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Maximum path sum that starting with any cell of 0-th row and ending with any cell of (N-1)-th row in C++
In this tutorial, we will be discussing a program to find maximum path sum that starting with any cell of 0-th row and ending with any cell of (N-1)-th row
For this we will be provided with a matrix with possible moves of (i+1, j), (i+1, j-1), (i+1, j+1). Our task is to start from zeroth position and move to last row finding out the maximum sum path.
Example
#include<bits/stdc++.h> using namespace std; #define N 4 //finding maximum sum path int MaximumPath(int Mat[][N]) { int result = 0 ; int dp[N][N+2]; memset(dp, 0, sizeof(dp)); for (int i = 0 ; i < N ; i++) dp[0][i+1] = Mat[0][i]; for (int i = 1 ; i < N ; i++) for (int j = 1 ; j <= N ; j++) dp[i][j] = max(dp[i-1][j-1], max(dp[i-1][j], dp[i-1][j+1])) + Mat[i][j-1] ; for (int i=0; i<=N; i++) result = max(result, dp[N-1][i]); return result ; } int main() { int Mat[4][4] = { { 4, 2 , 3 , 4 }, { 2 , 9 , 1 , 10}, { 15, 1 , 3 , 0 }, { 16 ,92, 41, 44 } }; cout << MaximumPath ( Mat ) <<endl ; return 0; }
Output
120
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