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Author: Muhammad-Magdi

Cumulative Sum & Frequency Array.txt

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+Frequency Array:
+  -Introduction Problem:
+    Given n Integers, for each number from 1 to 3 print the number of its occurrences.
+      ans   ---->   Three variables.
+
+  -Classical Problem:
+    Given n<=1e5 Integers ranging from 1 to 1e5,for each given number print the number of its occurrences.
+      ans1    ---->   O(n^2) time.
+      ans2    ---->   O(n)  time.
+
+  int x, freq[N] = {0};
+  for(int i = 0 ; i < n ; ++i){
+    scanf("%d", &x);
+    freq[x]++;
+  }
+  for(int i = 0 ; i < N ; ++i){
+    if(freq[i])
+      printf("The number %d was found %d times.\n");
+  }
+
+-What if the numbers are Integers in the range 1 to 1e9?
+-What if they weren't Integers (e.g. Chars, doubles or Strings)?
+
+
+Cumulative (Prefix) sum:
+  -Classical Problem:
+    Given n<=1e5 numbers, and q<=1e5 queries asking about sum of elements from l to r.
+      ans1    ---->   O(n*q)  time.
+      ans2    ---->   O(q)    time.
+
+  int n, A[N], pre[N], ans, l, r, q;
+  void prefixSum(){
+    scanf("%d", &n);
+    for(int i = 1 ; i <= n ; ++i){
+        scanf("%d", &A[i]);
+        pre[i] = pre[i-1] + A[i];
+    }
+    scanf("%d", &q);
+    while(q--){
+      scanf("%d%d", &l, &r);
+      printf("%d\n", pre[r]-pre[l-1]);
+    }
+  }
+
+-What about Suffix sum?
+-What about 2D .. what about ND?
+
+  int n, m, A[N][N], pre[N][N], ans, l1, r1, l2, r2, q;
+  void prefixSum2D(){
+    scanf("%d%d", &n, &m);
+    for(int i = 1 ; i <= n ; ++i){
+      for(int j = 1 ; j <= m ; ++j){
+        scanf("%d", &A[i][j]);
+        pre[i][j] = pre[i][j-1] + A[i][j];
+      }
+      for(int j = 1 ; j <= m ; ++j){
+        pre[i][j] += pre[i-1][j];
+      }
+    }
+    scanf("%d", &q);
+    while(q--){
+      scanf("%d%d%d%d", &l1, &r1, &l2, &r2);
+      printf("%d\n", pre[l2][r2] - pre[l1-1][r2] - pre[l2][r1-1] + pre[l1-1][r1-1]);
+    }
+  }
+
+
+Maximum Intersection:
+  -Classical Problem:
+    Given n<=1e5 friend who are free from time l to time r<=1e5
+    , what's the time in which maximum number of friends are free?
+      ans1    ---->   O(n*r)  time    ---->     TLE.
+      ans2    ---->   O(n)    time.
+
+
+  int q, f, t, day[N], maxi = 0, maxday;
+  void maximumIntersection(){
+    scanf("%d", &q);
+    while(q--){
+      scanf("%d%d", &f, &t);
+      ++day[l], --day[t+1];
+    }
+    for(int i = 1 ; i <= N ; ++i){
+      day[i] += day[i-1];
+      if(day[i] > maxi){
+        maxi = day[i];
+        maxday = i;
+      }
+    }
+    printf("The maximum number of friends is %d in day number %d.\n", maxi, maxday);
+  }

bitwise operations and bitmasks.txt

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+1- How does numbers are saved?
+  Binary Representation.
+
+Boolean algebra.
+
+What's bitwise operations?
+
+    operation          operator
+      and                 &
+      or                  |
+      Xor                 ^
+      invert              ~
+      left shift          <<
+      right shift         >>
+
+- How to get all the possible permutations of k(e.g k = 3) bits?
+
+  for(int msk = 0 ; msk < (1<<k) ; ++msk){
+    // Anything
+  }
+
+
+- How to check oddness of a variable x?
+
+  if(x&1)
+    printf("It's Odd\n");
+  else
+    printf("It's Even\n");
+
+
+- How to check the state of the bit at position k of some mask?
+
+  if(msk&(1<<k))
+    printf("It's ON");
+  else
+    printf("It's OFF");
+
+
+- How to ON the bit at position k of some mask?
+
+  msk |= (1<<k);
+
+
+- How to ON the first n bits of some mask?
+
+  msk |= ((1<<n)-1);
+
+
+- How to toggle the bit at position k of some mask?
+
+  msk ^= (1<<k);
+
+
+- How to OFF the bit at position k of some mask?
+
+  msk &= ~(1<<k);
+
+
+- How to count the number of ON bits in some mask of n bits?
+
+  int num = 0;
+  for(int j = 0 ; j < n ; ++j)
+    if(msk&(1<<j))
+      ++num;