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Min Cost Path.cpp
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Min Cost Path.cpp
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/*
Given a cost matrix cost[][] and a position (m, n) in cost[][], write a function that returns cost
of minimum cost path to reach (m, n) from (0, 0). Each cell of the matrix represents a cost to traverse
through that cell. Total cost of a path to reach (m, n) is sum of all the costs on that path (including
both source and destination). You can only traverse down, right and diagonally lower cells from a given cell,
i.e., from a given cell (i, j), cells (i+1, j), (i, j+1) and (i+1, j+1) can be traversed.
*/
#include<bits/stdc++.h>
using namespace std;
int minCost(int, int);
int min(int, int, int);
int main(){
int t, n, m;
cin >> t;
while(t--){
cin >> n >> m;
cout << minCost(n, m) << endl;
}
return 0;
}
int minCost(int n, int m){
int arr[n][m];
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
cin >> arr[i][j];
for(int i = 1; i < n; i++)
arr[i][0] = arr[i][0] + arr[i - 1][0];
for(int i = 1; i < m; i++)
arr[0][i] = arr[0][i] + arr[0][i - 1];
for(int i = 1; i < n; i++)
for(int j = 1; j < m; j++){
arr[i][j] = arr[i][j] + min(arr[i][j - 1], arr[i - 1][j - 1], arr[i - 1][j]);
}
return arr[n - 1][m - 1];
}
int min(int x, int y, int z){
int m = INT_MAX;
if(m > x)
m = x;
if(m > y)
m = y;
if(m > z)
m = z;
return m;
}