Suppose we have an array called points containing the coordinate points on a 2D plane, they are sorted by the x-values, where points[i] = (x_i, y_i) so x_i < x_j for all 1 <= i < j <= number of points. We also have another value k. We have to find the maximum value of the equation y_i + y_j + |x_i - x_j| where |x_i - x_j| <= k and 1 <= i < j <= number of points.
So, if the input is like points = [[2,4],[3,1],[6,11],[7,-9]] k = 1, then the output will be 6 because the first two points satisfy the condition |xi - xj| <= 1 now if we calculate the equation we get 4 + 1 + |2 - 3| = 6. Third and fourth points also satisfy the condition and returns a value of 11 + -9 + |6 - 7| = 3, so maximum is 6.
To solve this, we will follow these steps −
left := 0, right := 1
max_value := -inf
while right < size of points, do
(xl, yl) := points[left]
(xr, yr) := points[right]
diff := |xr - xl|
if left is same as right, then
right := right + 1
otherwise when diff <= k, then
m := yl + yr + diff
max_value := maximum of max_value and m
if yl >= yr - diff, then
right := right + 1
otherwise,
left := left + 1
otherwise,
left := left + 1
return max_value
Example
Let us see the following implementation to get better understanding
def solve(points, k):
left, right = 0, 1
max_value = float('-inf')
while right < len(points):
xl, yl = points[left]
xr, yr = points[right]
diff = abs(xr - xl)
if left == right:
right += 1
elif diff <= k:
m = yl + yr + diff
max_value = max(max_value, m)
if yl >= yr - diff:
right += 1
else:
left += 1
else:
left += 1
return max_value
points = [[2,4],[3,1],[6,11],[7,-9]]
k = 1
print(solve(points, k))Input
[[2,4],[3,1],[6,11],[7,-9]], 1
Output
6