Explanation of how Kadane's Algorithm Works.

1. Kadane Algorithm
1
@daywithalgo
Algorithm to compute maximum sum of continous sub array
DWA 1001 - Kadane Algorithm
daywithalgorithm.xyz
@day_with_algorithm

2. 2
@daywithalgo
DWA 1001 - Kadane Algorithm
daywithalgorithm.xyz
@day_with_algorithm
1. Consider two trackers (variables) , to track the local_max and global_max
Index 0 1 2 3 4
Value -1 -3 4 5 -6
local_max :
ARR:
global_max :
ARR[0] -> -1
ARR[0] -> -1

3. 3
@daywithalgo
DWA 1001 - Kadane Algorithm
daywithalgorithm.xyz
@day_with_algorithm
2. Incrementing itr by 1, ARR[itr] = 1
Index 0 1 2 3 4
Value -1 -3 4 5 -6
local_max :
ARR:
global_max :
ARR[0] -> -1 ARR[0] -> -1
local_max = max(ARR[itr], local_max + ARR[itr])
global_max = max_of(local_max , global_max)
= max(-3, -1+-3) => -3
= max(-3, -1) => -1

4. 4
@daywithalgo
DWA 1001 - Kadane Algorithm
daywithalgorithm.xyz
@day_with_algorithm
2. Incrementing itr by 2, ARR[itr] = 4
Index 0 1 2 3 4
Value -1 -3 4 5 -6
local_max :
ARR:
global_max :
ARR[0] -> -3 ARR[0] -> -1
local_max = max(ARR[itr], local_max + ARR[itr])
global_max = max_of(local_max , global_max)
= max(4, -3+4) => 4
= max(4, -1) => 4

5. 5
@daywithalgo
DWA 1001 - Kadane Algorithm
daywithalgorithm.xyz
@day_with_algorithm
2. Incrementing itr by 1, ARR[itr] = 5
Index 0 1 2 3 4
Value -1 -3 4 5 -6
local_max :
ARR:
global_max :
ARR[0] -> 4 ARR[0] -> 4
local_max = max(ARR[itr], local_max + ARR[itr])
global_max = max_of(local_max , global_max)
= max(5, 4+5) => 9
= max(9, 4) => 9

6. 6
@daywithalgo
DWA 1001 - Kadane Algorithm
daywithalgorithm.xyz
@day_with_algorithm
2. Incrementing itr by 1, ARR[itr] = -6
Index 0 1 2 3 4
Value -1 -3 4 5 -6
local_max :
ARR:
global_max :
ARR[0] -> 9 ARR[0] -> 9
local_max = max(ARR[itr], local_max + ARR[itr])
global_max = max_of(local_max , global_max)
= max(-6, 9) => 9
= max(9, 4) => 9

7. 7
@daywithalgo
DWA 1001 - Kadane Algorithm
daywithalgorithm.xyz
@day_with_algorithm
By using Kadane’s Algorithm, we derived the maximum sum of contigous
subarray
Index 0 1 2 3 4
Value -1 -3 4 5 -6
Max Sum: 9

8. 8
@daywithalgo
DWA 1001 - Kadane Algorithm
daywithalgorithm.xyz
@day_with_algorithm
Time Complexity :
Best Case Average Case Worst Case
O(N) O(N) O(N)