Question

Question 2 In the minimum grid-path problem we are given a two-dimensional grid, where each point on the grid has a value, which is a non-negative integer. We have to find a path from the top left corner of the grid to the bottom right corner, where each single step on the path must lead from one grid point to its neighbour to the right or below. The cost of the path is the sum of all values of the grid points visited. 0 1 2 3 4 5 15 3 12 7119 1 1 2 9 54 10 10 8 7 3 1 15 7|17|165 4 1 5 15 736 5 9 10 2 2 8 11 For example in the grid above, the gray points on the grid from a minimum grid-path of cost 5+1 +2 +8+1 +7 +1 +6+3+ 6 + 11 = 51. 3 15 B

Answer 1

grid palt is graph The minimum 6 + 6000) [01] G01 1 1 + 2 + 7 (2,1) 5 + G[2,2 1 @ G 23,2]G[337 + 5 +1 = 22. The answer is 22. Algorithm :- minimum grid path (G[h] [m]) { int mincost [n] [m] = ) mincost co] [o] = G[o][o]; minpath CG CAJ[m], mincast Cho emi na return minpath [n[mD; minpath (GG] (m), min costen] Cm), nama) { ifcncollmcol return oo else if (min cost [ [m-) to return mincest (n-1) [m-1). ③ elses min cost th-1] [m -13= min minpath (GGJ[m], mincos th]] nom), minpath (Gen] [m] mincost Ch] [m] # Gemma 27 return mincost [n 1] [n 1]: © explanation - (Algorithm) Note: Here have taken a indices starting from and written the code similar to gara. in this algorithm I used memoitation Concept of Dynamic programming to avoid multiple recursive calls of identical problem: for Storing tready called recuasi- in the algorithm, iused mincost chim] metrix recalls Ciri in the , it is the Basecase for if morn became less than o, which gives an error, to avoid it I have returned infinity (Base case) i in I checked mincest matrix, whether I have calculated it before or If calculated i returned it (Base case) in if it is not calculated, the calculated it using recursive relation minpath Ci Cj] = minimum & minpath (i-1] [j], minpalttigt-1]+G)] which is a square can be reached by either from left or from above . СС) [i][j-1] [i-1] [j]