target){
r=middle-1;
}else if(matrix[row][middle]<target){
l=middle+1;
}else{
return true;
}
}
return false; };