R.V.R. & J.C.
College of Engineering, Guntur – 522019
(Autonomous)
B. Tech. Semester-V [Third Year]
IT351 (R20) - Design & Analysis of Algorithms Lab
1. Write a program to find min-max in a given array using Divide and
Conquer.
#include <stdio.h>
void mimx(int a[], int l, int u, int *mi, int *mx)
{
int m, mi1, mx1;
if (l == u)
{
*mi = a[l];
*mx = a[l];
}
else if (l + 1 == u)
{
if (a[l] > a[u])
{
*mi = a[u];
*mx = a[l];
}
else
{
*mi = a[l];
*mx = a[u];
}
}
else
{
m = (l + u) / 2;
mimx(a, l, m, mi, mx);
mimx(a, m + 1, u, &mi1, &mx1);
if (mi1 < *mi)
*mi = mi1;
if (mx1 > *mx)
*mx = mx1;
}
}
int main()
R.V.R. & J.C. College of Engineering, Guntur – 522019
(Autonomous)
{
int i, n, a[10], mi = 0, mx = 0;
printf("enter list size:");
scanf("%d", &n);
printf("enter list:");
for (i = 0; i < n; i++)
scanf("%d", &a[i]);
mimx(a, 0, n - 1, &mi, &mx);
printf("min=%d max=%d\n", mi, mx);
}
2. Write a program to find the kth smallest element in a given array using
Divide and Conquer.
#include <stdio.h>
int partition(int a[], int l, int u)
{
int i = l, j = u, k = a[l], t;
while (i < j)
{
while (a[i] <= k && i <= u)
i++;
while (a[j] > k)
j--;
if (i < j)
{
t = a[i];
a[i] = a[j];
a[j] = t;
}
}
a[l] = a[j];
a[j] = k;
return j;
}
int KthSmall(int a[], int l, int u, int k)
{
int p;
if (l < u)
{
p = partition(a, l, u);
if (p < k)
R.V.R. & J.C. College of Engineering, Guntur – 522019
(Autonomous)
return KthSmall(a, p + 1, u, k);
else if (p > k)
return KthSmall(a, l, p - 1, k);
else
return a[p];
}
}
int main()
{
int k, i, n, a[10];
printf("enter n value:");
scanf("%d", &n);
printf("enter array elements:");
for (i = 1; i <= n; i++)
{
scanf("%d", &a[i]);
}
printf("enter k value:");
scanf("%d", &k);
printf("%dth minimum is %d\n", k, KthSmall(a, 1, n, k));
}
3. Write a program to find the optimal profit of a Knapsack using Greedy
method.
#include <stdio.h>
void read(int a[], int n)
{
int i;
printf("enter elements: ");
for (i = 0; i < n; i++)
scanf("%d", &a[i]);
}
void print(int a[], int n)
{
int i;
for (i = 0; i < n; i++)
printf("%d, ", a[i]);
printf("\n");
}
float Knapsack(int p[], int w[], int n, float m)
{
R.V.R. & J.C. College of Engineering, Guntur – 522019
(Autonomous)
float pro = 0.0;
int i = 0;
while (w[i] < m)
{
m -= w[i];
pro += p[i];
i++;
printf("%f\n", pro);
}
pro += (p[i] * (m / w[i]));
return pro;
}
void main()
{
int n, i, p[10], w[10];
float m;
printf("enter size: ");
scanf("%d", &n);
printf("enter profits 'sorted order('p/w')':");
read(p, n);
printf("enter weights:");
read(w, n);
printf("bag-size:");
scanf("%f", &m);
printf("profit:%.2f\n", Knapsack(p, w, n, m));
}
4. Write a program to find the minimum cost spanning tree for the given
graph. (Kruskal’s algorithm)
#include <stdio.h>
#include <stdlib.h>
struct edge
{
int v1, v2, w;
};
typedef struct edge edge;
int p[20];
edge e[20];
R.V.R. & J.C. College of Engineering, Guntur – 522019
(Autonomous)
void init(int n)
{
for (int i = 1; i <= n; i++)
p[i] = -1;
}
int find(int i)
{
while (p[i] != -1)
i = p[i];
return i;
}
void union1(int i, int j)
{
p[i] = j;
}
void sort(int m)
{
edge t;
for (int i = 1; i <= m; i++)
for (int j = 1; j <= m; j++)
if (e[i].w < e[j].w)
{
t = e[i];
e[i] = e[j];
e[j] = t;
}
}
void readedges(int m)
{
int i;
for (i = 1; i <= m; i++)
{
printf("Enter %d Edge details\n", i);
scanf("%d", &e[i].v1);
scanf("%d", &e[i].v2);
scanf("%d", &e[i].w);
}
}
R.V.R. & J.C. College of Engineering, Guntur – 522019
(Autonomous)
void printtree(int t[][2], int n)
{
int i, j;
printf("MST is\n");
for (i = 1; i < n; i++)
printf("%d\t%d\n", t[i][1], t[i][2]);
}
void kruskal(int n, int m)
{
int v, u, t[20][2], i = 0, j = 1, mincost = 0;
while (i < n && j < m)
{
u = find(e[j].v1);
v = find(e[j].v2);
if (u == v)
{
j++;
continue;
}
i++;
t[i][1] = e[j].v1;
t[i][2] = e[j].v2;
mincost += e[j].w;
union1(u, v);
j++;
}
printf("mincost:%d\n", mincost);
printtree(t, n);
}
void main()
{
int n, m;
printf("enter no.of vertices:");
scanf("%d", &n);
printf("enter no.of edges:");
scanf("%d", &m);
readedges(m);
sort(m);
init(n);
kruskal(n, m);
R.V.R. & J.C. College of Engineering, Guntur – 522019
(Autonomous)
}
5. Write a program to determine the shortest path length from a source
vertex to all the other vertices in a given graph. (Dijkstra’s algorithm)
#include <stdio.h>
void shp(int v, int g[10][10], int dist[10], int n)
{
int i, s[10], min, u, j, w;
for (i = 1; i <= n; i++)
{
s[i] = 0;
dist[i] = g[v][i];
}
s[v] = 1;
for (i = 2; i <= n; i++)
{
min = 999;
u = 0;
for (j = 1; j <= n; j++)
{
if (s[j] == 0 && dist[j] < min)
{
min = dist[j];
u = j;
}
}
if (u == 0)
break;
s[u] = 1;
for (w = 1; w <= n; w++)
{
if (g[u][w] != 0 && s[w] == 0)
{
if ((dist[u] + g[u][w]) < dist[w])
{
dist[w] = dist[u] + g[u][w];
}
}
}
R.V.R. & J.C. College of Engineering, Guntur – 522019
(Autonomous)
}
}
int main()
{
int cost[10][10], n, dist[10], i, j, v;
printf("Enter the number of vertices: ");
scanf("%d", &n);
printf("Enter the source vertex: ");
scanf("%d", &v);
printf("Enter the cost matrix:\n");
for (i = 1; i <= n; i++)
{
for (j = 1; j <= n; j++)
{
scanf("%d", &cost[i][j]);
}
}
shp(v, cost, dist, n);
printf("Shortest distances from vertex %d to all other vertices:\n", v);
for (i = 1; i <= n; i++)
{
printf("Vertex %d: %d\n", i, dist[i]);
}
return 0;
}
6. Write a program to determine shortest path from a source vertex s to
destination vertex t in a multistage graph using dynamic programming
(forward and backward).
7. Write a program to find shortest path distance between each and every
pair of vertices in a given graph using dynamic programming.
#include <stdio.h>
void read(int a[][10], int n)
{
printf("enter the graph(adj matrix):\n");
R.V.R. & J.C. College of Engineering, Guntur – 522019
(Autonomous)
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
scanf("%d", &a[i][j]);
}
void print(int a[][10], int n)
{
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
printf("%d ", a[i][j]);
printf("\n");
}
}
void main()
{
int i, j, k, min1, min2, a[10][10], cost[10][10], n;
printf("enter no.of vertices in the graph:");
scanf("%d", &n);
read(cost, n);
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
a[i][j] = cost[i][j];
for (k = 0; k < n; k++)
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
{
min1 = a[i][k] + a[k][j];
min2 = a[i][j];
a[i][j] = min1 <= min2 ? min1 : min2;
}
printf("all pairs shortest path:\n");
print(a, n);
}
8. Write a program to find the optimal profit of a 0/1 Knapsack using
dynamic programming.
9. Write a program to find the non-attacking positions of Queens in a given
chess board using backtracking.
10.Write a program to find Hamiltonian cycles in a given graph using
backtracking.
R.V.R. & J.C. College of Engineering, Guntur – 522019
(Autonomous)
11.Write a program for Robin Karp string matching algorithm.
