给你一个二维整数数组 ranges
和两个整数 left
和 right
。每个 ranges[i] = [starti, endi]
表示一个从 starti
到 endi
的 闭区间 。
如果闭区间 [left, right]
内每个整数都被 ranges
中 至少一个 区间覆盖,那么请你返回 true
,否则返回 false
。
已知区间 ranges[i] = [starti, endi]
,如果整数 x
满足 starti <= x <= endi
,那么我们称整数x
被覆盖了。
示例 1:
输入:ranges = [[1,2],[3,4],[5,6]], left = 2, right = 5 输出:true 解释:2 到 5 的每个整数都被覆盖了: - 2 被第一个区间覆盖。 - 3 和 4 被第二个区间覆盖。 - 5 被第三个区间覆盖。
示例 2:
输入:ranges = [[1,10],[10,20]], left = 21, right = 21 输出:false 解释:21 没有被任何一个区间覆盖。
提示:
1 <= ranges.length <= 50
1 <= starti <= endi <= 50
1 <= left <= right <= 50
方法一:差分数组
我们可以使用差分数组的思想,对于每个区间
最后遍历差分数组,累加每个位置的值,记为 false
。
否则遍历结束后,返回 true
。
时间复杂度
class Solution:
def isCovered(self, ranges: List[List[int]], left: int, right: int) -> bool:
diff = [0] * 52
for l, r in ranges:
diff[l] += 1
diff[r + 1] -= 1
cur = 0
for i, x in enumerate(diff):
cur += x
if left <= i <= right and cur == 0:
return False
return True
class Solution {
public boolean isCovered(int[][] ranges, int left, int right) {
int[] diff = new int[52];
for (int[] range : ranges) {
int l = range[0], r = range[1];
++diff[l];
--diff[r + 1];
}
int cur = 0;
for (int i = 0; i < diff.length; ++i) {
cur += diff[i];
if (i >= left && i <= right && cur == 0) {
return false;
}
}
return true;
}
}
class Solution {
public:
bool isCovered(vector<vector<int>>& ranges, int left, int right) {
int diff[52]{};
for (auto& range : ranges) {
int l = range[0], r = range[1];
++diff[l];
--diff[r + 1];
}
int cur = 0;
for (int i = 0; i < 52; ++i) {
cur += diff[i];
if (i >= left && i <= right && cur <= 0) {
return false;
}
}
return true;
}
};
func isCovered(ranges [][]int, left int, right int) bool {
diff := [52]int{}
for _, rg := range ranges {
l, r := rg[0], rg[1]
diff[l]++
diff[r+1]--
}
cur := 0
for i, x := range diff {
cur += x
if i >= left && i <= right && cur <= 0 {
return false
}
}
return true
}
function isCovered(ranges: number[][], left: number, right: number): boolean {
const diff = new Array(52).fill(0);
for (const [l, r] of ranges) {
++diff[l];
--diff[r + 1];
}
let cur = 0;
for (let i = 0; i < 52; ++i) {
cur += diff[i];
if (i >= left && i <= right && cur <= 0) {
return false;
}
}
return true;
}
/**
* @param {number[][]} ranges
* @param {number} left
* @param {number} right
* @return {boolean}
*/
var isCovered = function (ranges, left, right) {
const diff = new Array(52).fill(0);
for (const [l, r] of ranges) {
++diff[l];
--diff[r + 1];
}
let cur = 0;
for (let i = 0; i < 52; ++i) {
cur += diff[i];
if (i >= left && i <= right && cur <= 0) {
return false;
}
}
return true;
};