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ks.go
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ks.go
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package ks
func kthSmallest(matrix [][]int, k int) int {
return useBinarySearch(matrix, k)
}
// useBinarySearch time complexity O(log(5000*M)*M*K), space complexity O(M)
func useBinarySearch(matrix [][]int, k int) int {
m := len(matrix)
if m < 1 {
return 0
}
n := len(matrix[0])
if n < 1 {
return 0
}
left, right, ans := m, 5000*m, -1
for left <= right {
mid := left + (right-left)/2
cnt := countArraysHaveSumLessOrEqual(matrix, m, n, mid, 0, 0, k)
if cnt >= k {
right = mid - 1
ans = mid
} else {
left = mid + 1
}
}
return ans
}
// countArraysHaveSumLessOrEqual time complexity O(MK), space complexity O(M)
// countArraysHaveSumLessOrEqual() can run up to (m-i+1) * min(k,n^i), 1<=i<=m times.
// And n^i can go up to k very quickly while i is small, so time complexity will be O(m*k)
func countArraysHaveSumLessOrEqual(matrix [][]int, m, n, targetSum, row, sum, k int) int {
if sum > targetSum {
return 0
}
if row == m {
return 1
}
var ans int
// min(k, n^i)
for c := 0; c < n; c++ {
cnt := countArraysHaveSumLessOrEqual(matrix, m, n, targetSum, row+1, sum+matrix[row][c], k-ans)
if cnt == 0 {
break
}
ans += cnt
if ans > k {
break
}
}
return ans
}