1, 2 and 3 D Kadane Algorithm

Author: Muhammad-Magdi

Kadane Algorithm/1D-Kadane.cpp

@@ -0,0 +1,24 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+const int N = 1e6 + 5, OO = 0x3f3f3f3f, MOD = 1000000007;
+const double EPS = 0.000000001;
+
+int n;
+int A[N];
+long long sum, bestSum;
+
+int main(){
+	//freopen("i.in", "rt", stdin);
+	//freopen("o.out", "wt", stdout);
+	scanf("%d", &n);
+	for(int i = 0 ; i < n ; ++i)
+			scanf("%d", A+i);
+	for(int i = 0 ; i < n ; ++i){
+		sum += A[i];
+		sum = max(sum, 0ll);
+		bestSum = max(bestSum, sum);
+	}
+	printf("%lld\n", bestSum);
+	return 0;
+}

Kadane Algorithm/2D-Kadane.cpp

@@ -0,0 +1,33 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+const int N = 1e2 + 5, OO = 0x3f3f3f3f, MOD = 1000000007;
+const double EPS = 0.000000001;
+
+int n, m;
+int A[N][N];
+long long bestSum;
+
+int main(){
+	//freopen("i.in", "rt", stdin);
+	//freopen("o.out", "wt", stdout);
+	scanf("%d %d", &n, &m);
+	for(int i = 1 ; i <= n ; ++i){
+		for(int j = 1 ; j <= m ; ++j){
+			scanf("%d", A[i]+j);
+			A[i][j] += A[i-1][j];			//Cummulative Columns.
+		}
+	}
+	for(int top = 1 ; top <= n ; ++top){
+		for(int btm = top ; btm <= n ; ++btm){
+			long long sum = 0;
+			for(int i = 1 ; i <= m ; ++i){
+				sum += A[btm][i] - A[top-1][i];	//Add current element -Column-
+				sum = max(sum, 0ll);							//Does it worth?
+				bestSum = max(bestSum, sum);		//Is it the best?
+			}
+		}
+	}
+	printf("%lld\n", bestSum);
+	return 0;
+}

Kadane Algorithm/3D-Kadane.cpp

@@ -0,0 +1,35 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+const int N = 22 , OO = 0x3f3f3f3f, MOD = 1000000007;
+const double EPS = 0.000000001;
+
+int a, b, c;
+long long A[N][N][N];
+long long bestSum;
+
+int main(){
+	//freopen("i.in", "rt", stdin);
+	//freopen("o.out", "wt", stdout);
+	scanf("%d %d %d", &a, &b, &c);
+	for(int i = 1 ; i <= a ; ++i){
+		for(int j = 1 ; j <= b ; ++j){
+			for(int k = 1 ; k <= c ; ++k){
+				scanf("%lld", A[i][j]+k);
+				A[i][j][k] += A[i-1][j][k] + A[i][j-1][k] - A[i-1][j-1][k];	//Cummulative grids
+			}
+		}
+	}
+	for(int sa = 1 ; sa <= a ; ++sa)for(int ea = sa ; ea <= a ; ++ea){
+		for(int sb = 1 ; sb <= b ; ++sb)for(int eb = sb ; eb <= b ; ++eb){
+			long long sum = 0;
+			for(int i = 1 ; i <= c ; ++i){
+				sum += A[ea][eb][i] - A[sa-1][eb][i] - A[ea][sb-1][i] + A[sa-1][sb-1][i];
+				sum = max(sum, 0ll);						//Does it worth?
+				bestSum = max(bestSum, sum);		//Is it the best?
+			}
+		}
+	}
+	printf("%lld\n", bestSum);
+	return 0;
+}